Spectro-spatial evolution of the CMB. Part I. Discretisation of the thermalisation Green's function

Abstract

Spectral distortions of the cosmic microwave background (CMB) have been recognized as an important future probe of the early Universe. Existing theoretical studies primarily focused on describing the evolution and creation of average distortions, ignoring spatial perturbations in the plasma. One of the main reasons for this choice is that a treatment of the spectro-spatial evolution of the photon field deep into the primordial Universe requires solving a radiative transfer problem for the distortion signals, which in full detail is computationally challenging. Here we provide the first crucial step towards tackling this problem by formulating a new spectral discretisation of the underlying average thermalisation Green's function. Our approach allows us to convert the high-dimensional partial differential equation system (≃ 103–104 equations) into and set of ordinary differential equations of much lower dimension (≃ 10 equations). We demonstrate the precision of the approach and highlight how it may be further improved in the future. We also clarify the link of the observable spectral distortion parameters (e.g., μ and y) to the computational spectral basis that we use in our frequency discretisation. This reveals how several basis-dependent ambiguities can be interpreted in future CMB analysis. Even if not exact, the new Green's function discretisation can be used to formulate a generalised photon Boltzmann-hierarchy, which can then be solved with methods that are familiar from theoretical studies of the CMB temperature and polarisation anisotropies. We will carry this program out in a series of companion papers, thereby opening the path to full spectro-spatial exploration of the CMB with future CMB imagers and spectrometers.

Spectral distortion signatures of step-like inflationary potential

“…To successfully detect the CMB y-SD, perhaps influenced by inflation, it is not only important to attain high experimental sensitivity, O(10 3 ) the sensitivity for an experiment like PIXIE, but also find the most effective methods for isolating the different SD sources from the observational data. Different efforts have been made to address this problem, such as efforts include describing foreground contributions using a linear perturbation approach [115,116], looking for the cross-correlation between CMB temperature and polarization measurements with the µ-and y-SD [10,115,117], using the Cosmic Infrared Background dipole [111], and employing multi-frequency maps [118].…”

A cosmological tachyon collider: enhancing the long-short scale coupling

“…Correlations between CMB µ distortions and temperature anisotropies are sensitive to the squeezed limit of the bispectrum, so the amplitudes of bispectra with this squeezed behaviour are constrained by µT correlations. The relation between primordial non-Gaussianity and µT correlations was first described in [37], and although more refined and accurate treatments have since been developed, see for example [82][83][84][85][86][87][88][89], we follow closely the approach of [37] to estimate the µT correlation and forecast the constraining power of µT measurements on the amplitude of the squeezed bispectrum. First, let's very briefly review the physics of µ distortions.…”