Disformal Theories of Gravity: From the Solar System to Cosmology

TL;DR

This paper explores disformal scalar-tensor theories of gravity, analyzing their screening mechanisms, cosmological effects, and local gravity constraints, revealing new bounds on disformal couplings and implications for modified gravity models.

Contribution

It systematically derives the non-relativistic limit of disformal theories, identifies the conditions for screening, and constrains disformal couplings using local gravity tests.

Findings

No new non-linear screening mechanisms beyond known ones.

Disformal effects can influence solar system dynamics when cosmological expansion is considered.

Constraints on disformal coupling are established, with al > eV.

Abstract

This paper is concerned with theories of gravity that contain a scalar coupled both conformally and disformally to matter through the metric. By systematically deriving the non-relativistic limit, it is shown that no new non-linear screening mechanisms are present beyond the Vainshtein mechanism and chameleon-like screening. If one includes the cosmological expansion of the universe, disformal effects that are usually taken to be absent can be present in the solar system. When the conformal factor is absent, fifth-forces can be screened on all scales when the cosmological field is slowly-rolling. We investigate the cosmology of these models and use local tests of gravity to place new constraints on the disformal coupling and find $\mathcal{M}>\mathcal{O}(\textrm{eV})$, which is not competitive with laboratory tests. Finally, we discuss the future prospects for testing these theories and the implications for other theories of modified gravity. In particular, the Vainshtein radius of solar system objects can be altered from the static prediction when cosmological time-derivatives are non-negligible.