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

TL;DR

This work analyzes gravitational waves from inspiraling binaries in quadratic gravity, demonstrating that the theory’s extra modes can be mapped into the PPE framework by restricting the massive spin-2 sector to transverse-traceless polarizations. Using quadrupole radiation and the stationary phase approximation, the authors derive frequency-domain waveforms and extract PPE phase and amplitude corrections for both the scalar and tensor massive modes. By confronting these corrections with GW170817 and GW250114 data, they obtain significantly tighter bounds on the theory’s parameters $m_{\Phi}$, $\gamma$, $m_{\Psi}$, and $\alpha$, improving over previous astrophysical limits by orders of magnitude. Forecasts for the Einstein Telescope indicate even stronger constraints, highlighting the power of GW tests to probe higher-curvature extensions of GR in the strong-field regime.

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.