Beyond general relativity: gravitational waves in non-minimally coupled theories

TL;DR

This workDevelops a model-independent parameterization for gravitational-wave propagation in theories with non-minimal matter-curvature couplings, including parity-even and parity-odd effects and extensions to $O(\mathcal{H}^2/k^2)$ and $O(\mathcal{H}'/k^2)$. It maps this framework onto three concrete models—Kalb-Ramond dark matter with dimension-four operators, axion-dilaton-Chern-Simons-Gauss-Bonnet with dimension-five operators, and dimension-six couplings to a (dark) vector field—showing how each model modifies GW dispersion, group/phase velocities, and helicity-dependent waveform features. The analysis highlights amplitude and velocity birefringence from parity-violating terms, and provides explicit expressions for modified dispersion relations and GW amplitudes across the models, along with constraints from GW170817. The work offers a practical tool for testing beyond-GR physics with GWs and dark matter interactions, and points to interesting early-universe implications where EFT validity may permit larger effects.

Abstract

Non-minimal couplings between matter and curvature tensors arise in many different contexts. Such couplings modify solutions of general relativity (GR) and therefore can be probed in various astrophysical systems. A particularly interesting scenario arises if dark matter experiences non-minimal couplings, as dark matter densities are expected to spike in the vicinity of binary black hole mergers. This gives a novel setting for simultaneously studying dark matter and (beyond) GR physics via observations of gravitational waves (GWs). In this work, we explore effects of various non-minimal couplings on GWs by working with a model-independent parameterization for left- and right-handed GW strains. We extend the parameterization proposed in \cite{Jenks:2023pmk,Daniel:2024lev} to include early-universe effects, and we write down the generic solution assuming slowly-varying matter fields. We then systematically apply our results to three models: Kalb-Ramond dark matter with dimension-four operators, axion-dilaton-Chern-Simons-Gauss-Bonnet dimension-five operators, and dimension-six couplings to a (dark) vector field.

Figures (3)

• Figure 1: Example modification to a binary black hole waveform for $h_R$ (left) and $h_L$ (right) in the KR model. To generate the waveform, we employ the GW Analysis Tools code Perkins:2021mhb. We see that the amplitude is slightly suppressed due to the parity-invariant modification to the amplitude, while there is a larger phase shift in the left-handed mode compared to the right-handed mode, due to the parity-violating phase modification. For the source parameters we take $m_1 = 20 M_\odot$, $m_2 = 18 M_\odot$, $\iota = 2.6$ rad, $\psi = 3.14$ rad, $RA = 3.45$ rad, $Dec = -3968$ rad. For computational ease we rescale $f/100$ Hz, and $D_2/\text{Gpc}$. The modification parameters are chosen to be artificially large in order to visually see the effects; in dimensionless units $\tilde{\mathcal{V}}_e = \tilde{\mathcal{V}}_m = 3$.
• Figure 2: Example modification to a binary black hole waveform for $h_R$ (left) and $h_L$ (right) in the axion-dilaton-Chern-Simons-Gauss-Bonnet model. The right-handed mode is attenuated while the left-handed mode is amplified, due to the parity-violating modification to the amplitude. The phase shift is a much smaller effect, and it arises due to the parity-invariant phase modification. Other notes from Fig. \ref{['fig:waveform-kr']} apply here, with the modification parameters again being chosen to be artificially large in order to visually see the effects; in dimensionless units $\phi_0' = \varphi_0' = 6$.
• Figure 3: Example modification to a binary black hole waveform for $h_R$ (left) and $h_L$ (right) in the $U(1)$ model. The phase shift affects the right-handed mode more than the left-handed mode, due to the parity-violating modification. The amplitude modification is a much smaller effect, and it is due to the parity-invariant modification to the amplitude. Other notes from Fig. \ref{['fig:waveform-kr']} apply here, with the modification parameters again being chosen to be artificially large in order to visually see the effects; in dimensionless units $\tilde{B}^2 = 2$.