Extended running vacuum model: cosmological equations and thermodynamical implications

Abstract

In this work, we consider an extension of a Running Vacuum Model (RVM), a particular subclass of dynamical vacuum model based on a renormalisation group equation that establishes the time-dependence of the vacuum energy density as a function of the Hubble parameter H. We aim to inspect the thermodynamical implications of considering a RVM that presumes two different in ation scales. In particular, we want to analyse the behaviour of the entropy of the universe that arises from considering a dynamical vacuum energy density with such particular behaviour. To this end, we introduce the Generalised Second Law (GSL) of Thermodynamics together with the concept of cosmological horizons, emphasising on the apparent horizon. Moreover, we review a deduction of the Einstein field equations and a derivation of the Friedmann equations in arbitrary dimensions, both from thermodynamical principles, following our objectives of maintaining this work as thermodynamically-focused as possible and to wit the possible deep connection between Thermodynamics and General Relativity. Finally, we study the RVM in the early universe and the entropy production within, reviewing recent work on the matter considering a RVM and introducing our extended RVM with two different higher powers of the Hubble parameter H, which poses the possible existence of two different epochs of in ation.