Abstract
We study the consistency of Scalar Gauss-Bonnet Gravity, a generalization of General Relativity where black holes can develop non-trivial hair by the action of a coupling F(Φ) mathcal{G} between a function of a scalar field and the Gauss-Bonnet invariant of the space-time. When properly normalized, interactions induced by this term are weighted by a cut-off, and take the form of an Effective Field Theory expansion. By invoking the existence of a Lorentz invariant, causal, local, and unitary UV completion of the theory, we derive positivity bounds for n-to-n scattering amplitudes including exchange of dynamical gravitons. These constrain the value of all even derivatives of the function F(Φ), and are highly restrictive. They require some of the scales of the theory to be of Planckian order, and rule out most of the models used in the literature for black hole scalarization.
Highlights
— propagating no ghosts — dubbed as degenerate higher order scalar-tensor theories (DHOST) [9, 10]
We study the consistency of Scalar Gauss-Bonnet Gravity, a generalization of General Relativity where black holes can develop non-trivial hair by the action of a coupling F (Φ)G between a function of a scalar field and the Gauss-Bonnet invariant of the space-time
In this work we focus on a single term in the DHOST Lagrangian, which has attracted a lot of interest recently — a coupling between an arbitrary function of the scalar field Φ and the Euler density of the space-time, given by the Gauss-Bonnet invariant — F (Φ)G [33–37]
Summary
— propagating no ghosts — dubbed as degenerate higher order scalar-tensor theories (DHOST) [9, 10]. The parameter space of scalar-tensor theories, once promising as effective models for dark energy [13], has been strongly constrained in the recent years [14–21] Most of these constraints are explicitly applicable only at cosmological scales and there is still hope that some scalar-tensor theories survive as EFTs to describe other gravitational phenomena. The theory out-coming from appending this to the Einstein-Hilbert Lagrangian is known as Scalar Gauss-Bonnet Gravity (SGBG) This term gives rise to interactions between the scalar field and the background space-time which, around non-trivial topologies, will influence the evolution of the system [38]. The terms arising from the expansion of the Gauss-Bonnet term around a constant scalar field configuration are suppressed by increasing powers of a dimensionful coupling This structure matches that of an EFT, whose irrelevant interactions are 1) higher order in derivatives and 2) suppressed by an ultra-violet (UV) cut-off. This is in addition to the statement that any gravitational theory is naturally an EFT from first principles, due to the non-renormalizability of the Einstein-Hilbert action, with cut-off at the Planck Mass MP
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