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.
Highlights
In this work we examine covariant theories describing scalar fields interacting with themselves, with vectors, or with tensors, where symmetries prevent the propagation of linearized scalar excitations around solutions of the equations of motion
We address the problem of determining scalarless scalar-tensor theories of gravity making use of symmetry principles that guide us for building covariant scalarless theories and for better understanding the dynamics of the propagating modes
We demonstrate that no scalar excitations arise around a Schwarzschild solution, the dynamics of spin-2 fluctuations is different with respect to Einstein gravity, making the theory distinguishable from general relativity (GR)
Summary
In this work we examine covariant theories describing scalar fields interacting with themselves, with vectors, or with tensors, where symmetries prevent the propagation of linearized scalar excitations around solutions of the equations of motion. If scalar fluctuations do not propagate, long range scalar interactions are absent These systems circumvent the Lovelock theorem [1] by spontaneously breaking Lorentz invariance by a nontrivial profile for the scalar background configuration. These theories might avoid instabilities associated with scalar fluctuations in scalar-tensor systems, as for example graviton decay into dark energy [2], or scalar instabilities around spherically symmetric black holes [3,4,5,6,7]. The system spontaneously breaks Lorentz invariance, and the new symmetry can prevent the propagation of scalar excitations, leading to theories where only transverse vector modes are dynamical, even in the absence of Abelian Uð1Þ gauge invariance.
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