Dynamical Dark Energy or Modified Gravity? Signatures in Gravitational Wave Propagation

Abstract: We discuss the implications of the most recent DESI Baryon Acoustic Oscillations (BAO) DR2 and DESyr5 compilation of supernovae (SNe) datasets for modified gravity focusing on non-metricity based $f(Q)$ theory, by employing a `model-independent' approach. We reconstruct of dark energy density which is then extended to estimate the perturbation-level quantities, sourced by the modified gravity, namely the effective gravitational coupling, $\mu$, and the amplitude damping parameter of gravitational wave propagation, $\nu$. In light of the remarkable hints for a dynamical dark energy emerging from the analysis of background cosmological data, we discuss the possibility to distinguish between dark energy and modified gravity scenarios from their scalar and tensor perturbation-level signatures. We contrast our findings between the older Pantheon+ and the newer DESyr5 compilations of SNe datasets, which predict a significant distinct signature in the damping parameter of the gravitational wave propagation amplitude. On the other hand, the prediction for the effective gravitational coupling remains insensitive to the choice of the SNe datasets. Our results provide a strong case for the study of gravitational wave propagation in modified gravity theories, in light of the new generation of gravitational wave detectors such as LISA, Einstein Telescope and Cosmic Explorer.