Thermodynamic constraints and future singularities in Unimodular Gravity driven by phantom and non-phantom fluids

TL;DR

This paper explores how thermodynamic constraints and energy diffusion in unimodular gravity influence the occurrence of future singularities like Big Rip and Big Crunch, revealing new mechanisms absent in standard General Relativity.

Contribution

It introduces a model where diffusion induces phantom behavior and singularities in unimodular gravity, expanding understanding of future cosmological singularities under thermodynamic constraints.

Findings

Big Rip singularities are excluded for non-phantom fluids with positive cosmological constant.

Diffusion can induce phantom regimes even with non-phantom fluids.

Explicit realization of Big Rip in unimodular gravity with negative cosmological constant.

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 $Q(t)$ 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. This requirement leads to non-trivial constraints on the model parameters, with direct implications for the admissible singularity structure. 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, as well as Big Crunch solutions for negative cosmological constant. More importantly, we show that diffusion can induce an effective phantom regime even when the fundamental fluid is non-phantom. In particular, for a negative cosmological constant, we present an explicit realization of a Big Rip singularity in unimodular gravity driven by diffusion, while consistently preserving a non-phantom equation of state and positive entropy production. These results reveal a novel mechanism for the emergence of future singularities, with no direct analogue in standard General Relativity.