  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.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology