Parameterised post-Newtonian formalism for the effective field theory of dark energy via screened reconstructed Horndeski theories

Abstract

We bring together two popular formalisms which generically parameterise deviations from General Relativity on astrophysical and cosmological scales, namely the parameterised post-Newtonian (PPN) formalism and the effective field theory (EFT) of dark energy and modified gravity. These separate formalisms are successfully applied to independently perform tests of gravity in their respective regimes of applicability on vastly different length scales. Nonlinear screening mechanisms indeed make it imperative to probe General Relativity across a wide range of scales. For a comprehensive interpretation of the complementary measurements it is important to connect them to effectively constrain the vast gravitational model space. We establish such a connection within the framework of Horndeski scalar-tensor theories restricted to a luminal propagation speed of gravitational waves. This is possible via the reconstruction of the family of linearly degenerate covariant Horndeski actions from the set of EFT functions and the subsequent derivation of the PPN parameters from the reconstructed theory. We outline the required conditions which ensure a reconstructed Horndeski model possesses a screening mechanism that enables significant modifications on cosmological scales while respecting stringent astrophysical bounds. Employing a scaling method, we then perform the general post-Newtonian expansion of the reconstructed models to derive their PPN parameters γ and β in their screened regimes.

New horizons for fundamental physics with LISA

“…• An interesting open problem regarding GW propagation is the mixture of propagation and source effects for extended theories of gravity and the role of screening mechanisms. A PN expansion for the source emission in screened regimes can be performed using a scaling relation (McManus et al 2017;Perkins and Yunes 2019;Renevey et al 2020). For some GR extensions the relevant modification in m are in fact determined by the screened environments of emitter and observer rather than the cosmological background, whereas for c T screening effects may safely be neglected.…”

Scalar Fields Near Compact Objects: Resummation versus UV Completion

“…Now we turn to the scalar-tensor theory (1.1), and similarly ask for what values of the EFT couplings is there an obstruction to resummation in the classical theory or to UV completion in the quantum theory? Scalar-tensor theories in this Horndeski class (and its generalisations) form the basis of recent model-independent parameterised approaches that systematically explore modified gravity effects in linear cosmology [20][21][22][23][119][120][121][122][123][124][125][126], resulting in various cosmological constraints on deviations from GR [23,[127][128][129][130][131][132][133][134][135][136][137][138][139][140][141][142][143][144][145][146]. (1.1) is also the theory previously studied in [92,93] and has the convenient feature that positivity bounds can be mapped directly onto constraints on the effective parameters which control linearised cosmological perturbations [23].…”

Inspiral gravitational waveforms from compact binary systems in Horndeski gravity

“…This amounts to neglecting nonlinear Galileon-type self-interactions [79,80] relative to the linear kinetic term. Hence it is difficult to accommodate the case in which the field derivative is suppressed in the exterior region of NSs by the Vainshtein mechanism [81][82][83][84][85], unless some specific scaling methods [86][87][88] are employed. However, if the Vainshtein radius r V is of the same order as the NS radius r s (∼ 10 km), the PN analysis used for the derivation of solutions to scalar perturbations from r = r s to an observer does not lose its validity.…”