TY - JOUR

T1 - Finding Horndeski theories with Einstein gravity limits

AU - McManus, Ryan

AU - Lombriser, Lucas

AU - Peñarrubia, Jorge

N1 - Near final version deposited to arXiv 10.06.16 before publication date 04.11.16..

PY - 2016/11/4

Y1 - 2016/11/4

N2 - 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.

AB - 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.

U2 - 10.1088/1475-7516/2016/11/006

DO - 10.1088/1475-7516/2016/11/006

M3 - Article

VL - 11

JO - Journal of Cosmology and Astroparticle Physics (JCAP)

JF - Journal of Cosmology and Astroparticle Physics (JCAP)

SN - 1475-7516

IS - 11

ER -