Holographic Principle and the Second Law in Stephani Cosmology Revisited

Abstract

We show in a model-independent way that the inhomogeneous cosmological class II Stephani model fulfills both the the cosmological holographic principle, and that the entropy is increasing with time. By this we mean the result does not depend on any assumption on the time evolution of the scale factor, or on the matter content of the Universe, we also do not need to use the numerical values of the cosmological parameters, which are inferred in the framework of the usual homogeneous Friedmann model. Therefore our analysis is not affected by the tension of the current estimates of the Hubble parameter, and does not rely on any model-dependent assumption of the entropy amount at the present epoch. Our analysis allows us to set an upper limit for the inhomogeneity parameter of the model, an upper bound for the size that this type of universe can reach during the time evolution, a lower bound for the entropy abundance, and an estimate of the present day value of the deceleration parameter.