Encoding the scaling of the cosmological variables with the Euler Beta function

TL;DR

This paper explores how the Euler Beta function relates cosmological variables' scaling exponents in flat isotropic models, revealing dual scenarios and reproducing holographic bounds.

Contribution

It introduces a novel application of the Euler Beta function to connect cosmological parameters and scaling exponents, highlighting dualities and holographic bounds.

Findings

Reproduces the Fischler-Susskind holographic bound.

Identifies dual cosmological scenarios via Beta function properties.

Establishes a relationship between space dimension, fluid equation of state, and scaling exponents.

Abstract

We study the scaling exponents for the expanding isotropic flat cosmological models. The dimension of space, the equation of state of the cosmic fluid and the scaling exponent for a physical variable are related by the Euler Beta function that controls the singular behavior of the global integrals. We encounter dual cosmological scenarios using the properties of the Beta function. For the entropy density integral we reproduce the Fischler-Susskind holographic bound.