Probing the dynamical system and thermal behaviours of the model, $\Lambda_0+3 \beta H^2.$

TL;DR

This paper investigates a cosmological model with a decaying vacuum energy, analyzing its thermal and dynamical properties, and comparing its predictions with supernovae data to understand its evolution and stability.

Contribution

It introduces a specific decaying vacuum model and analyzes its thermal behavior and phase-space stability, providing new insights into its cosmological evolution.

Findings

Model fits supernovae data with specific parameter values.

The thermal evolution obeys the generalized second law of entropy.

The dynamical analysis shows a transition from deceleration to acceleration, with a stable late-time attractor.

Abstract

In this work we study the cosmological evolution of a two component model with non-relativistic dark matter and decaying vacuum of the form $\Lambda = \Lambda_0 + 3 \beta H^2.$ We contrast the model the model with the supernovae data and found that the model parameter $\beta=-0.010$ when the interaction parameter is zero and is $\beta=-0.002$ when $b=0.001.$ The thermal evolution study of the model indicates that it obeys the generalized second of entropy and also satisfies the convexity condition, $\ddot S <0$ so that the model behaves like an ordinary macroscopic system which approaching a stable equilibrium thermal state is the asymptotic condition. The dynamical system analysis reveals that, the model posses a prior decelerated epoch represented by a saddle critical point and the late critical point represents an accelerating epoch which posses a convergence of phase-space trajectories form both the regions of the point hence can be considered as stable.