Gravitational-wave dispersion over inhomogeneous space-times: General relativity, screened theories of gravity and non-minimal dark energy

TL;DR

This paper investigates how gravitational waves are affected by inhomogeneous space-times, especially in modified gravity theories like symmetron, revealing potential for new tests of dark energy models and effects on GW observability.

Contribution

It extends the analysis of GW dispersion to inhomogeneous and screened gravity theories, highlighting novel phenomena and implications for GW detection and dark energy testing.

Findings

GW dispersion is detectable in GR for spherical matter distributions.

Enhanced GW dispersion occurs in symmetron theories compared to GR and Brans-Dicke.

Earth can act as a GW shield, affecting the observability of events.

Abstract

Gravitational waves (GWs) are direct probes of cosmological gravity, sensitive to space-time inhomogeneities along their propagation. The presence of massive objects breaks homogeneity and isotropy, allowing for new interactions between different GW polarizations, and opening up the intriguing opportunity to test modified gravity theories. This setup generalizes the notion of gravitational deflection and lensing, revealing novel phenomena in modified theories. Any non-minimal theory introduces effective mass terms for GWs, causing \textit{lens-induced dispersion} (LID), a frequency-dependent phase shift on the waveform. We compute GW dispersion in Einstein's general relativity (GR) for a spherical matter distribution, finding a small but non-zero phasing that is potentially accessible to next-generation detectors. We then extend our analysis to scalar-tensor theories, focusing on symmetron gravity as an example of screened theory, combining cosmological deviations and consistency with local gravity tests. We find enhanced GW dispersion in a large region of the symmetron parameter space, compared to both GR and Brans-Dicke theory. We argue that dispersion, associated to an effective mass for the metric fluctuations, can in some cases prevent the propagation of GWs through some astrophysical bodies, turning them into reflectors. Our analysis shows that the Earth becomes an efficient GW shield for a hitherto unconstrained region of the symmetron parameter space, leading to a $\sim 50\%$ fraction of events becoming unobservable or at least displaying a dramatic modification of the detector antenna response. The richness and universality of dispersive phenomena in non-minimal theories open a new avenue to test theories of dynamical dark-energy, relevant in light of recent observational results challenging the $\Lambda$CDM paradigm.