Time-dependent spherically symmetric covariant Galileons

TL;DR

This paper investigates spherically symmetric solutions in the cubic covariant Galileon model, revealing how cosmological evolution influences local scalar fields, affects stability, and induces damping of scalar perturbations.

Contribution

It demonstrates the impact of cosmological time evolution on local Galileon solutions, including matter-scalar coupling, stability analysis, and perturbation damping in curved spacetime.

Findings

Different asymptotic boundary conditions lead to distinct solution branches.

Cosmological evolution induces matter-scalar coupling via kinetic braiding.

Scalar perturbations experience efficient damping due to kinetic mixing with gravity.

Abstract

We study spherically symmetric solutions of the cubic covariant Galileon model in curved spacetime in presence of a matter source, in the test scalar field approximation. We show that a cosmological time evolution of the Galileon field gives rise to an induced matter-scalar coupling, due to the Galileon-graviton kinetic braiding, therefore the solution for the Galileon field is non trivial even if the bare matter-scalar coupling constant is set to zero. The local solution crucially depends on the asymptotic boundary conditions, and in particular, Minkowski and de Sitter asymptotics correspond to different branches of the solution. We study the stability of these solutions, namely, the well-posedness of the Cauchy problem and the positivity of energy for scalar and tensor perturbations, by diagonalizing the kinetic terms of the spin-2 and spin-0 degrees of freedom. In addition, we find that in presence of a cosmological time evolution of the Galileon field, its kinetic mixing with the graviton leads to a friction force, resulting to efficient damping of scalar perturbations within matter.