Inhomogeneous Equation of State of the Universe: Phantom Era, Future Singularity and Crossing the Phantom Barrier

TL;DR

This work investigates FRW cosmologies where the dark energy equation of state includes an inhomogeneous term dependent on the Hubble rate, motivated by time-dependent bulk viscosity and modified gravity. By analyzing a single inhomogeneous EOS $p=-\rho + f(\rho) + G(H)$ and extensions to two interacting fluids, the authors derive how $G(H)$ relates to $f(\rho)$ via energy conservation and produce explicit solutions showing crossing of the phantom barrier at $w=-1$ and modifications to future singularities. They present solvable examples and implicit/oscillatory EOS scenarios that realize phantom crossing, including cases where the inhomogeneous term effectively absorbs fluid couplings; they also discuss thermodynamic implications using BNOV-type models where the entropy remains positive across crossing. The results extend the space of viable late-time cosmologies, connect to modified gravity and brane-world ideas, and offer concrete predictions for how inhomogeneous EOS terms could influence the evolution of dark energy in a testable way.

Abstract

The dark energy universe equation of state (EOS) with inhomogeneous,Hubble parameter dependent term is considered. The motivation to introduce such a term comes from time-dependent viscosity considerations and modifications of general relativity. For several explicit examples of such EOS it is demonstrated how the type of future singularity changes, how the phantom epoch emerges and how crossing of phantom barrier occurs. Similar cosmological regimes are considered for the universe with two interacting fluids and for universe with implicit EOS. For instance, the crossing of phantom barrier is realized in easier way, thanks to the presence of inhomogeneous term. The thermodynamical dark energy model is presented where the universe entropy may be positive even at phantom era as a result of crossing of w=-1 barrier.