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arXiv · 2508.20000

Scalar-induced gravitational waves in spatially covariant gravity

Jiehao Jiang·Jieming Lin·Xian Gao
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Abstract

We investigate scalar-induced gravitational waves (SIGWs) in the framework of spatially covariant gravity (SCG), a broad class of Lorentz-violating modified gravity theories respecting only spatial diffeomorphism invariance. Extending earlier SCG formulations, we compute the general kernel function for SIGWs on a flat Friedmann-Lema\^itre-Robertson-Walker background, focusing on polynomial-type SCG Lagrangians up to $d=3$, where $d$ denotes the total number of derivatives in each monomial. We derive explicit expressions for the kernel in the case of power-law time evolution of the coefficients, and restrict attention to the subset of SCG operators whose tensor modes propagate at the speed of light, thereby avoiding late-time divergences in the fractional energy density of SIGWs. Instead of the usual Newtonian gauge, the breaking of time reparametrization symmetry in SCG necessitates a unitary gauge analysis. We compute the energy density of SIGWs for representative parameter combinations, finding distinctive deviations from general relativity (GR), including scale-dependent modifications to both the amplitude and the spectral shape. Our results highlight the potential of stochastic GW background measurements to probe spatially covariant gravity and other Lorentz-violating extensions of GR.

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Jiehao Jiang, Jieming Lin, Xian Gao. 2025-08-27. Scalar-induced gravitational waves in spatially covariant gravity. https://doi.org/10.1140/epjc%2Fs10052-026-15286-y

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