Ultralight dark photon as a model for early universe dark matter

Dark photon is a massive vector field which interacts only with the physical photon through the kinetic mixing. This coupling is assumed to be weak so that the dark photon becomes almost unobservable in processes with elementary particles, but can serve as a dark matter particle. We argue that in very early Universe ($z>3000$) this vector field may have the equation of state of radiation ($w=1\mathrm{/}3$) but later behaves as cold dark matter ($w=0$). This may slightly change the expansion rate of the Universe at early time and reduce the value of the sound horizon of baryon acoustic oscillations (standard ruler). As a result, in this model the value of the Hubble constant appears to be larger than that in the standard $\mathrm{\Lambda }$CDM model. In particular, it is sufficient to have the dark photon mass of order $m\sim {10}^{-27}-{10}^{-25}$ eV to fit the value of the Hubble constant to $H_0=73$ km$\cdot$s${}^{-1}$Mpc${}^{-1}$ thus resolving the Hubble tension.