Probing cosmic inflation with the LiteBIRD cosmic microwave background polarization survey Open Access

Abstract

1. Introduction

1.1. CMB polarization as the new frontier and the LiteBIRD satellite

Observations of cosmic microwave background (CMB) temperature fluctuations have played a pivotal role in establishing the standard cosmological model, called the Λ cold dark matter model [1], and provide insights into the origin of structure, the density of baryons, dark matter, dark energy, the number of neutrino species, and the global properties of spacetime [2–5]. Observations have reached a point at which most of the information about the early Universe available in temperature fluctuations has been exhausted [6,7]. However, precise measurements of the fainter CMB polarization anisotropies hold the key to answering many remaining questions about the Universe. Observations have so far only begun to scratch the surface [8–13].

Perhaps the biggest remaining question is what mechanism created the small primordial fluctuations that seeded the observed CMB anisotropies and eventually grew into stars and galaxies. The most widely studied idea is “cosmic inflation” [14–19]. According to this idea, the primordial fluctuations originated as quantum fluctuations during a period of nearly exponential expansion of the very early Universe [20–24]. Eventually this period ended and the Universe became filled with a hot and dense plasma that subsequently cooled and led to the Universe that we see around us. As a consequence of the nearly exponential expansion that stretched microscopic regions of spacetimes to macroscopic scales, the plasma is homogeneous and isotropic, except for the minute quantum fluctuations that were also stretched to macroscopic scales.

Cosmic inflation predicts primordial density fluctuations that are consistent with the observed temperature fluctuations [20–24]. In addition, inflation predicts quantum fluctuations in the fabric of spacetime itself [25,26]. These primordial gravitational waves lead to a characteristic imprint in CMB polarization, commonly referred to as “B-mode” polarization [27–29], and many of the best-motivated models predict a signal that is large enough to be detected with LiteBIRD (the Lite (Light) satellite for the study of B-mode polarization and Inflation from cosmic background Radiation Detection) [30].

A detection of this signal would open an unexplored frontier of physics, shedding light on fundamental processes at energies far beyond the reach of CERN’s Large Hadron Collider, revolutionizing our understanding of physics and the early Universe [31]. A detection of primordial gravitational waves with LiteBIRD would have important implications for many aspects of fundamental physics. A detection would, for instance, indicate that inflation occurred near the energy scale associated with grand unified theories, providing additional evidence in favor of the idea of the unification of forces. Knowledge of the energy scale of inflation also has important implications for several other aspects of fundamental physics, such as axions and, in the context of string theory, the fields that control the shapes and sizes of the compact dimensions.

To search for the imprint of gravitational waves, LiteBIRD will conduct a survey of the entire sky that is 30 times more sensitive than previous full-sky experiments, corresponding to a raw sensitivity of nearly 1000 Planck missions.¹LiteBIRD will be the natural next step in the series of CMB space missions, following National Aeronautics and Space Administration (NASA)’s COBE [32] and WMAP [33], and the European Space Agency (ESA)’s Planck [34], each of which has made its own landmark scientific discoveries. See Ref. [2] for a comprehensive list of CMB experiments and their pioneering contributions.

The CMB polarization anisotropies can be decomposed according to their transformation properties under parity transformations into “E-modes” and “B-modes”. The E-mode polarization is predominantly caused by acoustic waves present at recombination, and the signal is strongest on angular scales of a few to tens of arcminutes (corresponding to multipoles of ℓ ∼ 1000). The B-mode polarization pattern imprinted by gravitational waves peaks on degree angular scales (corresponding to multipoles of ℓ ≃ 80) and on very large angular scales (corresponding to multipoles of ℓ ≲ 10) [27,35]. The “recombination peak” near ℓ ≃ 80 is imprinted during the epoch when electrons and protons combine to form hydrogen and the Universe becomes neutral, while the “reionization bump” below ℓ ≃ 10 is imprinted around the time when the first stars reionize the Universe [36]. At linear order, the density perturbations do not generate B-mode polarization, which makes the B-mode power spectrum the most natural observable to search for primordial gravitational waves. However, CMB photons are deflected by the gravitational potentials associated with the matter along the line of sight. This is referred to as weak gravitational lensing and converts some of the “E-mode” polarization generated by density perturbations into B-modes [37]. Like the E-modes, this effect peaks on much smaller scales of a few arcminutes (corresponding to multipoles of ℓ ≃ 1000) but must be taken into account. This contribution is well understood theoretically, and LiteBIRD targets any excess over the lensing signal caused by the imprint of gravitational waves. While ground-based experiments only target the recombination peak, LiteBIRD can see both peaks in the B-mode power spectrum.

In addition to the B-modes caused by weak gravitational lensing of E-modes, there are additional “foreground” sources of B-mode polarization at microwave frequencies. Thermal emission by interstellar dust grains that are aligned with the Galactic magnetic field and synchrotron emission from electrons spiraling in the Galactic magnetic field provide the dominant contributions. Fortunately, the frequency dependence of the primordial signal and foreground emission differ significantly so that multi-frequency observations allow us to disentangle the primordial and foreground contributions [38–40].

To separate these primordial and foreground components, LiteBIRD will survey the full sky in 15 frequency bands from 34 to 448 GHz, with effective polarization sensitivity of |$2\, \mu$|K-arcmin and angular resolution of 31 arcmin (at 140 GHz). Rapid polarization modulation, a densely linked observation strategy, and the stable environment of an orbit around L2 (the second Lagrangian point for the Sun–Earth system) provide unprecedented ability to control systematic errors, especially on the largest angular scales below ℓ ≃ 10. Taken together, the control of foregrounds and systematic errors gives LiteBIRD the ability to detect both the reionization and recombination bumps in the B-mode power spectrum, giving much higher confidence that a primordial signal has been uncovered. Importantly, if a hint of the recombination peak is seen by a ground-based or balloon-borne experiment, LiteBIRD will make a definitive statement on the detection of the signal and greatly improve the quantitative constraints on the physics of inflation. The forecast for LiteBIRD’s ability to measure the primordial B-mode power spectrum is shown in Fig. 1, together with currently available measurements.

Fig. 1.

CMB power spectra of the temperature anisotropy (top), E-mode polarization (middle), and B-mode polarization (bottom). The solid lines show the angular power spectra for the best-fitting ΛCDM model in the presence of a scale-invariant tensor (gravitational wave) perturbation with a tensor-to-scalar ratio parameter of r = 0.004. The thin dashed line shows the contribution to the B-mode spectrum from scale-invariant tensor perturbation with r = 0.004. A summary of present measurements of CMB power spectra (colored points) [8–10,12,41–47] and the expected polarization sensitivity of LiteBIRD (black points) are also shown.

Open in new tabDownload slide

Even in the absence of gravitational waves, on the largest angular scales, scattering of photons during the reionization epoch at z ≃ 6–10 generates E-mode polarization [36]. LiteBIRD will measure this signal with high precision and will make a definitive determination of the optical depth to the surface of last scattering. The optical depth contains key information about the nature of the epoch of reionization and will, for instance, constrain models of the first stars. The optical depth is currently the least well-constrained parameter of the standard cosmological model and currently limits any constraints that rely on comparisons of the amplitude of CMB anisotropies and clustering of the matter distribution, such as the measurement of the sum of neutrino masses [48–52]. LiteBIRD will provide a cosmic-variance-limited measurement² of E-modes at low multipoles. This will complement measurements by high-resolution ground-based CMB experiments such as the South Pole Observatory (SPO) [57], Simons Observatory (SO) [58], and CMB Stage-4 [59] and will significantly improve cosmological measurements of the sum of neutrino masses.

Finally, the LiteBIRD all-sky polarized maps in 15 frequency bands will be a rich legacy data set for understanding the large-scale magnetic field structure in the Milky Way, having five times greater sensitivity to Galactic magnetic fields than ESA’s Planck mission [60,61].

1.2. Outline of this review

This paper is arranged as follows. Section 2 introduces CMB B-mode tests of cosmic inflation, including constraints expected by LiteBIRD and an argument for the necessity of CMB B-mode measurements from space. Section 3 gives a broad overview of the LiteBIRD mission, including the science requirements, a description of the instrument, and a description of flight operations. Section 4 describes the LiteBIRD instrument, including the telescope designs, the bolometric detector arrays, the readout, the cryogenics, and calibration strategy. Section 5 gives a detailed analysis of the statistical and systematic uncertainties in the tensor-to-scalar ratio measurement; this section also includes an analysis of the impact of foregrounds and instrumental uncertainties. Section 6 describes the scientific outcomes of LiteBIRD beyond the detection of primordial gravitational waves, including measurement of the optical depth to reionization, determination of neutrino masses, a search for cosmic birefringence, mapping hot gas in the Universe, a search for anisotropic CMB spectral distortions, a probe of primordial magnetic fields, and measurements to elucidate the astrophysics of the Milky Way. Section 7 describes possible extensions to the LiteBIRD mission design, including extending the frequency range, as well as synergy with other cosmology and astrophysics projects. Section 8 concludes this review.

2. CMB B-modes as tests of cosmic inflation

2.1. CMB polarization power spectra

LiteBIRD will provide maps of the temperature and polarization anisotropies in 15 frequency bands from 34 to 448 GHz. Fundamental theory does not predict the detailed structure of the maps, only their statistical properties, like the expected correlations between temperature and polarization anisotropies between different points on the sky. Earlier measurements by WMAP and Planck imply that the anisotropies are nearly Gaussian so that their statistical properties are predominantly characterized by the two-point correlation functions [62–65]. The observations by WMAP and Planck also tightly constrain departures from statistical isotropy [66–69]. Under the assumption that the underlying probability distribution is isotropic, the correlations between anisotropies at different points in the sky only depend on the angle between them.

Given these properties, it is natural to consider angular correlation functions that measure the correlations between different points in the sky as a function of this angular separation. While it would be possible to work with maps and their angular correlation functions, in practice it is more convenient to expand the temperature T maps in terms of spherical harmonics,

and work with the coefficients of this expansion |$a^T_{\ell m}$|⁠, referred to as multipole coefficients.

Similarly, it is convenient to expand the maps of the Stokes Q and U parameters, which characterize the linear polarization, in terms of spin-weighted spherical harmonics, ₂Y_ℓm,

and work with the expansion coefficients |$a^E_{\ell m}$| and |$a^B_{\ell m}$|⁠. This decomposition into E- and B-mode polarization is convenient because E- and B-mode patterns have distinct parity; i.e., they transform differently under the inversion of spherical coordinates, |$\hat{n}\rightarrow -\hat{n}$|⁠. Specifically, the spherical harmonics coefficients transform as |$a^E_{\ell m}\rightarrow (-1)^\ell a^E_{\ell m}$| and |$a^B_{\ell m}\rightarrow (-1)^{\ell +1} a^B_{\ell m}$|⁠. As a result, when forming the angular power spectra³

where X and Y are either T, E, or B, there are “parity-even” combinations such as |$C^{TT}_{\ell }$|⁠, |$C^{TE}_{\ell }$|⁠, |$C^{EE}_{\ell }$|⁠, and |$C^{BB}_{\ell }$| that do not change sign under the inversion of spherical coordinates, as well as “parity-odd” combinations such as |$C^{TB}_{\ell }$| and |$C^{EB}_{\ell }$| that do change sign. All of the parity-even combinations from the density fluctuations (scalar perturbation) have been measured already, as seen in Fig. 1, whereas |$C^{BB}_{\ell }$| from the primordial gravitational waves (tensor perturbation), the target of the LiteBIRD mission, have not been detected yet [10,13,41,72]. The parity-odd combinations of the CMB polarization can be used to probe new physics that violates parity symmetry [73–77]. While no significant evidence for parity-odd power spectra of the CMB has been found (see Refs. [78–80] for summaries), |$C^{TB}_{\ell }$| from the polarized dust emission in our Galaxy has been found [60,78].

As we briefly mentioned in the introduction, the decomposition into E- and B-modes is also convenient because, to linear order, the well-measured density perturbations only generate temperature and E-mode anisotropies, whereas gravitational waves lead to B-modes in addition to temperature anisotropies and E-modes. Somewhat heuristically, this can be understood from the fact that E-modes behave much like the gradient component of a vector field, whereas the B-modes behave like the curl-like component. At linear order, one can construct a gradient component from density perturbations, but it is impossible to construct a curl-component. For more details, we refer the interested reader to Refs. [30,81]. So B-modes provide the cleanest way for CMB experiments to search for primordial gravitational waves.

To see more explicitly how the information about the very early Universe is encoded, note that the contributions of primordial density perturbations to the angular power spectra of temperature or E-mode anisotropies are schematically given by

where k is the wavenumber of a Fourier mode and τ is the so-called conformal time, which is related to the physical time t as dτ = dt/a(t) with a(t) being the scale factor for the homogeneous and isotropic expansion of space. The subscript “0” indicates the present-day epoch. The integrand factorizes into three pieces:

• The primordial power spectrum of density perturbations as a function of k (or equivalently radians per distance), |$\Delta ^2_\zeta (k)$|⁠, which contains information about the very early Universe.

• The source functions, |$S^X_{({\rm s})}(k,\tau )$|⁠, which contain information about the physics of the medium, largely from recombination to the present.

• The spherical Bessel functions, j_ℓ(x), for a spatially flat universe.

Similarly, the contributions of primordial gravitational waves to the angular power spectra of temperature, E-mode, and B-mode anisotropies are given by

where |$\Delta ^2_h(k)$| is now the primordial power spectrum of gravitational waves, |$S^X_{({\rm t})}(k,\tau )$| are source functions for tensor perturbations in the medium, and |$\chi ^X_\ell (x)$| is a function of the spherical Bessel functions and their derivatives appropriate for X = T, E, or B [29,35,82,83].

A wealth of information about the Universe is contained in the dependence of the source functions and the argument of the spherical Bessel function on cosmological parameters, like the matter density, the number of relativistic degrees of freedom, and so on. Here we are most interested in the information contained in the primordial power spectra, |$\Delta ^2_\zeta (k)$| and |$\Delta ^2_h(k)$|⁠, which are conventionally parametrized as [84]

where k_* is a pivot scale that will be taken to be |$k_\ast =0.05\, {\rm Mpc}^{-1}$| throughout this document, and n_s and n_t are referred to as the scalar and tensor spectral indices, respectively. In general n_s and n_t are functions of k. However, the scale dependence is expected to be weak, and the default analyses typically report n_s = n_s(k_⋆). So-called “scale-invariant” spectra correspond to n_s = 1 and n_t = 0.

Unfortunately,⁴B-modes are not only generated by primordial gravitational waves, but also by weak lensing of the CMB by matter along the line of sight, which converts E-modes into B-modes [37], and by polarized Galactic emission from interstellar dust grains and relativistic electrons [38–40]. As a consequence, in order to detect the B-modes from primordial gravitational waves, both lensing and foreground contributions must be carefully accounted for. As we will discuss in more detail, LiteBIRD employs 15 frequency bands to characterize and remove the foreground emission. The weak lensing signal has the same frequency dependence as the gravitational wave signal, but its angular dependence is theoretically well understood. Furthermore, because the weak lensing is caused by large-scale structure along the line of sight, some of the weak lensing signal can be removed by combining LiteBIRD with other data sets [85–89].

The theoretical predictions and current measurements of the angular power spectra are shown in Fig. 1. The LiteBIRD error bars, which are used for the constraints presented in the next sections, include foreground residuals as detailed in Sect. 5.

2.2. Cosmic inflation

The remarkable insight gained from analyzing cosmological data is that all cosmic structures, such as galaxies, stars, planets, and eventually us, appear to have originated from tiny quantum fluctuations in the early Universe. Within this inflationary picture, there was a very early period of nearly exponential expansion that generated the seed fluctuations for today’s structure.

According to general relativity, spacetime expands exponentially if the energy budget is dominated by vacuum energy. However, from our existence, we know that this early period of cosmological inflation must have ended. This requires a clock, or more formally a scalar field, that keeps track of time and eventually causes inflation to end. Within quantum mechanics, this scalar field will experience quantum fluctuations, and according to cosmic inflation these initially microscopic quantum fluctuations were stretched to macroscopic scales by the nearly exponential expansion, serving as the seeds of structure formation [20–24].

In this scenario, the matter sector must include a scalar field, the “inflaton”, ϕ. For the simplest models of inflation, the action contains

and is characterized by the potential V(ϕ). As usual, we denote the expansion rate of the Universe (called the “Hubble rate”) by |$H=\dot{a}/a$|⁠, where a(t) is the scale factor appearing in the Friedmann–Lemaître–Robertson–Walker (FLRW) line element. For a flat FLRW universe this line element is |$ds^2=-dt^2+a^2(t)d\mathbf {x}^2$|⁠, and the dynamics of the scale factor is governed by the Friedman equation

where |$\rho ={1\over 2}\dot{\phi }^2+V(\phi )$| is the energy density in the inflaton.

The slow-roll parameter ϵ, the fractional rate of change of the expansion rate in one Hubble time (1/H), is given by [84]

If the energy density of the scalar field is dominated by the potential energy density |$\dot{\phi }^2\ll V(\phi )$|⁠, the slow-roll parameter is small, ϵ ≪ 1. In this case the scale factor grows nearly exponentially. To be phenomenologically viable, inflation must last sufficiently long to solve the horizon and flatness problems [16]. The simplest way to satisfy this requirement is to have a potential that is flat enough so that the fractional rate of change of the inflaton velocity per Hubble time is small. Such models of inflation, based on a single slowly rolling scalar field, predict statistically homogeneous and isotropic, adiabatic, and nearly Gaussian primordial density perturbations with a spectrum of primordial density perturbations given by [84]

where the slow-roll parameter ϵ and the Hubble rate H are to be evaluated at a time when k = aH, and M_P is the (reduced) Planck mass. Since both ϵ and H are slowly varying functions of time, the spectrum is expected to be nearly (but not exactly) scale invariant n_s ≃ 1. Furthermore, as inflation proceeds, the Hubble rate decreases. The slow-roll parameter ϵ is small during inflation, approaches unity as inflation ends, and in the simplest models increases monotonically. Decreasing H and increasing ϵ implies that the simplest models predict a red spectrum, i.e., an amplitude of the power spectrum that decreases with increasing wavenumber, corresponding to n_s < 1. All these predictions, including the deviation from an exactly scale-invariant spectrum, have been confirmed by CMB data from WMAP [42,90,91], the Planck satellite [92–94], and various ground-based observations [95–98].

So far we have discussed the period during which the Universe expands nearly exponentially. From the cosmos today, we know that eventually this period must have ended, and the energy density in the inflaton must have been converted to a plasma of standard-model particles. This process is referred to as “reheating” [99–101]. The details of reheating are unknown but, rather remarkably, the observational predictions only weakly depend on these details, at least for the single-field models discussed here [102–104]. The main effect on observables arises from the amount by which the Universe expands during reheating. The amount of expansion during this period affects how physical scales today are related to physical scales during inflation, or more quantitatively how long has elapsed before the end of inflation k_* = aH.

2.3. Primordial gravitational waves from cosmic inflation

Constraints on the primordial spectrum of density perturbations from observations of temperature and E-mode anisotropies provide strong evidence for the quantum mechanical origin of cosmic structure, and to many they already suggest that the early Universe underwent a period of inflation. However, extraordinary claims require extraordinary evidence.

Like the scalar field, the spacetime metric also fluctuates, and just like the fluctuations in the scalar field, the microscopic fluctuations in the spacetime metric were also stretched to macroscopic scales by the inflationary expansion. So inflation predicts a statistically homogeneous and isotropic, nearly Gaussian background of primordial gravitational waves [25,26,105]. For models based on a single slowly rolling scalar field the power spectrum is given by [84]

where H is again to be evaluated when k = aH. Since H is a slowly decreasing function of time, the primordial gravitational wave spectrum is expected to be nearly scale invariant (n_t ≃ 0) and red (n_t < 0). According to Eq. (11), in the context of inflation a detection of a primordial gravitational wave signal would allow a determination of the expansion rate of the Universe during inflation. In single-field slow-roll models, the expansion rate is directly related to the energy scale of inflation, |$V\simeq 3 H^2 M_{\rm P}^2$|⁠.

These gravitational waves are a remarkable prediction of inflation, and their detection would provide strong independent evidence for inflation, arguably providing definitive confirmation. A detection of this signal would also be the first observation of quantum fluctuations of spacetime itself, and have other important implications to be discussed below.

2.4. Implications of LiteBIRD power spectrum measurements for inflation

To discuss the implications of LiteBIRD’s B-mode power spectrum measurements for inflation, it is convenient to introduce the ratio of the power in primordial gravitational waves, given in Eq. (11), to the power in primordial density perturbations, defined in Eq. (10), referred to as the “tensor-to-scalar ratio”:

Key quantities like the energy scale of inflation and the range traveled by the scalar field are closely related to this parameter, and different classes of models of inflation make different predictions for r.

In single-field slow-roll models, the amplitude of the primordial density perturbations inferred from measurements of temperature and E-mode perturbations, together with the Friedmann equation, allows us to express the energy scale of inflation in terms of r through

Thus, a detection achievable by LiteBIRD would imply that the inflationary energy scale is close to that associated with grand unified theories, and would provide additional evidence for the idea of grand unification [31].

Under the same assumptions, the tensor-to-scalar ratio not only constrains the energy scale of inflation, but also the distance traveled by the inflaton [31],

where N_* represents the number of “e-folds”, the natural logarithm of the change in linear scale of the Universe, between the time when k_* = aH and the end of inflation. As briefly discussed earlier, the exact time when k_* = aH, and hence the value of N_*, depends on the details of reheating, the process that converts the energy density in the inflaton into a hot plasma of standard-model particles. This process is not well constrained, but taking N_* = 30 as a conservative lower limit, we see that a detection of gravitational waves above r = 0.01 would imply an excursion in field space that exceeds M_P. Such a detection would significantly constrain theories of quantum gravity, such as superstring theories (see, e.g., Ref. [106] and references therein).

In the absence of a detection, LiteBIRD will set an upper limit of r < 0.002 at 95% CL (accounting for both statistical and systematic uncertainties). Since both the energy scale and the field range vary slowly with r, an upper limit does not immediately translate into stringent constraints on either the energy scale or the distance traveled by the inflaton. To explain the implications of an upper limit and to understand the motivation for the LiteBIRD design sensitivity we will require an additional concept, that of the characteristic scale of the potential [59,107]. To introduce this quantity and highlight its importance, we will begin with an argument that does not involve the microscopic details of a particular model of inflation.

Provided the fractional rate of change of the expansion rate is small compared to the expansion rate, ϵ ≪ 1, the tensor-to-scalar ratio r obeys a simple differential equation in terms of the number of e-folds N until the end of inflation [108–110]:

The cosmic microwave background allows us to observe a window of a few e-folds around N_*, which we typically expect to be between 50 and 60. The observed departure of the primordial power spectrum from scale invariance is numerically close to (p + 1)/N_*, where p is some number of order unity. In the simplest models of inflation, we expect additional small or large numbers beyond N_* to be absent, which means that we expect n_s(N) − 1 = −(p + 1)/N. In this case, we can solve the differential equation and find the general solution up to an integration constant N_eq. If we continue with the assumption that there are no additional large or small numbers, the solution is well described by one of two limiting behaviors,

where p is constrained to be positive, consistent with the observed red spectrum n_s < 1 [42,92], and by assumption N_eq is expected to be of order unity.

We previously saw that the simplest single-field models are completely characterized by a potential. It is then natural to ask which potentials give rise to these solutions. It can be shown that the first solution in Eq. (16) corresponds to potentials that at least during inflation are well approximated by a monomial V(ϕ) ≃ μ^{4 − 2p}ϕ^2p. For p of order unity, we see that this class of models predicts r ≳ 0.01, which is easily within reach of LiteBIRD.

For the second solution, the qualitative behavior depends on the value of p. For p > 1 the potential corresponds to so-called “hilltop” inflation models [111] for which the potential near the origin in field space approaches a constant from below like a power of the field set by p. Inflation occurs as the field rolls off the hill toward a minimum at larger field values. For p < 1 the potentials correspond to so-called “plateau” models, for which the potential approaches a constant from below at large field values, again with a power set by p. In this case inflation occurs as the field rolls off the plateau toward a minimum near the origin.

Rather intriguingly, the current measurement of n_s favors p ≃ 1, which is a special case. It corresponds to plateau models in which the plateau is approached exponentially:

This behavior occurs in many models of inflation, including the Starobinsky R² model for inflation [14] (discussed in more detail below), models in which inflation is driven by the Higgs boson [112,113], or more generally models with a non-minimally coupled inflaton [114], fiber inflation [115], Poincaré disk models [116,117], α-attractors more generally [93,118–120], or the Goncharov–Linde model [121,122], to name just a few.

The “characteristic scale of the potential” |${\cal M}$| is related to the integration constant N_eq according to |${\cal M}=\sqrt{N_{\rm eq}}M_{\rm P}$|⁠. This allows us to express the tensor-to-scalar ratio in this class of models in terms of the characteristic scale as

Instantaneous reheating corresponds to N_* ≃ 57. Any delay in reheating will decrease N_*, and hence will increase the expected tensor-to-scalar ratio for a given characteristic scale. As a consequence, for |${\cal M}\gtrsim M_{\rm P}$| we expect r ≳ 0.0025, so that an upper limit from LiteBIRD with r < 0.002 at 95% CL (accounting for both statistical and systematic uncertainties) would disfavor any of the simplest models of inflation with a characteristic scale of the potential larger than the Planck scale.

In models such as the Starobinsky model, the Planck scale does not occur by accident, but appears because the characteristic scale and the Planck scale are set by the same dimensionful coefficient in the action, the coefficient of the Einstein–Hilbert term. This makes models with |${\cal M}\gtrsim M_{\rm P}$| a natural target for LiteBIRD. In Fig. 2 we take the Starobinsky model as our fiducial model to showcase what a detection of primordial gravitational waves with LiteBIRD would look like in the n_s–r plane.

Fig. 2.

LiteBIRD constraints on the tensor-to-scalar ratio r and the scalar spectral index n_s assuming Starobinsky’s R² model for inflation [14] with N_* = 51 (specifically the analytic prediction described in the text) as the fiducial model. The lighter and darker green regions show 68% and 95% confidence-level limits achievable with LiteBIRD and Planck. The lighter and darker orange regions (partly hidden behind the green regions) show 68% and 95% confidence-level limits achievable with LiteBIRD alone. The current limits are shown in light blue. The dotted blue lines show representative cases of the first class of models described in the text, monomial models. The red line and the dark purple dot show the predictions of the Starobinsky model [14] (labeled as R²) and models that invoke the Higgs field as the inflaton [112,113], respectively. The light purple lines shows the prediction for Poincaré disk models [116,117].

Open in new tabDownload slide

For a given reheating history, a model makes a definitive prediction, corresponding to a point in the n_s–r plane. However, since the reheating history is uncertain, we represent the predictions of models by bars corresponding to 47 < N_* < 57. One exception to this general rule is the Starobinsky model. Unlike for most models, the underlying idea of this example is that inflation is a consequence of a short-distance modification of the theory of gravity rather than a consequence of the matter sector. Even though the Starobinsky model can be written as a scalar–tensor theory, like any generic f(R) theory [123,124], this idea naturally predicts that the couplings to matter fields responsible for reheating are gravitational couplings in the f(R) frame. In this case, reheating is somewhat delayed. More detailed studies suggest that the delay corresponds to a change in N_* of about 5. Thus, we take N_* = 51 for our fiducial model. In our simple analytic approximation, this leads to r ≃ 0.0046 and n_s ≃ 0.961. Since reheating is expected to be slower, but the details are uncertain in the Starobinsky model as well, we show the model prediction with 42 < N_* < 52. The second exception to the rule are models in which the inflaton is identified with the Higgs field. In this case we know the couplings to the matter fields, and the reheating history is calculable. To reflect this, we represent these models by a single point in the n_s–r plane at N_* = 57, even though some uncertainty exists here as well.

Among the examples given above, the Goncharov–Linde model [121,122] predicts a sub-Planckian characteristic scale, and α-attractors [93,118–120] with a sub-Planckian characteristic scale also exist. So a detection of primordial gravitational waves with LiteBIRD is by no means guaranteed. We thus also showcase what an upper limit would look like in Fig. 3. Let us note that in addition to being simpler in the sense that they do not contain a large hierarchy of scales, models with |${\cal M}\gtrsim M_{\rm P}$| are also simpler in a different sense. One may ask whether inflation will begin for general initial conditions for a given model, and it has recently become possible to investigate this question in numerical general relativity, assuming that the description in terms of a single scalar field is already appropriate at that time [125–128]. The simulations show that models with |${\cal M}\gtrsim M_{\rm P}$| are significantly more robust to inhomogeneities than those with |${\cal M}\lt M_{\rm P}$| [128]. This does not imply that inflation cannot begin in models with a sub-Planckian characteristic scale, but it does suggest that additional dynamics (which could simply be in the form of another field) is needed to set up initial conditions that are appropriate for inflation to begin in such models. So an upper limit from LiteBIRD would disfavor the simplest models of inflation that naturally predict the observed value of n_s and would also be a milestone for early Universe cosmology that provides key information about the inner workings of the earliest moments of the cosmos.

Fig. 3.

LiteBIRD constraints for a fiducial model with r = 0. The lighter and darker green regions show 68% and 95% confidence-level upper limits achievable with LiteBIRD and Planck. The lighter and darker orange regions (partly hidden behind the green regions) show 68% and 95% confidence-level upper limits achievable with LiteBIRD alone. The blue band shows the first class of models mentioned in the text, monomial models. The gray band shows a concrete representative second class of plateau models with p = 1, α-attractors [118]. As discussed in the text, the second class of models depends on the characteristic scale of the potential |${\cal M}$|⁠. The darker gray lines show α-attractors with |${\cal M}=M_{\rm P}$| and |${\cal M}=5 M_{\rm P}$|⁠. In the absence of a detection, LiteBIRD will exclude the first class of models at high significance, and will exclude models in the second class with a super-Planckian characteristic scale, which includes the Starobinsky model [14] and models that invoke the Higgs field as the inflaton [112,113], shown as the red line and the purple dot, respectively.

Open in new tabDownload slide

2.5. Beyond the B-mode power spectrum

Single-field slow-roll inflation predicts a stochastic background of gravitational waves that originated from quantum vacuum fluctuations in spacetime and is nearly scale invariant, nearly Gaussian, and parity conserving [25,26,105]. The detection of a violation of any of these properties would point to new physics beyond the simplest models of inflation [129]. The first condition can be tested by reconstructing the power spectrum |$\Delta _h^2(k)$| from the observed B-mode power spectrum [130,131], the second property can be tested through measurements of the three-point function (bispectrum) [132–135], and the third property can be tested by parity-violating correlation functions such as the cross-correlation between the temperature and the B-mode polarization, between the E- and B-mode polarizations [73,76,77,136,137], or parity-violating contributions to the three-point function [138].

These conditions can be violated when non-minimal couplings of the inflaton are present [73,139,140], or when other fields are present during inflation and source gravitational waves. The energy density in these fields must be sub-dominant compared to the energy density in the inflaton. However, their energy density may still be sufficient to produce gravitational waves with an amplitude within reach of LiteBIRD.

The additional sources could be scalar fields [141–144], a U(1) gauge field [136,145–149], or an SU(2) gauge field [150–157]. All these sources can produce strongly scale-dependent gravitational waves (and, in general, density perturbations) that are highly non-Gaussian. The latter two types of source can produce parity-violating gravitational waves. Hence a stochastic gravitational wave background generated during inflation need not satisfy any of the conditions predicted by single-field slow-roll inflation. If the gravitational waves sourced by the matter fields dominate over the vacuum fluctuations in the metric, then detecting B-mode polarization from primordial gravitational waves no longer generally implies the discovery of the quantum nature of space (although the matter that created them was still produced quantum mechanically). Nevertheless, such a discovery would still provide definitive evidence for inflation because we need inflation to stretch the wavelengths of gravitational waves to billions of light years.

An example of a U(1) gauge field is the primordial magnetic field, which can source tensor perturbations that are non-scale invariant, non-Gaussian, and parity violating (see Ref. [138] and references therein). Magnetic fields can also induce a spatially dependent rotation of polarization angles of the CMB by means of Faraday rotation. The effect can be detected using multi-frequency data because the Faraday rotation angle is inversely proportional to the square of the frequency. We discuss this possibility further in Sect. 6.5.

The axion–SU(2) model described in Ref. [157] provides an example that illustrates the benefits of a satellite mission with full sky coverage and access to the reionization bump. This model contains the inflaton, an axion, and SU(2) gauge fields. The energy density is always dominated by the inflaton field. The axion field χ has a potential of the form V(χ)∝1 + cos (χ/f), where f is the axion decay constant, and the axion is coupled to the gauge fields through a Chern–Simons term, |$\chi F\tilde{F}$|⁠. For time-dependent χ, one of the helicities of the gauge field is amplified. This produces chiral gravitational waves [152,154,158] with parity-violating correlations in the CMB power spectra and circular polarization for laser interferometers [137]. The shape of the tensor power spectrum is determined by the evolution of χ during inflation, and hence by the shape of V(χ). For the cosine potential, the axion velocity increases initially, reaches the maximum at the inflection point, χ(t_*) = πf/2, and then decreases. The resulting tensor power spectrum is approximately log-normal [137,159],

where r_{*, sourced} (hereafter r_*) and k_p are the tensor-to-scalar ratio and the wavenumber at the maximum, and σ² is the width of the power spectrum. The subscript “L” (for “left”) stands for one of the polarization states (determined by the sign of |$\dot{\chi }$|⁠), while the other polarization state is not amplified and is negligible. These quantities are determined by the parameters of the model [137,159,160]. This sourced contribution is added to the vacuum contribution characterized by the vacuum tensor-to-scalar ratio, r_vac. The self-interaction of the gauge fields leads to non-Gaussian gravitational waves [133–135].

In Fig. 4, we compare example B-mode power spectra of this model (dot–dashed and dashed lines) and that of the Starobinsky model (dotted line). The parameters are chosen such that they all have indistinguishable recombination bumps (ℓ ≃ 80), whereas they are very different in their reionization bumps (ℓ ≃ 4). Therefore, a full-sky survey enabled by a space mission such as LiteBIRD is necessary for establishing the origin of the primordial gravitational waves: tensor vacuum fluctuation versus sourced gravitational waves.

Fig. 4.

B-mode power spectra, |$D_\ell =\ell (\ell +1)C^{BB}_{\ell }/2\pi$|⁠, for the Starobinsky model with r = 0.004 61 and n_t = −r/8 (black dotted line) and for axion–SU(2) inflation with two sets of parameters (see Eq. (19) for the definition): one with r_* = 0.004 61, |$k_{p}=0.01\, {\rm Mpc}^{-1}$|⁠, and σ = 1 (purple dashed line) and another with r_* = 0.041, k_p = 9 × 10⁻⁶ Mpc⁻¹, and σ = 3.2 (orange dot–dashed line). The tensor-to-scalar ratio of the vacuum fluctuations is chosen to be r_vac = 10⁻⁴. The cosmic-variance-only (including primordial and lensing B-mode variance) and total LiteBIRD|$\pm 1\, \sigma$| error bars (including foreground residuals) are shown as the gray and blue regions, respectively.

Open in new tabDownload slide

We conclude that, in the case of a detection, it will be important to confirm the detailed predictions of single-field slow-roll models using the LiteBIRD data before claiming discovery of the quantum nature of spacetime. Applying the established methodology for the CMB bispectrum estimation to the LiteBIRD B-mode data will allow us to improve constraints on tensor non-Gaussianities by several orders of magnitude [138]. A violation of any of the basic predictions of single-field slow-roll models of inflation for gravitational waves (i.e., nearly scale invariant, nearly Gaussian, parity conserving) would have profound implications for our understanding of the dynamics of inflation.

2.6. The need for measurements from space

The COBE, WMAP, and Planck data sets are recognized as the reference experiments for their respective CMB science goals. The success of these experiments depended on the advantages of the space environment for making high-fidelity observations of the CMB. These advantages include the following.

• All frequencies are accessible, unlike on the ground where water and oxygen lines block access and reduce the ability to build a detailed model of the foreground emission. In particular, space observations can measure frequencies far into the Wien tail of the CMB to distinguish CMB fluctuations from Galactic dust emission.

• Detector sensitivity is higher in space than on the ground due to the absence of atmospheric loading and the disparity increases rapidly with frequency, giving much better per-detector leverage on Galactic dust measurements from space. As a rule of thumb, one detector in space is equivalent to 100 detectors (of the same quality) on the ground.

• The absence of atmospheric emission and its large brightness fluctuations in space-based measurements give high-fidelity maps on large angular scales corresponding to 2 ≤ ℓ ≲ 30.

• Bright sources such as the Earth and Sun are kept far from the boresight of the telescope by a large angle, giving very low systematic errors due to pickup of those sources in the telescope sidelobes.

LiteBIRD’s ability to measure the entire sky at the largest angular scales with 15 frequency bands is complementary to that of ground-based experiments, which will focus on deep observations of low-foreground sky to search for an inflationary signal. LiteBIRD observations have the potential to detect both the recombination peak at |$\ell \, {\simeq }\, 80$|and the reionization peak at |$\ell \, {\simeq }\, 4$|⁠. As highlighted earlier, high significance detections of both peaks would provide firm evidence that we have detected the signature of inflation. A primary science requirement for LiteBIRD is to detect both peaks with greater than |$5\, \sigma$| significance for a relatively high value of |$r\, {=}\, 0.01$|⁠. Detection of both peaks is necessary to distinguish between cosmological models with a similar recombination peak, as discussed in the previous section. For all detectable values of r, the all-sky data from LiteBIRD can be tested for isotropy, which is a critical feature of a true cosmological B-mode signal.

Finally, LiteBIRD can provide valuable foreground information for ground-based experiments. Ground-based experiments can improve LiteBIRD’s observations with high-resolution lensing data. The LiteBIRD data set will be timely, since it will be available at the same time as ground-based CMB data from Chile and the South Pole, as well as other powerful cosmological data sets such as those from the Vera C. Rubin Observatory, Euclid, and the Nancy Grace Roman Space Telescope.

2.7. Comparison with other probes

Several methods have been proposed for observing primordial gravitational waves other than through CMB polarization measurements. These include future projects for a gravitational wave interferometer [161], a technique using pulsar timing arrays [162,163], and a method using the 21-cm line [164]. The sensitivity of the CMB to primordial gravitational waves is much better than those of the other probes, assuming the spectrum expected from standard cosmology; for instance, the sensitivity of LiteBIRD is about 10 million times greater than that of LISA [160]. Therefore, the discovery of primordial gravitational waves seems dramatically more likely to come from CMB observations in this case. Once the primordial gravitational waves are discovered with CMB polarization observations, it will give us a concrete target for future projects using other methods. In some non-standard models, primordial gravitational waves can be enhanced at shorter wavelengths. Their observability by various probes including that of LiteBIRD is discussed elsewhere [160] with the conclusion that LiteBIRD is competitive even in those non-standard models.

3. LiteBIRD overview

3.1. Project overview

After some initial conceptual studies [165–169] that started in 2008, we proposed LiteBIRD in 2015 as JAXA’s large-class (L-class) mission candidate. JAXA’s L-class is for flagship science missions with a 30 billion yen cost cap. There will be three L-class missions in about ten years, launched using JAXA’s H3 rocket. LiteBIRD passed an initial down-selection and completed a two-year Pre-Phase-A2 concept development phase in 2018. JAXA selected LiteBIRD in May 2019 as the second L-class mission after MMX, the Martian Moons Exploration, which will be launched in the mid-2020s.

The LiteBIRD Collaboration has more than 300 researchers as of January 2022, based in Japan, North America, and Europe, with experience in CMB experiments, X-ray satellite missions, and other large projects in high-energy physics and astronomy. In particular, a large number of researchers who worked on the Planck satellite are members of LiteBIRD. We thus consider LiteBIRD to be the successor to the Planck satellite.

LiteBIRD will survey the polarization of the CMB radiation over the full sky with unprecedented precision. The full success criterion of LiteBIRD is to achieve δr < 0.001 for a fiducial model with r = 0, where δr is the total error on the tensor-to-scalar ratio.

Specifically, we define this as the value covering the 68% area of the posterior probability function for r:

The posterior, L(r), including both statistical and systematic components, will be described in Sect. 5.

This section gives a concise overview of LiteBIRD. In Sect. 3.2, we describe our Level-1 mission requirements, or scientific requirements, and the rationale behind them. In Sect. 3.3, we introduce our measurement requirements and their flow down to system requirements. After describing the launch vehicle (Sect. 3.4), we introduce the spacecraft and the payload module (Sect. 3.5), the service module (Sect. 3.6), and the operation concept (Sect. 3.7.)

3.2. Science requirements

In Fig. 1 (Sect. 2 above), we summarized the present measurements of the CMB power spectra, including B-modes, with the expected polarization sensitivities of LiteBIRD displayed. The B-mode power is proportional to the tensor-to-scalar ratio, r, which has been observationally constrained by BICEP/Keck to be r < 0.036 (95% CL) [12], with a recent update folding in a re-analysis of Planck data yielding r < 0.032 (95% CL) [72,170] and r < 0.037 (95% CL) [171]. The next generation of CMB polarization experiments on the ground have the potential to observe the signal around ℓ ≃ 80, coming from the recombination epoch. However, if r is less than approximately 0.03, the B-modes due to gravitational lensing become dominant. Removing contamination of the lensing B-modes, often called “delensing”, is needed in this case. In contrast, the other primordial signal, at ℓ < 10, which is due to reionization, is larger than the lensing B-modes, even for r = 0.001. In order to access the reionization peak, one needs to survey the full sky, where the advantage of observing in space is clear.

The critical question is: to what precision should r be measured? Here we introduce the total uncertainty on r, δr, which consists of five components: (instrumental) statistical uncertainties; systematic uncertainties; uncertainties due to contamination of foreground components; uncertainties due to gravitational lensing; and uncertainties due to observer biases. There are many different inflationary models under active discussion, which predict different values of r. Among them, there are well-motivated inflationary models that predict r > 0.01 [30]. If our requirement is δr < 0.001, we can provide more than |$10\, \sigma$| detection significance for such models. On the other hand, if LiteBIRD finds no primordial B-modes and obtains an upper limit on r, then this limit will be stringent enough to set severe constraints on the physics of inflation. As discussed in Sect. 2.4, if we obtain an upper limit at r ∼ 0.002, we can completely rule out one important category of models, namely any single-field model in which the characteristic field-variation scale of the inflaton potential is greater than the reduced Planck mass.

Based on all the considerations described above, we decided to impose the requirements described in Table 1. The first, Lv1.01, shall be achieved without delensing using external data; if external data are available, we may further reduce δr [172]. The second requirement, Lv1.02, is essential to cover the case where r turns out to be large. If there are already indications of the primordial B-modes before the observations by LiteBIRD, that would imply a relatively large value of r. In this case, data from LiteBIRD will allow us to measure the B-mode signals from reionization and recombination simultaneously. If the spectral shape is consistent with expectations from the standard cosmology, that will narrow down the list of possible inflationary scenarios, and provide a much deeper insight into the correct model. If we observe an unexpected power spectrum, beyond the standard-model prediction, that will lead to a revolution in our picture of the physics of the early Universe. Lv1.02 also sets the angular resolution requirement for LiteBIRD.

3.3. Measurement requirements and system requirements

To satisfy the science requirements described in the previous section, we use the requirements flow-down framework shown in Table 2. To derive Lv2 measurement requirements from Lv1 science requirements, we also consider program-level constraints, such as the cost cap, which are not controlled by the LiteBIRD team. We use agreed-upon assumptions between the LiteBIRD team and other parties or within the LiteBIRD team; examples include assumptions on the complexity of the astronomical foreground components, the cooling-chain lifetime, and basic system redundancy guidelines. There are in total 11 Lv2 measurement requirements on the statistical uncertainty (Lv2.01), the systematic uncertainty (Lv2.02), the scan strategy (Lv2.03), the angular resolution (Lv2.04), calibration measurements (Lv2.05), error budget allocation (Lv2.06), systematic error budget allocation (Lv2.07), the duration of the normal observation phase (Lv2.08), the orbit (Lv2.09), observer bias (Lv2.10), and noise-covariance knowledge (Lv2.11). Our error budget (Lv2.06) is defined such that an equal amount is given to the total statistical error after foreground separation σ_stat and the total systematic error σ_syst. The requirements that we chose are thus σ_stat < 0.6 × 10⁻³ on the statistical uncertainty (Lv2.01) and σ_syst < 0.6 × 10⁻³ on the systematic uncertainty (Lv2.02).⁵ Since we assume no delensing using external data, σ_stat includes uncertainties from the lensing B-mode component. Uncertainties due to foreground separation are also in σ_stat. The observer bias (Lv2.10) shall be much smaller than σ_syst. The requirement on the statistical uncertainty (Lv2.01) has six sub-requirements on: (1) CMB sensitivity; (2) dust emission; (3) synchrotron emission; (4) separation of CO lines; (5) the number of observing bands; and (6) the observing frequency range. These are determined through detailed simulation. We require full-sky surveys (Lv2.03) to obtain the B-modes to the lowest multipole of ℓ = 2. The angular resolution (Lv2.04) shall be better than 80 arcmin full width at half maximum (FWHM) in the lowest-frequency band in order to perform precision measurements at |$\ell \, {=}\, 200$|⁠. The regular observation phase (Lv2.08) shall be three years, considering the total cost cap and cooling-chain lifetime. The lifetime is determined by the degradation of working gas and moving parts of the mechanical coolers. The degradation is suppressed through our technology development to assure the required lifetime. The satellite shall be in a Lissajous orbit (Lv2.09) around the Sun–Earth L2 point to avoid the influence of radiation from the Sun, Moon, and Earth (discussed further in Sect. 3.7). Requirements on calibration measurements (Lv2.05, Lv2.11) and systematic error budget allocation (Lv2.07) will be explained in Sect. 4.

Lv1 and Lv2 requirements are collectively called “mission requirements”. In general, several possible designs meet mission requirements, and so we performed implementation trade-off studies to choose the best design. We also considered program-level constraints and assumptions that we used to set Lv2 requirements.

Lv3 integrated system requirements constitute top-level system requirements. An essential distinction between Lv2 and Lv3 is that Lv3 requirements are for the system chosen from trade-off studies, while Lv2 measurement requirements do not assume a specific system in principle. Lv3 requirements include general system requirements not only for mission instruments but also for the bus system,⁶ ground segments, and ground-support equipment. There are too many Lv3 requirements to list here. The requirement flow’s tree structure is also too detailed to show, since some Lv3 requirements derive from more than one Lv2 requirement; however, we will explain some essential Lv3 requirements in Sect. 4.

3.4. Launch vehicle

LiteBIRD will be launched on an H3 [173], Japan’s new flagship rocket. It will achieve greater flexibility, reliability, and performance at a lower cost than the currently used H-IIA rocket. The H3 rocket is under development through its prime contractor, Mitsubishi Heavy Industries, with a maiden flight scheduled in 2022. The first stage of the H3 rocket will adopt the newly developed liquid engine, LE-9, which achieves a thrust 1.4 times larger than the LE-7A engine currently in use. Its second-stage engine, LE-5B-3, and the solid rocket booster, SRB-3, will also be improved. The launch capability of the H3 rocket to a geostationary transfer orbit will be the highest ever among JAXA’s launch vehicles, exceeding that of the existing H-IIA and H-IIB launch vehicles. The launch facility at Tanegashima Space Center will also be upgraded following the development of H3.

The design of the H3 rocket allows for several different configurations. The rocket type is defined by the combination of the number of first-stage engines (2 or 3), the number of solid rocket boosters (0, 2, or 4), and the length of the fairing (short or long). These setups make it possible to cope with various payload sizes and orbits. Considering the size, weight, and orbit of LiteBIRD, we plan to adopt the H3-22L configuration, which means two first-stage engines, two boosters, and a long fairing. The estimated launch capability with this configuration is larger than 3.5 t. We thus set a provisional requirement on the total weight of LiteBIRD as |${\lt }\, 3.5$| t. This requirement may be updated after the first flight of the H3 rocket.

In most cases, the launch environment of H3 is expected to be similar to or more moderate than that of H-IIA. Details of the launch environment may depend on the rocket configuration, especially on the number of solid rocket boosters, the satellite mass, and the flight path. We conservatively assume the launch environment of H-IIA in general for the design of LiteBIRD. However, when the launch environment is critical in the design, such as for the mechanical requirement on the fundamental frequency of the satellite, we adopt requirements based on the current best estimation of the performance of H3.

3.5. Spacecraft overview

The overall structure of the spacecraft for LiteBIRD is determined directly from the mission requirements. The axisymmetric shape of the spacecraft is selected for reducing the moment of inertia to make the spin easier. We chose to place the payload module (PLM), including the telescopes, at the top of the spacecraft and the solar panels at its bottom, perpendicular to the spin axis. The high-gain antenna should be placed on the bottom side of the satellite, i.e., opposite the mission instruments, to point to the Earth and reduce interference with the telescopes. Based on these considerations, we show the basic structure of the spacecraft in Fig. 5.

Fig. 5.

Conceptual design of the LiteBIRD spacecraft. The payload module (PLM) houses the low-frequency telescope (LFT), the mid-frequency telescope (MFT), and the high-frequency telescope (HFT).

Open in new tabDownload slide

In this configuration, the whole spacecraft spins, and the possibility of using a slip-ring to rotate only the PLM is not adopted. The main reasons for this selection are to handle large heat dissipation in the PLM and to reduce the possibility of a single-point failure. The PLM is equipped with mechanical coolers, which dissipate a fairly large amount of heat. A radiator of sufficient size to dissipate the heat can be equipped only in the service module (SVM) and it is not easy to transfer heat from the spinning PLM through the slip-ring to a non-spinning SVM. The slip-ring introduces a single point whose failure would be critical for the mission. Furthermore, a slip-ring might produce micro-vibration and could increase the detector noise significantly. For these reasons, we decided to rotate the whole spacecraft and not to adopt the slip-ring.

The spacecraft has a thrust tube at its center, which transfers the PLM launch load to the rocket. We will install the fuel tank inside the thrust tube to utilize the inner space effectively. The insides of the side panels are used to mount various electric components of both the SVM and PLM. PLM components are preferentially placed on the upper parts of the side panels, whereas SVM components are on the lower parts of the side panels. The outer sides of the upper parts of the side panels are used to mount radiators, which radiate the heat dissipated in the PLM, such as from the mechanical coolers and electronics boxes.

We show a block diagram of the spacecraft in Fig. 6. The LiteBIRD spacecraft uses a typical satellite configuration. Observation of the entire sky is conducted through the scan strategy that is detailed in Sect. 5.1. The slow spin rate of 0.05 rpm makes it possible to adopt three-axis attitude control that satisfies the LiteBIRD attitude accuracy requirements, even if the spacecraft spins. The spacecraft will have a total weight of 2.6 t, including the fuel of approximately 400 kg, and a total height of 5.3 m. Thus the current weight has a large margin compared to the rocket’s capability. We estimate the total power of the spacecraft to be 3.0 kW. The downlink rate will be 10 Mbps in the X band and will transfer a total of 17.9 GB of scientific data every day. All these parameters are subject to change as the conceptual design of the satellite continues to be developed.

Fig. 6.

Block diagram of the spacecraft for LiteBIRD. Boxes with broken lines represent electric equipment, while those with solid lines are subsystems composed of multiple equipment types. Lines and arrows connecting boxes are only representative.

Open in new tabDownload slide

3.6. Service module

The service module (SVM) of LiteBIRD includes an attitude orbit-control system (AOCS), thermal control system, communication system, data-handling system, power system, and other subsystems. The SVM of LiteBIRD utilizes existing technology as much as possible to reduce the development cost and risks. In what follows, we briefly describe some characteristics of the SVM.

LiteBIRD is a zero-momentum, three-axis stabilized spacecraft designed to realize the required pattern of an all-sky survey, i.e., the combination of spin and precession. Momentum wheels (MWs) are used to control the attitude of the spacecraft, and the reaction control system (RCS) is used to unload the MWs and to control the orbit. Because the spacecraft is operated with zero momentum, relatively large MWs are required to cancel the angular momentum due to the spin. The MWs also cancel the spin-axis component of the angular momentum due to the polarization modulators. Other wheels are used to control the precession of the spacecraft. The spacecraft receives a small amount of external torque even at L2, mostly from solar radiation. This causes a steady increase or decrease of the rotational frequencies of the MWs, and thus the RCS is used to unload the MWs regularly. The RCS also provides the required ΔV for the initial correction of the orbit and for the orbit insertion at L2. In addition, we use the RCS once every few months to correct orbit errors, since L2 is a gravitational saddle point and any orbit around it is intrinsically unstable.

The AOCS uses star trackers (STTs) and inertial reference units (IRUs) to determine the spacecraft’s attitude because a good attitude solution is required for LiteBIRD. The spin rate of 0.05 rpm corresponds to 0.3 deg s⁻¹. This spin speed is easily handled by the currently available STTs and the degradation of the attitude solution is negligible. The situation is the same for the currently available IRUs. We expect that the STTs can track stars continuously, but the IRUs will be used to interpolate the attitude in case the STTs temporarily fail to track stars.

A thermal control system keeps the temperature of the on-board components in the required range. This is not easy when some of the components have large heat dissipation or require tight temperature stability. Components with large heat dissipation are the mechanical coolers, their drivers, and the signal-processing units. Adiabatic demagnetization refrigerator controllers and SQUID controller units require tight temperature stability. The total heat dissipation of the payload module is about 1.4 kW. Because there is no room in the payload module for sufficient radiators for this amount of heat dissipation, radiators are placed on the upper parts of the side panels of the spacecraft. The total area of the radiators may be estimated to be approximately 10 m². Heat pipes may be used to transfer heat from the components to the radiators. When accurate temperature control is required, heaters are used in combination with the radiators.

LiteBIRD uses the X band for telemetry and command (and ranging), and also for the downlink of the mission data. The main reason to use the X band for telemetry and command is that the primary GRound station for deep space Exploration And Tele-communication (GREAT) supports only the X band, not the S band, for uplink. We will also use the 34-m antenna at Uchinoura Space Center (USC) as a secondary station. Because GREAT is the only deep space station in Japan, many interplanetary satellites will use the station. The secondary station is useful when GREAT is unavailable due to tracking other satellites. However, the USC 34-m antenna is smaller than GREAT (54-m antenna), and so the downlink rate at USC 34m will be only 1/3 of that of GREAT. The required downlink rate for the mission data, 10 Mbps, will be achieved only with GREAT. To achieve this rate, we will use a parabolic antenna with a diameter of 0.5 m mounted on a 2D gimbal with 20 W of output power. The total amount of mission data is estimated to be 17.9 GB d⁻¹. This means that approximately 4.5 h are needed for the downlink of the mission data every day.

The power system and data-handling system of LiteBIRD use the heritage of past JAXA science missions, such as ASTRO-H, as much as possible. Thus we adopt Space Wire for the on-board data-handling system. This makes the interface checks of the electronic components easier. We adopt a 50 V unregulated bus for the power system. Because of the scan strategy, the solar array panels (SAPs) receive solar radiation at an incident angle of 45^○. This may reduce the efficiency of the SAPs by |$1/\sqrt{2}$|⁠, but we selected fixed panels to make the system simple. We choose the SAPs to be close to disk-shaped to avoid diffraction of microwaves from the Sun interfering with the telescopes.

3.7. Operation concepts

3.7.1. Basic principles of operation

Because LiteBIRD needs to observe the whole sky as much as possible, we adopt the following principles of operation: (1) LiteBIRD does not make real-time observations or target-of-opportunity (TOO) observations, but continuously makes an all-sky survey; (2) mission data will be downlinked to the primary tracking station, GREAT, once a day for a duration of about 4.5 h; (3) observations may be interrupted during the unloading of the MWs and orbit-keeping maneuvers; and (4) precession of the spacecraft may be stopped and observations may be interrupted in the case of an emergency in the SVM, such as a hardware failure.

In what follows, we describe the outline of mission operation for each operations phase.

3.7.2. Outline of operation

LiteBIRD will be launched from the Tanegashima Space Center with the H3 rocket. It will be directly inserted into an orbit that approaches the L2 point. Soon after separation from the rocket, the spacecraft establishes three-axis controlled attitude and deploys solar panels to obtain enough power. Then, the spacecraft starts to spin, but not to precess, in order to achieve uniform temperature distribution around the spin axis, which is followed by an initial checkout of the SVM. This initial operations phase and checkout will take approximately a week.

After the initial checkout of the SVM, we will start the health check of the PLM. The launch-locks of the PMUs are released after the health check. The half-wave plate will be supported by the holding mechanism. We then start cooling the telescopes with a combination of radiative cooling and the shield cooler. The Joule–Thomson (JT) coolers and the adiabatic demagnetization refrigerators (ADRs) are turned on at the appropriate timing. This initial cooling takes a relatively long time, approximately 70 or 80 d. When the nominal operation temperature of the focal-plane detectors is reached, their function and performance are checked. Thus most of the cruising phase out to L2, which may last approximately 100 d, will be spent on initial cooling.

When the spacecraft arrives at L2, an insertion maneuver into the Lissajous orbit will be carried out. Then, test observations are conducted in the all-sky scanning mode, i.e., combination of precession and spin. Various functions and the performance of the mission instruments are verified, and operational parameters are optimized.

When the test observations are completed, regular observations begin and continue for three years. In this phase, all-sky survey observations are conducted steadily and we obtain as much data as possible. Our scan strategy is described in Sect. 5.1. As for calibration of the instruments, our baseline plan is to rely on data from the regular observations, not to pause them for special calibration data taking. Our in-flight calibration plan is discussed in more detail in Sect. 4.8. After these regular observations, we may extend the mission, if approved by the Japan Aerospace Exploration Agency (JAXA) review.

3.8. Data processing and analyses

CMB missions typically scan the sky continuously with many detectors at multiple frequencies, measuring temperature and linear polarization, while simultaneously recording the orientation of the telescope. The time-ordered data (TOD) then consist of the time stamp, observation direction determined by satellite attitude monitor, HWP position, thermal and electric monitor for the instruments, and the measured signal for each detector sample. The measured signal includes not just the CMB, but also emission from astrophysical foregrounds, together with other systematic effects, as well as instrumental noise.

The processing of CMB experimental data can be described as a series of steps that move from the TOD to sky maps at each frequency, which are then separated into different physical components. The statistics of the CMB map are finally compared to the cosmological prediction from theoretical models. These data-processing steps, indicated in Fig. 7, reduce the statistical and systematic uncertainties in the data, first reducing the systematic contamination by appropriate mitigation in a given data domain, and then reducing the dimensionality of the data set by exploiting its redundancies to project onto a lower-dimensional domain.

Fig. 7.

Flowchart indicating the sequence of steps leading to the determination of cosmological parameters from mission TOD via several intermediate products that can also be scientifically exploited. Note the iterative nature of the processing.

Open in new tabDownload slide

Systematic mitigations include removing glitches (e.g., from cosmic-ray hits) in the time domain, separating the CMB from the astrophysical foreground components in the map domain, and quantifying contamination from unresolved emission sources in the spectral domain. Throughout the analysis process we also have to account for non-idealities in the instrument, both optical (e.g., from asymmetric and mismatched beams, including sidelobes, differences in the bandpass for each detector) and electronic (e.g., gain drift, non-linearity, and crosstalk).

Finally, we need an accurate description of the uncertainties in the products and their correlations. The data volumes that we need to amass in order to detect the tiny CMB signals preclude exact analyses, and so we typically use Monte Carlo methods for debiasing and forward propagation of uncertainties. We therefore need to be able to generate and reduce large numbers of very accurate simulated data sets, whose input mission and sky models are themselves informed by our analyses of the satellite data.

With 4508 detectors sampling at 19.1 Hz for three years, the LiteBIRD mission will gather 8 × 10¹² detector samples. Manipulating this data volume while capturing all of the correlations in the CMB signals, foregrounds, and instrumental noise and systematics, with sufficient precision to yield reliable, unbiased results, is a computationally challenging task, requiring the use of state-of-the-art high-performance computing systems. Similarly, tracking the provenance of all of the data products, including the myriad data cuts used to check the robustness of the analysis, requires dedicated databases accessible to all collaboration members. The biggest data challenges for LiteBIRD will be removing astrophysical foreground contamination using the sky maps at the 15 observing frequency bands (Sect. 5.2), and mitigating systematic effects and precise characterization of their residuals (Sect. 5.3).

4. Payload module of LiteBIRD

4.1. Overview

The LiteBIRD PLM consists of three telescopes—at low, medium, and high frequencies—with their respective cryostructure and focal planes cooled down to 0.1 K. The PLM also includes the global cooling chain from 300 K to 4.8 K, and room-temperature elements, such as drivers and warm readout electronics of the detectors. Requirements for the PLM have been derived from the top-level requirement of achieving a tensor-to-scalar ratio error of δr < 0.001 (see Sect. 3.2). Table 3 gives information on the frequency bands, beam sizes, and noise-equivalent temperatures (NETs) for each of the 15 frequency channels. A discussion of the NET calculations is given in Sect. 5.1.