Cosmological scalar field perturbations can grow

TL;DR

This paper demonstrates that scalar field perturbations in an expanding universe can grow similarly to cold dark matter, challenging previous claims, by analytically and numerically solving the Einstein-Klein-Gordon system without relying on fluid approximations.

Contribution

It provides a rigorous analysis showing growth of scalar field perturbations without time-averaging, clarifies misconceptions, and identifies potential observational effects in dark matter models.

Findings

Scalar perturbations grow like cold dark matter at the Compton wavelength scale.

Growth does not depend on fluid approximation or time-averaging.

Identifies a time-dependent modulation with potential observational implications.

Abstract

It has been argued that the small perturbations to the homogeneous and isotropic configurations of a canonical scalar field in an expanding universe do not grow. We show that this is not true in general, and clarify the root of the misunderstanding. We revisit a simple model in which the zero-mode of a free scalar field oscillates with high frequency around the minimum of the potential. Under this assumption the linear perturbations grow like those in the standard cold dark matter scenario, but with a Jeans length at the scale of the Compton wavelength of the scalar particle. Contrary to previous analyses in the literature our results do not rely on time-averages and/or fluid identifications, and instead we solve both analytically (in terms of a well-defined series expansion) and numerically the linearized Einstein-Klein-Gordon system. Also, we use gauge-invariant fields, which makes the physical analysis more transparent and simplifies the comparison with previous works carried out in different gauges. As a byproduct of this study we identify a time-dependent modulation of the different physical quantities associated to the background as well as the perturbations with potential observational consequences in dark matter models.