Cosmological constraints on very dark photons

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 big bang nucleosynthesis and the cosmic microwave background. This leads to new constraints on the parameter space of mass $m_V$ vs kinetic mixing parameter $\kappa$.

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 [1, 8], including the more recent limits [9]. 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 ${\alpha }_{\text{eff}}=10^{-35}$ (upper) and ${\mathrm{\Gamma }}_V^{-1}=10^{14}\mathrm{s}$ (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 $\mathrm{D}/\mathrm{H}$ derived from (17). 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 $\mathrm{\Gamma }$. For comparison, we include the WMAP3 curve and the Planck forecast (2007) from Ref. [21].

Figure 6

Effective deposition efficiency for each decay channel with the sum weighted by the branching ratios for ${\mathrm{\Gamma }}_V^{-1}=10^{14}\mathrm{s}$.

Figure 7

The solid contours bound the regions excluded by the CMB constraints on VDP. Contours of the lifetime in seconds and relative number density of dark photons to baryons prior to their decay are also shown.

Figure 8

Relativistic degrees of freedom as a function of temperature.

Figure 9

The dependence of the resonant temperatures $T_{r,L}$ (black) and $T_{r,T}$ (gray) on frequency $\omega$, all in units of $m_V$. The transverse resonance frequency asymptotes to $T_{\min }=m_V(3/(2\pi \alpha ){)}^{1/2}$.

Figure 10

The average number of particles per $V$ decay with $m_V>2.5\mathrm{GeV}$, from a Pythia simulation. Also shown is the average electromagnetic energy injected after all particles have decayed to electrons and photons ($e^{+}$ are assumed to have annihilated on $e^{-}$.) When including leptonic channels, to a good approximation $1/3$ of the energy is carried away in the form of neutrinos. Resonances like $J/\psi$ are not captured by the resolution of the simulation and we neglect such isolated points in the parameter space.

Figure 11

The adopted effective branching ratios into the various final states that are relevant for BBN considerations. As multi-pion and kaon states become relevant in the kinematically allowed region, we stitch together BaBar measurements of the $e^{\pm }\to {\pi }^{\pm }$ and $e^{\pm }\to K^{\pm }$ cross sections up to $m_V=1.8\mathrm{GeV}$ with our Pythia simulation for $m_V\ge 2.5\mathrm{GeV}$. In this plot, any branching to $K_L$ was neglected. Also shown is the fraction of vector mass that is converted into EM-energy, denoted ${\mathrm{Br}}_{\mathrm{em}}$.