Cosmological evolution of a complex scalar field with repulsive or attractive self-interaction

TL;DR

This paper investigates the cosmological evolution of a complex scalar field with self-interaction, providing a general relativistic framework, analyzing different regimes, and constraining parameters with astrophysical data.

Contribution

It generalizes the hydrodynamic representation of Klein-Gordon-Einstein equations and derives the scalar field's equation of state for arbitrary potentials.

Findings

Derived the evolution equations for a homogeneous complex scalar field in an expanding universe.

Analyzed the phase diagram for quartic potentials with self-interaction.

Constrained scalar field parameters using astrophysical and cosmological observations.

Abstract

We study the cosmological evolution of a complex scalar field with a self-interaction potential $V(|\varphi|^2)$, possibly describing self-gravitating Bose-Einstein condensates, using a fully general relativistic treatment. We generalize the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field approximation developed in our previous paper. We establish the general equations governing the evolution of a spatially homogeneous complex scalar field in an expanding background. We show how they can be simplified in the fast oscillation regime and derive the equation of state of the scalar field in parametric form for an arbitrary potential. We explicitly consider the case of a quartic potential with repulsive or attractive self-interaction and determine the phase diagram of the scalar field. We show that the transition between the weakly self-interacting regime and the strongly self-interacting regime depends on how the scattering length of the bosons compares with their effective Schwarzschild radius. We also constrain the parameters of the scalar field from astrophysical and cosmological observations. Numerical applications are made for ultralight bosons without self-interaction (fuzzy dark matter), for bosons with repulsive self-interaction, and for bosons with attractive self-interaction (QCD axions and ultralight axions).