Resolving Hubble Tension by Self-Interacting Neutrinos with Dirac Seesaw

Abstract

Self-interacting neutrinos that begin to free-stream at close to matter-radiation equality can reduce the physical size of photon sound horizon at last scattering surface. This mechanism can be the reason why standard $\Lambda$CDM cosmology sees a lower value of the Hubble constant than local measurements from distance ladder. We propose a new realization of self-interacting Dirac neutrinos (SID$\nu$) with light-dark-photon mediator for a viable interaction mechanism. Our model is UV completed by a Dirac seesaw with anomaly-free dark $U(1)_X^{}$ gauge group which charges the right-handed neutrinos. This model naturally generates small masses for Dirac neutrinos and induces self-scattering of right-handed neutrinos. The scattering with left-handed neutrinos is suppressed by a chirality-flip mass insertion when the neutrino energy is much larger than its mass. The resultant neutrino self-scattering is not operative for $E_{\nu}\gtrsim O(\text{keV})$, which avoids the cosmological and laboratory constraints. By evolving Boltzmann equations for left- and right-handed neutrino number densities, we show that about $2/3$ of the left-handed neutrinos are converted into right-handed neutrinos in a short epoch between the Big-Bang Nucleosynthesis and the recombination, and interact with each other efficiently afterwards. The resultant neutrino non-free-streaming is the crucial ingredient to shrink down the comoving sound horizon at drag epoch, which can reconcile the Hubble tension between early and late time measurements.