Gravitational-wave cosmological distances in scalar-tensor theories of gravity

Abstract

We analyze the propagation of high-frequency gravitational waves (GW) in scalartensor theories of gravity, with the aim of examining properties of cosmological distances as inferred from GW measurements. By using symmetry principles, we first determine the most general structure of the GW linearized equations and of the GW energy momentum tensor, assuming that GW move with the speed of light. Modified gravity effects are encoded in a small number of parameters, and we study the conditions for ensuring graviton number conservation in our covariant set-up. We then apply our general findings to the case of GW propagating through a perturbed cosmological space-time, deriving the expressions for the GW luminosity distance d (GW) L and the GW angular distance d (GW) A. We prove for the first time the validity of Etherington reciprocity law dfor a perturbed universe within a scalar-tensor framework. We find that besides the GW luminosity distance, also the GW angular distance can be modified with respect to General Relativity. We discuss implications of this result for gravitational lensing, focussing on time-delays of lensed GW and lensed photons emitted simultaneously during a multimessenger event. We explicitly show how modified gravity effects compensate between different coefficients in the GW time-delay formula: lensed GW arrive at the same time as their lensed electromagnetic counterparts, in agreement with causality constraints.

Gravitational wave stochastic background in reduced Horndeski theories

“…This relation was proven to be true in [37] for a general scalar-tensor theory and a GW signal of the eikonal form…”

“…This change in the GW propagation through cosmological distances can be used to probe modified gravity [33][34][35][36]. It is common to find works [34,37] referring to D (GW ) h as the GW luminosity distance, but here we distinguish it from D (GW ) L , which is the distance directly related with the luminosity of the source, since in general D…”

Modified gravitational wave propagation: information from strongly lensed binaries and the BNS mass function

“…In particular, in the case of a quadruply lensed event, having the four signals, it is possible to extract 1,9 a measurement of the distance from the time delays, D ∆t and four measurements from the amplitudes, which can be used to perform a cosmological analysis. In particular, it can be shown 1,11 that the former is not affected by the phenomenon of modified GW propagation, while the latter are, according to Eq. 2, so their combination can be directly used to infer Ξ(z) without imposing any prior on H 0 .…”

Testing gravity with gravitational waves $\times$ electromagnetic probes cross-correlations

“…The expressions we used for GW lensing in the auto-and cross-correlation rely on calculations of the relativistic corrections to the luminosity distance of GW in Horndeski and DHOST theories with the speed of sound c 2 T = 1 [141]. In this case, it is not straightforward to find an explicit expression for Ξ(z) in terms of µ, Σ and/or η which is valid on all linear scales.…”