CMB signatures of gravity-mediated dark radiation in $\mathbf{\Delta N_{\rm eff}}$

Abstract

Measurement of $N_{\rm eff}$ in the CMB (Cosmic Microwave Background) observations, like Planck 2018 and BBN (Big Bang Nucleosynthesis) has already set stringent constraints on the interaction strength of light particles beyond the Standard Model (BSM). Despite such negligible couplings of such BSM particles to the visible sector, they are inevitably produced in the early universe through gravity-mediated processes. If a sizable density of light particles survives around CMB formation, they may act as dark radiation (DR) contributing to $N_{\rm eff}$ at CMB epoch. In this work, we study the production of such light BSM particles through the gravity-mediated scatterings in an effective field theory (EFT) setup assuming that all non-gravitational couplings of the BSM particle are negligible. Since the production is sensitive to the spin of the produced particle, we perform a concrete analysis for two representative cases: scalar dark Higgs DR and vector dark photons DR.Using the Planck 2018 observations, we find constraints on the reheating temperature ($T_{\rm RH}$) and background equation of state ($w_\Phi$) during reheating in such scenarios featuring dark Higgs and dark photon. A comparative discussion involving gravity-mediated production of Dirac right-handed neutrinos ($\nu_R$) and light axion-like particles (ALP) is also presented. Finally, for completeness, we also analyze the scenario where the production occurs through a generic spin-2 mediator characterized by an effective scale $\Lambda$ delineating the parameter space that is currently ruled out from Planck-2018 and can be probed by the future CMB experiments like LiteBird, Simon Observatory, CMB-S4, CMB-HD.