Cosmic Hysteresis in Reconstructed $f(R)$ Bounce Models: A Thermodynamic Study

TL;DR

This paper investigates cosmic hysteresis in cyclic bouncing universes within reconstructed $f(R)$ gravity, revealing asymmetric pressure evolution and thermodynamic irreversibility that support the arrow of time.

Contribution

It reconstructs specific $f(R)$ models from exact bouncing solutions and analyzes thermodynamic behavior, highlighting the natural emergence of irreversibility in modified gravity.

Findings

Asymmetric pressure leads to non-zero work integral per cycle

Hysteresis loops in equation-of-state space are identified

Reconstructed $f(R)$ models support irreversible cyclic evolution

Abstract

We study the emergence of cosmic hysteresis in cyclic bouncing universes within the framework of analytically reconstructed $f(R)$ gravity. Using exact bouncing scale factor solutions of exponential and power-law forms, we reconstruct the corresponding $f(R)$ models and investigate the thermodynamic behavior of a minimally coupled scalar field in these geometries. The pressure evolution during expansion and contraction phases is shown to be asymmetric, leading to a non-vanishing thermodynamic work integral over each cycle, defined by $\oint p_\phi\, dV$. We identify closed hysteresis loops in the equation-of-state space and quantify the net energy transfer per cycle. Our results reveal that such reconstructed $f(R)$ models generically support irreversible evolution, demonstrating a natural emergence of the thermodynamic arrow of time. These findings provide new insight into the dissipative features of modified gravity and the long-term dynamics of cyclic cosmological scenarios.