Dark Photons in the Early Universe: From Thermal Production to Cosmological Constraints

TL;DR

This paper thoroughly analyzes the thermal production of dark photons in the early universe across a wide mass range, deriving cosmological constraints on their properties and interactions.

Contribution

It provides a comprehensive calculation of dark photon production rates, including analytical estimates and numerical verification, and establishes new cosmological bounds on dark photon parameters.

Findings

Analytical estimates of production rates are accurate for dark photons below 1 MeV.

A ratio of approximately 0.14 is derived to compare on- and off-resonance contributions.

Cosmological constraints are most stringent for dark photon masses between 0.1 and 6 MeV.

Abstract

Dark photons, a generic class of light gauge bosons that interact with the Standard Model (SM) exclusively through kinetic mixing, arise naturally in many gauge extensions of the SM. Motivated by these theoretical considerations, we present a comprehensive analysis of their thermal production in the early universe. Our calculation covers a broad range of dark photon masses from 0.1 keV to 100 MeV and include inverse decay, annihilation, and semi-Compton processes. Wherever possible, we present analytical estimates of the production rates and yields, and verify their accuracy numerically. For dark photons lighter than twice the electron masses (around 1 MeV), we find that our analytical estimate of the freeze-in yield based on resonant production is very accurate, implying that off-resonance contributions can be neglected in practice. For heavy dark photons, although this conclusion no longer holds, we derive an interesting ratio, $4\pi e/27\approx0.14$, with $e$ the coupling constant of QED, that can be used to estimate the relative importance of on- and off-resonance contributions. Finally, using the calculated abundance of dark photons in the early universe, we derive cosmological constraints on the dark photon mass and kinetic mixing. Compared with bounds from stellar cooling and supernovae, the cosmological constraints are most stringent in the mass range from 0.1 MeV to 6 MeV, within which kinetic mixing at the level of $10^{-12}\sim10^{-10}$ can be probed.