Cosmological Constraints on Very Dark Photons

TL;DR

We address cosmological constraints on very dark photons with mass m_V in the MeV–GeV range and an effective coupling alpha_eff = alpha * kappa^2. The authors compute the freeze-in abundance dominated by inverse leptonic decays, giving Y_V,f^e ~ (9/(4 pi)) * (m_V^3 * Gamma_V_to_ee) / ((H s)_{T=m_V}) with Gamma_V_to_ee ~ alpha_eff * m_V / 3, plus a resonant contribution Delta Y_f_r ~ 0.17 * (m_V^3 * Gamma_V_to_ee) / ((H s)_{T=m_V}); hadronic production is modeled separately. Late decays inject electromagnetic energy after BBN and during recombination, enabling BBN and CMB constraints mapped through the deposition efficiency f_eff, yielding sensitivity to alpha_eff ~ 1e-37–1e-38 and excluding large regions of the (m_V, kappa) plane. The work shows that cosmological data probe ultra-weak couplings far beyond terrestrial sensitivity and provides a framework to extend to other portals or heavier mass scales.

Abstract

We explore the cosmological consequences of kinetically mixed dark photons with a mass between 1 MeV and 10 GeV, and an effective electromagnetic fine structure constant as small as $10^{-38}$. We calculate the freeze-in abundance of these dark photons in the early Universe and explore the impact of late decays on BBN and the CMB. This leads to new constraints on the parameter space of mass $m_V$ vs kinetic mixing parameter $κ$.

Figures (11)

• Figure 1: An overview of the constraints on the plane of vector mass versus kinetic mixing, showing the regions excluded due to their impact on BBN and the CMB anisotropies, in addition to various terrestrial limits Essig:2013lkasnowmassrefs, including the more recent limits recentlimits. These excluded regions are shown in more detail in later sections.
• Figure 2: Illustration of the coalescence production of the dark photon $V$ via an off-shell photon.
• Figure 3: Total energy stored per baryons for $\alpha_{\rm eff} = 10^{-35}$ (upper) and $\Gamma_V^{-1} = 10^{14}$s (lower) from the various production channels as labeled.
• Figure 4: Effects on BBN from the decay of relic dark photons as a function vector mass of $m_V$ and kinetic mixing parameter $\kappa$. The diagonal gray lines are contours of lifetime $\tau_V$ (solid) and abundance per baryon $n_V/n_b$ prior to decay (dotted). Shaded regions are excluded as they are in conflict with primordially inferred light element abundances. The solid (orange) closed line is a potential $2\sigma$ constraint from underproduction of D/H derived from (\ref{['eq:cooke']}). The dashed black lines are contours of decreasing ${}^7\mathrm{Li}/\mathrm{H}$ abundance, $4\times 10^{-10}$ and $3\times 10^{-10}$, going from the outside to the inside, respectively. The dotted line shows ${}^6\mathrm{Li}/\mathrm{H} = 10^{-12}$ which corresponds to an extra production by about two orders magnitude but without being in conflict with observations.
• Figure 5: CMB constraints on the energy injection parameters $\zeta$ and $\Gamma$. For comparison, we include the WMAP3 curve and the Planck forecast (2007) from Ref. Zhang:2007zzh.