Finding Horndeski theories with Einstein gravity limits

Abstract

The Horndeski action is the most general scalar-tensor theory with at most second-order derivatives in the equations of motion, thus evading Ostrogradsky instabilities and making it of interest when modifying gravity at large scales. To pass local tests of gravity, these modifications predominantly rely on nonlinear screening mechanisms that recover Einstein's Theory of General Relativity in regions of high density. We derive a set of conditions on the four free functions of the Horndeski action that examine whether a specific model embedded in the action possesses an Einstein gravity limit or not. For this purpose, we develop a new and surprisingly simple scaling method that identifies dominant terms in the equations of motion by considering formal limits of the couplings that enter through the new terms in the modified action. This enables us to find regimes where nonlinear terms dominate and Einstein's field equations are recovered to leading order. Together with an efficient approximation of the scalar field profile, one can then further evaluate whether these limits can be attributed to a genuine screening effect. For illustration, we apply the analysis to both a cubic galileon and a chameleon model as well as to Brans-Dicke theory. Finally, we emphasise that the scaling method also provides a natural approach for performing post-Newtonian expansions in screened regimes.

33 pages

References in corpus (13)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• The Confrontation between General Relativity and Experiment
• Resummation of Massive Gravity
• Tests of general relativity with GW150914
• Beyond the Cosmological Standard Model
• Covariant Galileon
• Healthy theories beyond Horndeski
• Disformal Theories of Gravity: From the Solar System to Cosmology
• Shaken, not stirred: kinetic mixing in scalar-tensor theories of gravity
• Classifying Linearly Shielded Modified Gravity Models in Effective Field Theory
• The Parametrized Post-Newtonian-Vainshteinian Formalism
• Classical Duals of Derivatively Self-Coupled Theories

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