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We analyze the propagation of high-frequency gravitational waves (GW) in scalar-tensor 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 $d_L^{({rm GW})}$ and the GW angular distance $d_A^{({rm GW})}$. We prove for the first time the validity of Etherington reciprocity law $d_L^{({rm GW})},=,(1+z)^2,d_A^{({rm GW})}$ for 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.
We investigate the cosmological applications of new gravitational scalar-tensor theories, which are novel modifications of gravity possessing 2+2 propagating degrees of freedom, arising from a Lagrangian that includes the Ricci scalar and its first a
The detection of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory opens a new era to use gravitational waves to test alternative theories of gravity. We investigate the polarizations of gravitational waves in $f(R)$ grav
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Kinetic mixing between the metric and scalar degrees of freedom is an essential ingredient in contemporary scalar-tensor theories. This often makes hard to understand their physical content, especially when derivative mixing is present, as it is the
We study the bounce and cyclicity realization in the framework of new gravitational scalar-tensor theories. In these theories the Lagrangian contains the Ricci scalar and its first and second derivatives, in a specific combination that makes them fre