In this paper, we explore in detail the cosmological implications of an abelian L µ − L τ gauge extension of the Standard Model featuring a light and weakly coupled Z . Such a scenario is motivated by the longstanding ∼ 4σ discrepancy between the measured and predicted values of the muon's anomalous magnetic moment, (g − 2) µ , as well as the tension between late and early time determinations of the Hubble constant. If sufficiently light, the Z population will decay to neutrinos, increasing the overall energy density of radiation and altering the expansion history of the early universe. We identify two distinct regions of parameter space in this model in which the Hubble tension can be significantly relaxed. The first of these is the previously identified region in which a ∼ 10 − 20 MeV Z reaches equilibrium in the early universe and then decays, heating the neutrino population and delaying the process of neutrino decoupling. For a coupling of g µ−τ (3 − 8) × 10 −4 , such a particle can also explain the observed (g − 2) µ anomaly. In the second region, the Z is very light (m Z ∼ 1 eV to MeV) and very weakly coupled (g µ−τ ∼ 10 −13 to 10 −9 ). In this case, the Z population is produced through freeze-in, and decays to neutrinos after neutrino decoupling. Across large regions of parameter space, we predict a contribution to the energy density of radiation that can appreciably relax the reported Hubble tension, ∆N eff 0.2.

Precision measurements of the number of effective relativistic neutrino species and the primordial element abundances require accurate theoretical predictions for early Universe observables in the Standard Model and beyond. Given the complexity of accurately modelling the thermal history of the early Universe; in this work, we extend a previous method presented by the author in [1] to obtain simple, fast and accurate early Universe thermodynamics. The method is based upon the approximation that all relevant species can be described by thermal equilibrium distribution functions characterized by a temperature and a chemical potential. We apply the method to neutrino decoupling in the Standard Model and find N SM eff = 3.045 -a result in excellent agreement with previous state-of-the-art calculations. We apply the method to study the thermal history of the Universe in the presence of a very light (1 eV < m φ < 1 MeV) and weakly coupled (λ 10 −9 ) neutrinophilic scalar. We find our results to be in excellent agreement with the solution to the exact Liouville equation. Finally, we release a code: NUDEC BSM (available in both Mathematica and Python formats), with which neutrino decoupling can be accurately and efficiently solved in the Standard Model and beyond: https://github.com/MiguelEA/nudec_BSM.

The number of effective relativistic neutrino species represents a fundamental probe of the thermal history of the early Universe, and as such of the Standard Model of Particle Physics. Traditional approaches to the process of neutrino decoupling are either very technical and computationally expensive, or assume that neutrinos decouple instantaneously. In this work, we aim to fill the gap between these two approaches by modeling neutrino decoupling in terms of two simple coupled differential equations for the electromagnetic and neutrino sector temperatures, in which all the relevant interactions are taken into account and which allows for a straightforward implementation of BSM species. Upon including finite temperature QED corrections we reach an accuracy on N eff in the SM of 0.01. We illustrate the usefulness of this approach to neutrino decoupling by considering, in a model independent manner, the impact of MeV thermal dark matter on N eff . We show that Planck rules out electrophilic and neutrinophilic thermal dark matter particles of m < 3.0 MeV at 95% CL regardless of their spin, and of their annihilation being s-wave or p-wave. We point out that thermal dark matter particles with non-negligible interactions with both electrons and neutrinos are more elusive to CMB observations than purely electrophilic or neutrinophilic ones. In addition, assisted by the accuracy of our approach, we show that CMB Stage-IV experiments will generically test thermal dark matter particles with m 15 MeV. We make publicly available the codes developed for this study at https://github.com/MiguelEA/ nudec_BSM.