A dynamical systems perspective on the thermodynamics of late-time cosmology

Abstract: A thermodynamic description of cosmological spacetimes may provide insights into the fundamentals of the cosmic evolution that remain otherwise obscure, in close analogy with 'black hole thermodynamics'. We investigate the thermodynamic properties of late-time cosmological evolution using the dynamical systems approach, focusing on the $\Lambda$CDM model and quintessence models with an exponential potential. Thermodynamic quantities obtained through the Hayward-Kodama formalism are mapped onto the phase space of these models, allowing us to investigate thermodynamic stability and phase transitions in a manner independent of the initial condition of the evolution of the universe. In both models, the universe inevitably undergoes a thermodynamic phase transition, marked by diverging specific heats, irrespective of its initial configuration. We further demonstrate that the thermodynamic stability can occur only during an accelerating phase of the universe. However, the necessary stability conditions are never satisfied anywhere in the phase space, rendering both models inherently thermodynamically unstable within the Hayward-Kodama framework. Importantly, our analysis highlights the dynamical system approach as a natural and powerful framework to probe the thermodynamic aspects of cosmological evolution.