Probing the dark Universe with gravitational waves

TL;DR

This paper develops a gauge-invariant theoretical framework to model how gravitational waves interact with dark energy and dark matter, enabling the use of GW observations to probe the properties of the dark Universe across different frequencies and redshifts.

Contribution

It introduces a comprehensive gauge-invariant effective action for all GW polarizations, linking their propagation characteristics to dark sector properties in a unified way.

Findings

Derived a polarization, frequency, and time dependent effective speed for GWs.

Established a method to relate GW propagation to dark energy and dark matter properties.

Provided a framework to use GW observations to probe the dark Universe at various redshifts.

Abstract

Gravitational waves (GW) are expected to interact with dark energy and dark matter, affecting their propagation on cosmological scales. In order to model this interaction, we derive a gauge invariant effective equation and action valid for all GWs polarizations, based on encoding the effects of the interaction of GWs at different order in perturbations, in a polarization, frequency and time dependent effective speed. The invariance of perturbations under time dependent conformal transformations and the gauge invariance of the GWs allow to obtain the unitary gauge effective action in any conformally related frame, making transparent the relation between Einstein and Jordan frame. The propagation time and luminosity distance of different GWs polarizations allow to probe at different frequencies and redshift the dark Universe, which act as an effective medium, whose physical properties can be modeled by the GWs effective speed.