Scalar-induced gravitational waves in spatially covariant gravity
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| Format: | Preprint |
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2025
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| author | Jiang, Jiehao Lin, Jieming Gao, Xian |
| author_facet | Jiang, Jiehao Lin, Jieming Gao, Xian |
| contents | 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-Lemaître-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_20000 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalar-induced gravitational waves in spatially covariant gravity Jiang, Jiehao Lin, Jieming Gao, Xian General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics 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-Lemaître-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. |
| title | Scalar-induced gravitational waves in spatially covariant gravity |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2508.20000 |