Cosmological perturbations in coherent oscillating scalar field models

TL;DR

This paper analyzes the behavior of cosmological perturbations in models with oscillating scalar fields, deriving effective sound speeds and corrections for different potentials, enhancing understanding of their role in cosmology.

Contribution

It provides a new analytical framework for understanding perturbations in scalar field models with power law potentials, including corrections and anharmonic effects.

Findings

Derived a simple expression for effective sound speed $c_{eff}^2 = rac{n-2}{n+2}$.

Obtained first-order corrections in $k^2/ ext{effective frequency}^2$ for perturbations.

Analyzed anharmonic contributions to the effective sound speed in massive scalar field models.

Abstract

The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials $V(\phi)=\lambda \vert\phi\vert^{n}/n$. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained $c_{\text{eff}}^2 = \omega=(n-2)/(n+2)$ with $\omega$ the effective equation of state. We also obtain the first order correction in $k^2/\omega_{\text{eff}}^2$, when the wavenumber $k$ of the perturbations is much smaller than the background oscillation frequency, $\omega_{\text{eff}}$. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the natural ansatz for $\delta\phi$; and for sub-Hubble modes, exploiting Floquet's theorem.