Long-lived inert Higgs boson in a fast expanding universe and its imprint on the cosmic microwave background

Abstract

The presence of any extra radiation energy density at the time of cosmic microwave background formation can significantly impact the measurement of the effective relativistic neutrino degrees of freedom or $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\mathrm{eff}}$, which is very precisely measured by the Planck Collaboration. Here, we propose a scenario where a long-lived inert scalar, which is very weakly coupled to the dark sector, decays to a fermion dark matter via a ``freeze-in'' mechanism plus standard model neutrinos at very low temperature $(T<{T}_{\mathrm{BBN}})$. We explore this model in the fast expanding Universe, where it is assumed that the early epoch $(T>{T}_{\mathrm{BBN}})$ of the Universe is dominated by a nonstandard species $\mathrm{\ensuremath{\Phi}}$ instead of the standard radiation. In this nonstandard cosmological picture, such late-time decay of the inert scalar can inject some entropy to the neutrino sector after it decouples from the thermal bath and this will make substantial contribution to $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\mathrm{eff}}$. Additionally, in this scenario, the new contribution to $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\mathrm{eff}}$ is highly correlated with the dark matter sector. Thus, one can explore such feebly interacting dark matter particles by the precise measurement of $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\mathrm{eff}}$ using the current (Planck 2018) and forthcoming (CMB-S4 and SPT3G) experiments.