Thermodynamic Constraints and Future Singularities in Unimodular Gravity Driven by Phantom and Non-Phantom Fluids

Abstract

This work investigates future cosmological singularities in a flat FLRW universe filled with a single barotropic fluid, ($p=(\gamma -1)\rho$), within the framework of unimodular gravity. In this setting, the non-conservation of the energy–momentum tensor is encoded through an energy diffusion function $Q$. While a constant diffusion term leads to an effective cosmological constant and preserves adiabatic evolution, a time-dependent $Q\left(t\right)$ induces non-adiabatic dynamics. We consider a power-law Ansatz for $Q$ as a function of the redshift and impose the condition of positive entropy production. In particular, within the thermodynamically allowed sector, we show that Big Rip singularities are excluded for non-phantom fluids when the cosmological constant is positive. For phantom fluids, the model reproduces the expected Big Rip behavior, whereas non-phantom fluids with a negative cosmological constant end in a Big Crunch. Diffusion can induce an effective phantom behavior of the fluid itself, but it is always compensated by the decrease of the effective vacuum energy $\Lambda +Q$, so the total effective equation of state never crosses the phantom divide. Moreover, positive entropy production forces the diffusion term to decrease in time. When it decreases without bound (), the effective vacuum energy becomes negative and the universe recollapses into a Big Crunch even for $\Lambda >0$. All the singularities found are strong according to the Tipler and Królak criteria. We also present a phase-space analysis of the model and discuss its connection with recent cosmological data on dark energy.