Abstract
The lack of information before Big Bang Neucleosynthesis (BBN) allow us to assume the
presence of a new species ϕ whose energy density redshifts as a-4+n where n > 0 and a is the scale factor. This non-standard cosmological setup facilitates a larger portal
coupling (
) between the dark and the visible sectors even when the two sectors are not
in thermal equilibrium. Here, we have considered U(1)Lμ-Lτ ⊗ U(1)X gauge
extension of the Standard Model (SM) and studied different phases of the cosmological evolution of
a thermally decoupled dark sector such as leak-in, freeze-in, reannihilation, and late-time
annihilation in the presence of fast expansion. Due to the tree level kinetic mixing between
U(1)X and U(1)Lμ-Lτ gauge bosons, the dark sector couples with the μ and τ
flavored leptons of the SM. We show that in our scenario it is possible to reconcile the dark
matter relic density and muon (g-2) anomaly. In particular, we show that for 2 × 10-4 ≲ ≲ 10-3, 5.5 MeV ≲ mZ' ≲ 200
MeV, n = 4, and 1 TeV ≲ mχ ≲ 10 TeV relic density constraint
of dark matter, constraint from muon (g-2) anomaly, and other cosmological, astrophysical
constraints are satisfied.