# Holographic Principle and the Second Law in Stephani Cosmology Revisited

## TL;DR

This paper demonstrates that the Stephani cosmological model inherently satisfies the holographic principle and exhibits increasing entropy over time, independent of specific assumptions about the universe's matter content or scale factor evolution.

## Contribution

It provides a model-independent analysis confirming the holographic principle and entropy increase in Stephani cosmology, setting bounds on inhomogeneity and universe size.

## Key findings

- Fulfillment of holographic principle in Stephani models
- Entropy increases with cosmic time in this framework
- Constraints on inhomogeneity and universe size

## 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.