Constraints on $\gamma$-CDM interactions matching the Planck data precision

TL;DR

This paper derives precise constraints on dark matter-photon interactions using Planck CMB data, incorporating new formalism and approximations, and finds tighter bounds than previous studies, impacting dark matter models.

Contribution

It presents the first detailed formalism for dark matter-photon scattering constraints from CMB data, including modifications to Boltzmann equations and the tight coupling approximation.

Findings

Most stringent constraint on dark matter-photon cross section to date.

Negligible effect of dark matter sound speed on CMB spectra.

Constraint tightens by approximately 35% with full Planck dataset.

Abstract

The Planck experiment has measured the Cosmic Microwave Background (CMB) angular spectrum with unprecedented accuracy, and these results are likely to remain the state-of-the art for a decade or more. Since these measurements are going to be used to forecast Euclid's ability to test alternative dark matter models, we aim to set the final CMB constraint on the cross section of dark matter-photon scattering in the early universe. As the formalism has not been published in the literature yet, we present the key steps to derive the full set of linearized Einstein and Boltzmann equations and elucidate necessary modifications to the line of sight and the tight coupling approximation. These approximation schemes are commonly used in Boltzmann codes to reduce computational costs, but the tight coupling regime has been neglected in previous works related to dark matter-photon interactions. Our computations account for a dark matter sound speed, which was neglected in previous work. We find that its effect is negligible on the CMB spectra but fairly important on the linear matter power spectrum. We then analyze the Planck data, with and without the 2015 polarization data at high multipoles. In both cases our constraint on the ratio of the elastic scattering cross section to the dark matter mass becomes more stringent with respect to previous constraints. The change is about 35\% when the full Planck dataset is added (which includes E-mode polarization at high multipoles and the lensing potential power spectrum) and about 20\%. when we only account for the polarization data at low multipoles and the full temperature spectrum. Our most conservative limit reads as $\sigma_{\mathrm{DM}-\gamma} \leq 2.25\times 10^{-6}\,\sigma_\mathrm{Th}\left(m_\mathrm{DM}/\mathrm{GeV}\right)$ at 95\% confidence. We do not expect this limit to change by adding the recently published SPT data.