Eur. Phys. J. C (2014) 74: 3217
https://doi.org/10.1140/epjc/s10052-014-3217-4

Regular Article - Theoretical Physics

Polytropic equation of state and primordial quantum fluctuations

Departamento de Física, Universidade Federal do Espírito Santo, Av. Fernando Ferrari, 514, Campus de Goiabeiras, Vitória, Espírito Santo, CEP 29073-910, Brazil

^* e-mail: sergiovbg@gmail.com
^** e-mail: sergio.vitorino@pq.cnpq.br

Received: 16 June 2014
Accepted: 1 December 2014
Published online: 18 December 2014

Abstract

We study the primordial Universe in a cosmological model where inflation is driven by a fluid with a polytropic equation of state $$p = \alpha \rho + k\rho ^{1 + 1/n}$$. We calculate the dynamics of the scalar factor and build a Universe with constant density at the origin. We also find the equivalent scalar field that could create such an equation of state and calculate the corresponding slow-roll parameters. We calculate the scalar perturbations, the scalar power spectrum, and the spectral index.