Cosmological models based on a complex scalar field with a power-law potential associated with a polytropic equation of state

TL;DR

This paper develops cosmological models using a complex scalar field with power-law potentials linked to various equations of state, unifying several known models and exploring their dynamics in a fast oscillation regime.

Contribution

It introduces a comprehensive framework connecting scalar field potentials with different equations of state, recovering known models and analyzing their cosmological implications.

Findings

Unified description of cosmological models with scalar fields and polytropic equations of state.

Recovery of $ ext{Lambda}$CDM, Chaplygin gas, and Bose-Einstein condensate models as special cases.

Analysis of the fast oscillation regime of 'spintessence' scalar fields.

Abstract

We construct cosmological models based on a complex scalar field with a power-law potential $V=\frac{K}{\gamma-1}(\frac{m}{\hbar})^{2\gamma}|\varphi|^{2\gamma}$ associated with a polytropic equation of state $P=K\rho^{\gamma}$ (the potential associated with an isothermal equation of state $P=\rho k_B T/m$ is $V=\frac{m k_B T}{\hbar^2}|\varphi|^2 [\ln(m^2|\varphi|^2/\rho_*\hbar^2)-1]$ and the potential associated with a logotropic equation of state $P=A\ln(\rho/\rho_P)$ is $V=-A[\ln(m^2|\varphi|^2/\hbar^2\rho_P)+1]$). We consider a fast oscillation regime of ``spintessence'' where the equations of the problem can be simplified. We study all possible cases with arbitrary (positive and negative) values of the polytropic constant and polytropic index. The $\Lambda$CDM model, the Chaplygin gas model and the Bose-Einstein condensate model are recovered as particular cases of our study corresponding to a constant potential ($\gamma=0$), an inverse square-law potential ($\gamma=-1$), and a quartic potential ($\gamma=2$). We also derive the two-fluid representation of the Chaplygin gas model.