CMB at 2 × 2 order: the dissipation of primordial acoustic waves and the observable part of the associated energy release

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 nS = 1.027 and nrun = −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.

Prospects for measuring cosmic microwave background spectral distortions in the presence of foregrounds

“…This is a conservative estimate as with increased AGN feedback larger values for y could be feasible (De Zotti et al 2016). Note that the actual monopole y value measured by PIXIE or other experiments will also contain a primordial contribution in general, but this is expected to be 2-3 orders of magnitude smaller than the structure formation contributions (Chluba et al 2012b). We furthermore assume that the average y-distortion caused by the CMB temperature dipole, y sup = (2.525 ± 0.012) × 10 −7 (Chluba & Sunyaev 2004;Chluba 2016), is subtracted.…”

“…A negative µ distortion is also generated by the Compton-cooling of CMB photons off the adiabatically evolving electrons (Chluba 2005;Chluba & Sunyaev 2012). Here, we assume only the "vanilla" sources exist in our Universe, in particular the µ signals from acoustic damping and adiabatic cooling (Chluba et al 2012b;Chluba 2016). The latter signal is expected to be roughly one order of magnitude smaller than the former.…”

“…The latter are particularly important at z 2 × 10 6 , leading to a strong suppression of the distortion amplitude (e.g., Hu & Silk 1993a). Expected sources of µ-distortions include the Silk damping of smallscale acoustic modes in the early Universe (Sunyaev & Zeldovich 1970a;Daly 1991;Hu et al 1994a;Chluba et al 2012b) and the extraction of energy from the photon bath due to the adiabatic cooling of ordinary matter (Chluba 2005;Chluba & Sunyaev 2012).…”

Constraining the primordial power spectrum from SNIa lensing dispersion

“…Other methods of probing the primordial spectrum include methods such as Ly α [17], the absence of primordial black holes and Ultracompact Minihalos [19][20][21], measuring spectral distortions of the CMB blackbody spectrum [22][23][24], galaxy weak lensing [25], galaxy correlation functions [26] and cluster number counts [27]. All of which have either different systematics, different k range sensitivity, based on future data or some combination of the above.…”

Cosmological constraints fromμEcross correlations

“…On the other hand, there is an essential difficulty for the further improvement of the observable ranges in the CMB anisotropy experiments since Silk damping erases fluctuations on angular scales smaller than Op1˝q. In this sense, the CMB spectral deformation induced by Silk damping can be a complementary approach to the small scale physics [4][5][6][7][8][9][10][11][12][13][14]. This is because such distortions are sourced from second order effects of temperature perturbations which dissipated due to Silk damping.…”