Symmetries for scalarless scalar theories

TL;DR

This paper explores theories with scalar fields coupled to vectors or tensors that possess symmetries preventing scalar excitations, with implications for black hole stability and dark energy models.

Contribution

It introduces symmetry principles that eliminate scalar propagations in scalar-vector-tensor theories, impacting black hole physics and cosmological acceleration.

Findings

Scalar excitations are absent around spherically symmetric black holes.

Symmetries can lead to self-accelerating cosmological solutions.

Modifications in spin-2 dynamics compared to Einstein gravity.

Abstract

We consider theories containing scalar fields interacting with vector or with tensor degrees of freedom, equipped with symmetries that prevent the propagation of linearized scalar excitations around solutions of the equations of motion. We first study the implications of such symmetries for building vector theories that break Abelian gauge invariance without necessarily exciting longitudinal scalar fluctuations in flat space. We then examine scalar-tensor theories in curved space, and relate the symmetries we consider with a non-linear realization of broken space-time symmetries acting on scalar modes. We determine sufficient conditions on the space-time geometry to avoid the propagation of scalar fluctuations. We analyze linearized perturbations around spherically symmetric black holes, proving the absence of scalar excitations, and pointing out modifications in the dynamics of spin-2 fluctuations with respect to Einstein gravity. We then study consequences of this set-up for the dark energy problem, determining scalar constraints on cosmological configurations that can lead to self-accelerating universes whose expansion is insensitive to the value of the bare cosmological constant.