Gravitational waveforms from inspiraling compact binaries in quadratic gravity and their parameterized post-Einstein characterization

TL;DR

This paper derives gravitational waveforms from inspiraling binaries in quadratic gravity, maps deviations from general relativity into the PPE framework, and provides improved constraints on the theory using future detector forecasts.

Contribution

It extends the PPE formalism to include scalar and massive tensor modes in quadratic gravity and derives new bounds on theory parameters from gravitational wave data.

Findings

Derived Fourier-domain waveforms including scalar and tensor modes.

Extended PPE framework to quadratic gravity deviations.

Forecasted improved constraints for Einstein Telescope sensitivity.

Abstract

We investigate gravitational waveforms from the inspiral phase of compact binary systems within the framework of quadratic gravity and map their deviations from general relativity into the parameterized post-Einstein (PPE) formalism to constrain the theory parameters. Quadratic gravity generically includes a massive spin-2 ghost, which leads to ill-defined energy and angular momentum fluxes. Following earlier proposals, we remove these unphysical features by imposing a constraint on the massive spin-2 mode, restricting it to propagate only the same polarizations of general relativity. Within the quadrupole approximation, we derive the radiative degrees of freedom, including massless and massive tensor modes, as well as a massive scalar field. Using the stationary phase approximation, we compute the Fourier-domain waveform of the massless tensor modes and extract the phase corrections. For small deviations from general relativity, we show that both the scalar and massive tensor modes can be consistently embedded into the PPE framework, extending previous results that considered only scalar fields. We derive updated constraints on the parameters of quadratic gravity, finding bounds improved by several orders of magnitude compared to existing limits. Finally, we present forecasts for the sensitivity of the Einstein Telescope to these deviations.