Symmetries for scalarless scalar theories

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.

27 pages. References added, to appear in PRD

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Cited by in corpus (9)

• Minimally modified gravity with an auxiliary constraint: a Hamiltonian construction
• Gravitational-wave cosmological distances in scalar-tensor theories of gravity
• Distinguishing modified gravity with just two tensorial degrees of freedom from general relativity: Black holes, cosmology, and matter coupling
• Dynamical Dark Energy in Minimally Modified Gravity
• Testing gravity with the cosmic microwave background: constraints on modified gravity with two tensorial degrees of freedom
• Black hole perturbations in spatially covariant gravity with just two tensorial degrees of freedom
• Minimally modified gravity with auxiliary constraints formalism
• Ultracompact vector stars
• Spatially covariant gravity with two degrees of freedom in the presence of an auxiliary scalar field: Hamiltonian analysis