Exploring compensated isocurvature perturbations with CMB spectral distortion anisotropies

TL;DR

This paper proposes a new method using CMB spectral distortion anisotropies to detect and constrain compensated isocurvature perturbations, offering a lensing-free approach that improves sensitivity over previous techniques.

Contribution

It introduces a linear perturbation theory for CMB $y$-distortions related to CIPs, enabling more precise constraints through anisotropy measurements.

Findings

Y-distortion anisotropies can resolve degeneracies between baryon and dark matter isocurvature modes.

Future surveys like LiteBIRD and CVL can significantly tighten constraints on CIP parameters.

The method is robust against lensing contamination affecting previous approaches.

Abstract

We develop a linear perturbation theory for the spectral $y$-distortions of the cosmic microwave background (CMB). The $y$-distortions generated during the recombination epoch are usually negligible because the energy transfer due to the Compton scattering is strongly suppressed at that time, but they can be significant if there is a considerable amount of compensated isocurvature perturbation (CIP), which is not tightly constrained from the present CMB observations. The linear $y$-distortions explicitly depend on the baryon density fluctuations, therefore $y$ anisotropies can completely resolve the degeneracy between the baryon isocurvature perturbations and the cold dark matter ones. This novel method is free from lensing contaminations that can affect the previous approach to the CIPs based on the nonlinear modulation of the CMB anisotropies. We compute the cross correlation functions of the $y$-distortions with the CMB temperature and the $E$ mode polarization anisotropies. They are sensitive to the correlated CIPs parameterized by $f'\equiv\mathcal P_{\rm CIP\zeta}/\mathcal P_{\zeta \zeta}$ with $\mathcal P_{\zeta \zeta}$ and $\mathcal P_{\rm CIP\zeta}$ being the auto correlation of the adiabatic perturbations and the cross correlation between them and the CIPs. We investigate how well the $y$ anisotropies will constrain $f'$ in future observations such as those provided by a PIXIE-like and a PRISM-like survey, LiteBIRD and a cosmic variance limited (CVL) survey, taking into account the degradation in constraining power due to the presence of Sunyaev Zel'dovich effect from galaxy clusters. For example, our forecasts show that it is possible to achieve an upper limit of $f'< 2 \times 10^{5}$ at 68% C.L. with LiteBIRD, and $f'<2\times 10^{4}$ with CVL observations.