An entirely analytical cosmological model

TL;DR

This paper presents an analytical cosmological model with an affine equation of state, providing explicit formulas for key cosmological parameters and density contrast, useful for testing numerical methods and educational purposes.

Contribution

It introduces an analytical approach to a cosmological model with an affine equation of state, including explicit expressions for density contrast and power spectrum.

Findings

Reproduces features observed in previous numerical studies

Provides explicit formulas for density contrast and power spectrum

Useful for testing numerical codes and pedagogical purposes

Abstract

The purpose of the present study is to show that in a particular cosmological model, with an affine equation of state, one can obtain, besides the background given by the scale factor, Hubble and deceleration parameters, a representation in terms of scalar fields and, more important, explicit mathematical expressions for the density contrast and the power spectrum. Although the model so obtained is not realistic, it reproduces features observed in some previous numerical studies and, therefore, it may be useful in the testing of numerical codes and as a pedagogical tool.