Dark Photon Oscillations in Our Inhomogeneous Universe

A dark photon kinetically mixing with the ordinary photon represents one of the simplest viable extensions to the standard model, and would induce oscillations with observable imprints on cosmology. Oscillations are resonantly enhanced if the dark photon mass equals the ordinary photon plasma mass, which tracks the free electron number density. Previous studies have assumed a homogeneous Universe; in this Letter, we introduce for the first time an analytic formalism for treating resonant oscillations in the presence of inhomogeneities of the photon plasma mass. We apply our formalism to determine constraints from cosmic microwave background photons oscillating into dark photons, and from heating of the primordial plasma due to dark photon dark matter converting into low-energy photons. Including the effect of inhomogeneities demonstrates that prior homogeneous constraints are not conservative, and simultaneously extends current experimental limits into a vast new parameter space.

Figure 1

(Top) A simulated realization of the plasma mass in a box of comoving thickness 5 Mpc, centered around $z=100$. An example photon path with conversion to a dark photon at the redshift marked “$\times$” is shown. (Middle) A line-of-sight section through the perturbed plasma mass (solid red line), as might be encountered by a traversing CMB photon, compared to the homogeneous plasma mass (dashed red line). For a dark photon mass of $m_{A^{\prime }}=2.73\times {10}^{-13}\mathrm{eV}$, the corresponding homogeneous transition occurs at $z\simeq 100$ where the plasma mass reaches $m_{A^{\prime }}$ (gray line). Multiple level crossings are possible after accounting for perturbations—individual crossings in this realization are shown as the vertical green lines. (Bottom) The corresponding analytical differential conversion probability (blue line) and a histogram of the crossing density corresponding to the specific realization shown (green) [27].

Figure 2

(Top) The photon plasma mass as a function of redshift corresponding to the lowest-frequency FIRAS band (${\nu }_0=2.27{\mathrm{cm}}^{-1}$), which dominates the total conversion probability. The middle 68% and 95% containment of plasma mass fluctuations in the log-normal prescription is shown in dark and light gray, respectively. Horizontal lines correspond to the fiducial mass points $m_{A^{\prime }}=4\times {10}^{-15}$ (red), ${10}^{-13}$ (blue), and ${10}^{-12}\mathrm{eV}$ (green), respectively. (Bottom) The differential resonant transition probability for this frequency as a function of redshift for the fiducial masses, normalized to unity total probability, showing efficient conversion probability over a wide range of redshifts [58].

Figure 3

(Left) The 95% confidence level constraints on the kinetic mixing parameter $\epsilon$ as a function of dark photon mass $m_{A^{\prime }}$, assuming log-normal (red line) or analytic (blue line) PDFs; the shaded region is ruled out by the more conservative of the two PDF choices. We also show the reach of the proposed PIXIE satellite [79] (dot-dashed red line) assuming a log-normal PDF. For comparison we show the previous limit assuming a homogeneous plasma (dotted gray line), a constraint from the magnetic field of Jupiter [80, 84] (shaded brown), and the projected reach of the Dark SRF experiment [30, 31] (dot-dashed orange line), which would be complementary to our cosmological constraints. (Right) Constraints on dark photon dark matter from anomalous heating of the IGM during the epoch of HeII reionization, for the same PDFs. Prior constraints (shaded brown) come from nonresonant heating of the IGM [23] and heating of the gas in the dwarf galaxy Leo T [26]. We also show the projected reach of DM Radio Stage 3 [28, 29, 85] (dot-dashed orange line). Limits from changes to the dark matter density and from IGM heating during the dark ages assuming a homogeneous plasma mass have been derived in Ref. [23] (dotted orange line) [86, 87].