Self Tuning Scalar Fields in Spherically Symmetric Spacetimes

TL;DR

This paper investigates self tuning scalar field solutions in spherically symmetric spacetimes within Fab-Four models, identifying conditions for vacuum energy screening and highlighting the limitations of certain terms in inhomogeneous settings.

Contribution

It extends the analysis of self tuning mechanisms from cosmological to spherically symmetric spacetimes, showing which Fab-Four terms enable vacuum energy screening in both contexts.

Findings

No asymptotically flat solutions with vacuum energy screening other than Minkowski space.

Only models with 'John' term and canonical kinetic term can screen vacuum energy in both FLRW and Schwarzschild de Sitter spacetimes.

The 'Paul' term fails to produce screening in inhomogeneous spacetimes.

Abstract

We search for self tuning solutions to the Einstein-scalar field equations for the simplest class of `Fab-Four' models with constant potentials. We first review the conditions under which self tuning occurs in a cosmological spacetime, and by introducing a small modification to the original theory - introducing the second and third Galileon terms - show how one can obtain de Sitter states where the expansion rate is independent of the vacuum energy. We then consider whether the same self tuning mechanism can persist in a spherically symmetric inhomogeneous spacetime. We show that there are no asymptotically flat solutions to the field equations in which the vacuum energy is screened, other than the trivial one (Minkowski space). We then consider the possibility of constructing Schwarzschild de Sitter spacetimes for the modified Fab Four plus Galileon theory. We argue that the only model that can successfully screen the vacuum energy in both an FLRW and Schwarzschild de Sitter spacetime is one containing `John' $\sim G^{\mu}{}_{\nu} \partial_{\mu}\phi\partial^{\nu}\phi$ and a canonical kinetic term $\sim \partial_{\alpha}\phi \partial^{\alpha}\phi$. This behaviour was first observed in (Babichev&Charmousis,2013). The screening mechanism, which requires redundancy of the scalar field equation in the `vacuum', fails for the `Paul' term in an inhomogeneous spacetime.