Testing modified gravity at cosmological distances with LISA standard sirens

Abstract

Modifications of General Relativity leave their imprint both on the cosmic\nexpansion history through a non-trivial dark energy equation of state, and on\nthe evolution of cosmological perturbations in the scalar and in the tensor\nsectors. In particular, the modification in the tensor sector gives rise to a\nnotion of gravitational-wave (GW) luminosity distance, different from the\nstandard electromagnetic luminosity distance, that can be studied with standard\nsirens at GW detectors such as LISA or third-generation ground based\nexperiments. We discuss the predictions for modified GW propagation from some\nof the best studied theories of modified gravity, such as Horndeski or the more\ngeneral degenerate higher order scalar-tensor (DHOST) theories, non-local\ninfrared modifications of gravity, bigravity theories and the corresponding\nphenomenon of GW oscillation, as well as theories with extra or varying\ndimensions. We show that modified GW propagation is a completely generic\nphenomenon in modified gravity. We then use a simple parametrization of the\neffect in terms of two parameters $(\\Xi_0,n)$, that is shown to fit well the\nresults from a large class of models, to study the prospects of observing\nmodified GW propagation using supermassive black hole binaries as standard\nsirens with LISA. We construct mock source catalogs and perform detailed Markov\nChain Monte Carlo studies of the likelihood obtained from LISA standard sirens\nalone, as well as by combining them with CMB, BAO and SNe data to reduce the\ndegeneracies between cosmological parameters. We find that the combination of\nLISA with the other cosmological datasets allows one to measure the parameter\n$\\Xi_0$ that characterizes modified GW propagation to the percent level\naccuracy, sufficient to test several modified gravity theories. [Abridged]\n