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We consider the effect on early Universe cosmology of the dark photonassociated with the gauging of $U(1)_{T3R}$, a symmetry group under which onlyright-handed Standard Model fermions transform non-trivially. We find thatcosmological constraints on this scenario are qualitatively much more severethan on other well-studied cases of a new $U(1)$ gauge group, because the darkphoton couples to chiral fermions. In particular, the dark photon of$U(1)_{T3R}$ is always produced and equilibrates in the early Universe, nomatter how small the gauge coupling, unless the symmetry-breaking scale isextremely large. This occurs because, no matter how the weak the coupling, theGoldstone mode (equivalently, the longitudinal polarization) does not decouple.As a result, even the limit of an extremely light and weakly-coupled darkphoton of $U(1)_{T3R}$ is effectively ruled out by cosmological constraints,unless the symmetry-breaking scale is extremely large. We also discuss thepossibility of ameliorating Hubble tension in this model.

Contributions to $\Delta N_{eff}$ from the dark photon of $U(1)_{T3R}$