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arXiv · 2504.15709

Gravitational Wave Backreaction in $f(R,G)$ Gravity

Farzad Milani
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Abstract

We develop a complete framework for gravitational wave propagation and backreaction in $f(R,G)$ modified gravity. Using a scalar-tensor formulation with two auxiliary fields, we derive the effective energy-momentum tensor for high-frequency gravitational waves, extending the Isaacson formalism to incorporate the coupled dynamics of the two scalar degrees of freedom arising from the Ricci scalar and Gauss-Bonnet terms. Applying our formalism to the concrete model $f(R,G) = R + \alpha R^2 + \beta G$ with dimensionless coupling $\tilde{\beta} = \beta H_{\text{inf}}^2$, we identify three observational signatures: (i) a stochastic background $\Omega_{GW}(f)$ too faint for direct detection; (ii) a frequency-dependent phase shift $\Delta\phi(f) \propto \tilde{\beta} f$ detectable for $\tilde{\beta} \gtrsim 10^{-9}$ via matched filtering of binary inspirals; and (iii) amplitude damping $\delta h/h \propto \tilde{\beta} f \ln(1+z)$ reaching the percent level for $\tilde{\beta} \sim 10^{-8}$, constrainable by multi-messenger standard sirens. These results show that $f(R,G)$ gravity makes testable predictions for next-generation observatories, improving constraints on the Gauss-Bonnet coupling by 28 orders of magnitude over current bounds. The framework developed here provides a foundation for studying modified gravity through gravitational wave observations.

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Farzad Milani. 2025-04-22. Gravitational Wave Backreaction in $f(R,G)$ Gravity. https://arxiv.org/abs/2504.15709

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