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.
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PRISM (Polarized Radiation Imaging and Spectroscopy Mission) was proposed to ESA in May 2013 as a large-class mission for investigating within the framework of the ESA Cosmic Vision program a set of important scientific questions that require high resolution, high sensitivity, full-sky observations of the sky emission at wavelengths ranging from millimeter-wave to the far-infrared. PRISM's main objective is to explore the distant universe, probing cosmic history from very early times until now as well as the structures, distribution of matter, and velocity flows throughout our Hubble volume. PRISM will survey the full sky in a large number of frequency bands in both intensity and polarization and will measure the absolute spectrum of sky emission more than three orders of magnitude better than COBE FIRAS. The data obtained will allow us to precisely measure the absolute sky brightness and polarization of all the components of the sky emission in the observed frequency range, separating the primordial and extragalactic components cleanly from the galactic and zodiacal light emissions. The aim of this Extended White Paper is to provide a more detailed overview of the highlights of the new science that will be made possible by PRISM, which include: (1) the ultimate galaxy cluster survey using the Sunyaev-Zeldovich (SZ) effect, detecting approximately 106 clusters extending to large redshift, including a characterization of the gas temperature of the brightest ones (through the relativistic corrections to the classic SZ template) as well as a peculiar velocity survey using the kinetic SZ effect that comprises our entire Hubble volume; (2) a detailed characterization of the properties and evolution of dusty galaxies, where the most of the star formation in the universe took place, the faintest population of which constitute the diffuse CIB (Cosmic Infrared Background); (3) a characterization of the B modes from primordial gravity waves generated during inflation and from gravitational lensing, as well as the ultimate search for primordial non-Gaussianity using CMB polarization, which is less contaminated by foregrounds on small scales than the temperature anisotropies; (4) a search for distortions from a perfect blackbody spectrum, which include some nearly certain signals and others that are more speculative but more informative; and (5) a study of the role of the magnetic field in star formation and its interaction with other components of the interstellar medium of our Galaxy. These are but a few of the highlights presented here along with a description of the proposed instrument.
We calculate numerical solutions and analytic approximations for the intermediate-type spectral distortions. Detection of a μ-type distortion (saturated comptonization) in the CMB will constrain the time of energy injection to be at a redshift 2 × 106≳z≳2 × 105, while a detection of a y-type distortion (minimal comptonization) will mean that there was heating of CMB at redshift z≲1.5 × 104. We point out that the partially comptonized spectral distortions, generated in the redshift range 1.5 × 104≲z≲2 × 105, are much richer in information than the pure y and μ-type distortions. The spectrum created during this period is intermediate between y and μ-type distortions and depends sensitively on the redshift of energy injection. These intermediate-type distortions cannot be mimicked by a mixture of y and μ-type distortions at all frequencies and vice versa. The measurement of these intermediate-type CMB spectral distortions has the possibility to constrain precisely not only the amount of energy release in the early Universe but also the mechanism, for example, particle annihilation and Silk damping can be distinguished from particle decay. The intermediate-type distortion templates and software code using these templates to calculate the CMB spectral distortions for user-defined energy injection rate is made publicly available.
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