Deviations of the cosmic microwave background (CMB) frequency spectrum from a pure blackbody tell an exciting story about the thermal history of our Universe. In this paper, we illustrate how well ...future CMB measurements might decipher this tale, envisioning a PIXIE-like spectrometer, which could improve the distortion constraints obtained with COBE/FIRAS some 20 years ago by at least three orders of magnitude. This opens a large discovery space, offering deep insights to particle and early-universe physics, opportunities that no longer should be left unexplored. Specifically, we consider scenarios with annihilating and decaying relic particles, as well as signatures from the dissipation of primordial small-scale power. PIXIE can potentially rule out different early-universe scenarios and moreover will allow unambiguous detections in many of the considered cases, as we demonstrate here. We also discuss slightly more futuristic experiments, with several times improved sensitivities, to highlight the large potential of this new window to the pre-recombination universe.
Energy release in the early Universe leads to spectral distortions of the cosmic microwave background (CMB) which in the future might allow probing different physical processes in the ...pre-recombination (z 103) epoch. Depending on the energy-injection history, the associated distortion partially thermalizes due to the combined action of Compton scattering, double Compton scattering and Bremsstrahlung emission, a problem that in general is hard to solve. Various analytic approximations describing the resulting distortion exist; however, for small distortions and fixed background, the cosmology Green's function of the problem can be pre-computed numerically. Here, we show that this approach gives very accurate results for a wide range of thermal histories, allowing fast and quasi-exact computation of the spectral distortion given the energy-release rate. Our method is thus useful for forecasts of possible constraints on early-universe physics obtained from future measurements of the CMB spectrum.
In the expanding Universe, the average temperature of the cosmic microwave background (CMB) is expected to depend like T
CMB ∝ (1 + z) on redshift z. Adiabatic photon production (or destruction) or ...deviations from isotropy and homogeneity could modify this scaling and several observational tests have been carried out in response. Here, we explain why ‘adiabatic’ conditions are extremely difficult to establish in the redshift range targeted by these tests. Thus, instead of leading to a simple rescaling of the CMB temperature, a spectral distortion should be produced, which can be constrained using COBE/FIRAS. For scenarios with late photon production, tests of the temperature–redshift relation (TRR) should therefore be reinterpreted as weak spectral distortion limits, directly probing the energy dependence of the photon production process. For inhomogeneous cosmologies, an average y-type distortion is produced, but this type of distortion can be created in several other ways. Here, we briefly discuss possible effects that may help disentangling different contributions to the distortion signal, finding this to be very challenging. We furthermore argue that tests of the TRR using the Sunyaev–Zeldovich effect have limited applicability and that for non-gravitational changes to the TRR, the CMB anisotropy spectrum should exhibit an additional y-type dependence.
In this paper, we explore the potential effects of dark matter (DM) annihilations on the cosmological recombination spectrum. With this example, we want to demonstrate that the cosmological ...recombination spectrum in principle is sensitive to details related to possible extra energy release during recombination. We restrict ourselves to DM models which produce a negligible primordial distortion of the cosmic microwave background (CMB) energy spectrum (usually characterized as μ- and y-type distortions). However, since during the epoch of cosmological recombination (z∼ 1000) a large fraction of the deposited energy can directly go into ionizations and excitations of neutral atoms, both the cosmological recombination spectrum and ionization history can still be affected significantly. We compute the modifications to the cosmological recombination spectrum using our multilevel H i and He i recombination code, showing that additional photons are created due to uncompensated loops of transitions which are induced by DM annihilations. As we illustrate here, the results depend on the detailed branching of the deposited energy into heating, ionizations and excitations. This dependence in principle should allow us to shed light on the nature of the underlying annihilating DM model (or more generally speaking, the mechanism leading to energy injection) when measuring the cosmological recombination spectrum. However, for current upper limits on the potential DM annihilation rate during recombination the cosmological recombination spectrum is only affected at the level of a few per cent. Nevertheless, we argue here that the cosmological recombination spectrum would provide another independent and very direct way of checking for the presence of sources of extra ionizing or exciting photons at high redshifts. This would open a new window to possible (non-standard) processes occurring before, during and between the three epochs of recombination.
The energy spectrum of the cosmic microwave background (CMB) allows us to constrain episodes of energy release in the early Universe. In this paper, we revisit and refine computations of the ...cosmological thermalization problem. For this purpose a new code, called CosmoTherm, was developed that allows us to solve the coupled photon-electron Boltzmann equation in the expanding, isotropic Universe for a small spectral distortion in the CMB. We explicitly compute the shape of the spectral distortions caused by energy release due to (i) annihilating dark matter; (ii) decaying relict particles; (iii) dissipation of acoustic waves; and (iv) quasi-instantaneous heating. We also demonstrate that (v) the continuous interaction of CMB photons with adiabatically cooling non-relativistic electrons and baryons causes a negativeμ-type CMB spectral distortion of ΔI
ν/I
ν∼ 10−8 in the GHz spectral band. We solve the thermalization problem including improved approximations for the double Compton and Bremsstrahlung emissivities, as well as the latest treatment of the cosmological recombination process. At redshifts z≲ 103, the matter starts to cool significantly below the temperature of the CMB so that at very low frequencies, free-free absorption alters the shape of primordial distortions significantly. In addition, the cooling electrons down-scatter CMB photons, introducing a small late negative y-type distortion at high frequencies. We also discuss our results in the light of the recently proposed CMB experiment PIXIE, for which CosmoTherm should allow detailed forecasting. Our current computations show that for energy injection because of points (ii) and (iv), PIXIE should allow us to improve existing limits, while the CMB distortions caused by the other processes seem to remain unobservable with the currently proposed sensitivities and spectral bands of PIXIE.
The damping of primordial perturbations at small scales gives rise to distortions of the cosmic microwave background (CMB). Here, the dependence of the distortion on the different types of ...cosmological initial conditions is explored, covering adiabatic, baryon/cold dark matter isocurvature, neutrino density/velocity isocurvature modes and some mixtures. The radiation transfer functions for each mode are determined and then used to compute the dissipative heating rates and spectral distortion signatures, utilizing both analytic estimates and numerical results from the thermalization code CosmoTherm. Along the way, the early-time super-horizon behaviour for the resulting fluid modes is derived in conformal Newtonian gauge, and tight-coupling transfer function approximations are given. CMB spectral distortions caused by different perturbation modes can be estimated using simple k-space window functions which are provided here. Neutrinos carry away some fraction of the primordial perturbation power, introducing an overall efficiency factor that depends on the perturbation type. It is shown that future measurements of the CMB frequency spectrum have the potential to probe different perturbation modes at very small scales (corresponding to wavenumbers 1 k few × 104 Mpc− 1). These constraints are complementary to those obtained at large scales and hence provide an exciting new window to early-universe physics.
It is well known that our motion with respect to the cosmic microwave background (CMB) rest frame introduces a large dipolar CMB anisotropy, with an amplitude ∝β=v/c∼ 10−3. In addition it should lead ...to a small breaking of statistical isotropy which becomes most notable at higher multipoles. In principle this could be used to determine our velocity with respect to the CMB rest frame using high angular resolution data from Planck, without directly relying on the amplitude and direction of the CMB dipole, allowing us to constrain cosmological models in which the cosmic dipole arises partly from large-scale isocurvature perturbations instead of being fully motion-induced. Here, we derive simple recursion relations that allow precise computation of the motion-induced coupling between different spherical harmonic coefficients. Although the lowest order approximations for the coupling kernel can be deficient by factors of 2-5 at multipoles l∼ 1000-3000, using our results for the aberration kernel we explicitly confirm that for a statistical detection of the aberration effect only first-order terms in β matter. However, the expressions given here are not restricted to β∼ 10−3, but can be used at much higher velocities. We demonstrate the robustness of these formulae, illustrating the dependence of the kernel on β, as well as the spherical harmonic indices l and m.
A new approach to the cosmological recombination problem is presented, which completes our previous analysis on the effects of two-photon processes during the epoch of cosmological hydrogen ...recombination, accounting for ns-1s and nd-1s Raman events and two-photon transitions from levels with n≥ 2. The recombination problem for hydrogen is described using an effective 400-shell multilevel approach to which we subsequently add all important recombination corrections discussed in the literature thus far. We explicitly solve the radiative transfer equation of the Lyman-series photon field to obtain the required modifications to the rate equations of the resolved levels. In agreement with earlier computations, we find that 2s-1s Raman scattering leads to a delay in recombination by ΔN
e/N
e∼ 0.9 per cent at z∼ 920. Two-photon decay and the Raman scattering from higher levels (n > 3) result in small additional modifications, and precise results can be obtained when including their effect for the first three to five shells. This work is a major step towards a new cosmological recombination code (cosmorec) that supersedes the physical model included in recfast, and which, owing to its short run time, can be used in the analysis of future cosmic microwave background data from the PLANCK Surveyor.
Abstract
Silk damping of primordial small-scale perturbations in the photon-baryon fluid due to diffusion of photons inevitably creates spectral distortions in the cosmic microwave background (CMB). ...With the proposed CMB experiment PIXIE it might become possible to measure these distortions and thereby constrain the primordial power spectrum at comoving wavenumbers 50 ≲ k ≲ 104 Mpc−1. Since primordial fluctuations in the CMB on these scales are completely erased by Silk damping, these distortions may provide the only way to shed light on otherwise unobservable aspects of inflationary physics. A consistent treatment of the primordial dissipation problem requires going to the second order in perturbation theory, while thermalization of these distortions necessitates the consideration of the second order in Compton scattering energy transfer. Here we give a full 2 × 2 treatment for the creation and evolution of spectral distortions due to the acoustic dissipation process, consistently including the effect of polarization and photon mixing in the free-streaming regime. We show that 1/3 of the total energy (9/4 larger than previous estimates) stored in small-scale temperature perturbations imprints observable spectral distortions, while the remaining 2/3 only raises the average CMB temperature, an effect that is unobservable. At high redshift dissipation is mainly mediated through the quadrupole anisotropies, while after recombination peculiar motions are most important. During recombination the damping of the higher multipoles is also significant. We compute the average distortion for several examples using CosmoTherm, analysing their dependence on parameters of the primordial power spectrum. For one of the best-fitting 7-year Wilkinson Microwave Anisotropy Probe cosmologies, with n
S = 1.027 and n
run = −0.034, the cooling of baryonic matter practically compensates the heating from acoustic dissipation in the μ-era. We also derive the evolution equations for anisotropic spectral distortions in the first order perturbation theory. We furthermore argue that the first order anisotropies of spectral distortions may dominate over the corresponding second order contributions from recombination if an average fractional distortion ≃10−5 is already present before recombination.
ABSTRACT
Correlations between cosmic microwave background (CMB) temperature, polarization, and spectral distortion anisotropies can be used as a probe of primordial non-Gaussianity. Here, we perform ...a reconstruction of μ-distortion anisotropies in the presence of Galactic and extragalactic foregrounds, applying the so-called Constrained ILC component separation method to simulations of proposed CMB space missions (PIXIE, LiteBIRD, CORE, and PICO). Our sky simulations include Galactic dust, Galactic synchrotron, Galactic free–free, thermal Sunyaev–Zeldovich effect, as well as primary CMB temperature and μ-distortion anisotropies, the latter being added as correlated field. The Constrained ILC method allows us to null the CMB temperature anisotropies in the reconstructed μ-map (and vice versa), in addition to mitigating the contaminations from astrophysical foregrounds and instrumental noise. We compute the cross-power spectrum between the reconstructed (CMB-free) μ-distortion map and the (μ-free) CMB temperature map, after foreground removal and component separations. Since the cross-power spectrum is proportional to the primordial non-Gaussianity parameter, fNL, on scales $k\simeq 740\,\rm Mpc^{-1}$, this allows us to derive fNL-detection limits for the aforementioned future CMB experiments. Our analysis shows that foregrounds degrade the theoretical detection limits (based mostly on instrumental noise) by more than one order of magnitude, with PICO standing the best chance at placing upper limits on scale-dependent non-Gaussianity. We also discuss the dependence of the constraints on the channel sensitivities and chosen bands. Like for B-mode polarization measurements, extended coverage at frequencies ν ≲ 40 GHz and ν ≳ 400 GHz provides more leverage than increased channel sensitivity.
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