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.

The effect of screening mechanisms on black hole binary inspiral waveforms

“…[40] and later extended to Horndeski theories with luminal propagation of gravitational waves in Ref. [41]. One can use these results to write the correction to the metric field up to 1PN,…”

“…Consequently, the non-linearity renders post-Newtonian approaches difficult to implement due to the linearisation of the relevant field equations. However, it was shown that this problem can be circumvented with the employment of the so-called scaling method [38][39][40][41] that enables an expansion in screened regions. More specifically, the method can be used to both identify the leading corrections from the scalar field to the metric field equations in the screened small-scale regions or conversely of the unscreened theory on large scales.…”

“…One can describe this contribution of the scalar field using the scaling method developed in Refs. [38][39][40][41], in which the metric and the scalar field are expanded as…”

“…µν . Allowing for an embedding of the chameleon, k-mouflage, and Vainshtein screening mechanisms, we have assumed that [38][39][40][41]89]. For the remainder of this work, we shall furthermore adopt a normalisation of the gravitational constant by G/φ 0 = 1.…”

Robustness of the Cosmological Constant Damping Mechanism Through Matter Eras

“…This has motivated the search for cosmological models achieving a dynamical self-tuning of the Hubble expansion rate to the small observed value, even in the presence of a large vacuum energy density; for some recent work in this direction, see [2][3][4][5][6][7][8][9]. We also refer the reader to the review [10] for a discussion of the cosmological constant problem from the EFT viewpoint, and to the literature on effective field theories of dark energy and quintessence [11][12][13][14][15][16][17] for a complementary perspective. It appears extremely hard, if not impossible, to come up with an EFT which would avoid large quantum contributions to the vacuum energy density, as in (1.4).…”