Probing the dynamical system and thermal behaviors of the model, Λ 0 + 3 β H 2 $\varLambda _{0}+3 \beta H^{2}$

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 $\varLambda = \varLambda _{0} + 3 \beta H^{2}$ . We contrast the model with the supernovae data and found that the model parameter $\beta =-0.010$ when the interaction parameter, $b=0$ 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 at asymptotic conditions. 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 from both the regions of the point hence can be considered as stable.