Thermodynamics and Bouncing Cosmology in Rastall-like Gravity

TL;DR

This work develops a Lagrangian-based Rastall-like gravity in which the stress-energy tensor is not covariantly conserved, enabling curvature-driven particle production within an irreversible thermodynamics framework. By deriving modified field equations and applying them to flat LFRW cosmologies, the authors show how a non-singular bouncing universe can arise, contingent on NEC/SEC violation near the bounce and a stability analysis based on the adiabatic sound speed. A concrete bouncing ansatz for the scale factor demonstrates how the Hubble parameter transitions through the bounce while curvature remains finite; particle production peaks at the bounce and entropy production can vanish in certain limits. The results suggest a coherent phenomenological path for curvature-matter coupling and non-standard cosmological evolution, laying groundwork for future observational tests and connections to quantum gravity.

Abstract

In this study, we explore the thermodynamic aspects of a modified version of Rastall's gravity theory and its implications for cosmological scenarios. We analyze the role of non-conserved energy-momentum tensor equations and investigate their influence on particle production within an irreversible thermodynamic framework. By introducing a novel Lagrangian, we derive modified field equations and establish their relationship with matter production, both with and without entropy generation. Our analysis focuses on ideal fluid models and extends to spatially flat LFRW cosmologies, providing key equations that govern energy density, pressure, and curvature dynamics. Furthermore, we propose a bouncing cosmological model, in which the universe undergoes cycles of contraction and expansion, avoiding the singularity associated with the Big Bang. Our results indicate that this bouncing scenario is feasible within the Rastall-like gravity framework, supported by particle production processes and stability conditions. The violation of energy conditions near the bounce point further confirms the consistency of this alternative cosmological model. The present work is focused on the theoretical foundations and internal consistency of the model; possible observational implications will be addressed in future investigations. We conclude that the proposed theory offers a coherent phenomenological approach to matter production and provides new insights into non-standard cosmological evolution.

Figures (5)

• Figure 1: Behavior of the scale factor, Hubble parameter, deceleration parameter, and Ricci scalar curvature as functions of cosmic time. The blue curve corresponds to $n = 2$, the orange curve to $n = 3$, and the green curve to $n = 4$.
• Figure 2: The behavior of the equation-of-state parameter $w$ as a function of cosmic time for the cases $\beta=0$ and $\beta\neq 0$. In the figure, the blue curve corresponds to $n = 2$ and the orange curve to $n = 3$
• Figure 3: Evolution of the energy conditions as functions of cosmic time for the case $w = -1$. The blue curve represents $n = 2$, while the orange curve corresponds to $n = 3$. The model exhibits a violation of the NEC and SEC at the bouncing point, a fundamental requirement to avoid gravitational collapse and enable the transition. The validity of the DEC ensures the energy density dominates over pressure, preserving the physical consistency of the cosmological framework.
• Figure 4: Cosmic time evolution of the sound velocity for increasing values of $n$ ($n = 1$ to $5$), represented by curves ranging from red to green.
• Figure 5: Evolution of the sound velocity as a function of cosmic time for $n = 1$ to $5$, represented by curves ranging from red to green.