Time-dependent spherically symmetric covariant Galileons

Understand

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.