Exact analytical framework connecting causal viscous inflation to standard late-time acceleration via smooth epoch transitions
Phys. Rev. D 114, 063553 – Published 29 September, 2026
DOI: https://doi.org/10.1103/47b2-8mpw
Abstract
We derive an exact analytical cosmological framework in which a single continuous solution for the Hubble parameter connects inflation, radiation domination, matter domination, and late-time acceleration through smooth transitions. The background is described by a causal Israel-Stewart fluid with an evolving barotropic equation of state and a cosmological constant. In the early Universe, this viscous fluid is reconstructed as an interacting dissipative scalar-field sector and radiation bath, coupled through the bulk viscous pressure and regulated by a dynamical transfer function. In this composite picture, inflation begins in a scalar sector–dominated quasi–de Sitter phase with a constant roll–like Hubble flow hierarchy and later enters a particle creation–driven accelerated stage as the energy transfer to radiation becomes efficient. In representative solutions, radiation becomes energetically dominant while the Universe is still accelerating, before the viscous source rapidly decays and the standard decelerating radiation era is established. The thermal evolution of the radiation bath is nonmonotonic: it is initially sub-Hubble but heating later becomes thermally active during accelerated expansion, passes through a quasi-isothermal stage, and finally approaches adiabatic cooling. After dissipation fades, the residual scalar sector redshifts as effective dark radiation. In the postinflationary regime, the unified fluid is reconstructed as a conglomerate of baryons, dark matter, standard radiation, and this relativistic remnant. Its evolving adiabatic equation of state allows the late-time dynamics to be reformulated as an effective interaction between dark matter and dark radiation, producing a mild energy transfer near matter-radiation equality. The model recovers asymptotic behavior at late times under a noninteracting limit, while controlled prerecombination deviations admit a background-feasible parameter space within which the framework offers a modest upward shift in the sound horizon–based estimate, relevant to alleviating the Hubble tension.
