Polarization modes of gravitational waves in general symmetric teleparallel gravity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915315236995072 |
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| author | Dong, Yu-Qi Lai, Xiao-Bin Fan, Yu-Zhi Liu, Yu-Xiao |
| author_facet | Dong, Yu-Qi Lai, Xiao-Bin Fan, Yu-Zhi Liu, Yu-Xiao |
| contents | In this paper, we investigate the polarization modes of gravitational waves within the most general symmetric teleparallel gravity theory that allows for second-order field equations We consider both scenarios where test particles either carry or do not carry a hypermomentum charge. Our findings reveal the existence of tensor, vector, and scalar modes of gravitational waves. Firstly, the theory supports the + and $\times$ tensor modes propagating at the speed of light. Secondly, in the case where particles do not carry hypermomentum, vector modes propagating at the speed of light exist only within a very specific parameter space. However, when particles do carry hypermomentum, there are two shear modes that propagate at the speed of light, while the vector-$x$ and vector-$y$ modes emerge only under very specific conditions. Thirdly, in the presence of hypermomentum, there is always a longitudinal mode propagating at the speed of light. The universal existence of the shear modes and the longitudinal mode in the presence of hypermomentum is a key feature of symmetric teleparallel gravity, distinguishing it from the Riemannian framework through gravitational wave polarization detection. We also analyze the polarization modes in two widely studied special theories: $f(Q)$ theory and quadratic non-metricity theory. Our study reveals that, within the $f(Q)$ gravity framework, it is crucial to assume that matter fields are independent of the connection, as any dependence would lead to unphysical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_13298 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polarization modes of gravitational waves in general symmetric teleparallel gravity Dong, Yu-Qi Lai, Xiao-Bin Fan, Yu-Zhi Liu, Yu-Xiao General Relativity and Quantum Cosmology High Energy Physics - Theory In this paper, we investigate the polarization modes of gravitational waves within the most general symmetric teleparallel gravity theory that allows for second-order field equations We consider both scenarios where test particles either carry or do not carry a hypermomentum charge. Our findings reveal the existence of tensor, vector, and scalar modes of gravitational waves. Firstly, the theory supports the + and $\times$ tensor modes propagating at the speed of light. Secondly, in the case where particles do not carry hypermomentum, vector modes propagating at the speed of light exist only within a very specific parameter space. However, when particles do carry hypermomentum, there are two shear modes that propagate at the speed of light, while the vector-$x$ and vector-$y$ modes emerge only under very specific conditions. Thirdly, in the presence of hypermomentum, there is always a longitudinal mode propagating at the speed of light. The universal existence of the shear modes and the longitudinal mode in the presence of hypermomentum is a key feature of symmetric teleparallel gravity, distinguishing it from the Riemannian framework through gravitational wave polarization detection. We also analyze the polarization modes in two widely studied special theories: $f(Q)$ theory and quadratic non-metricity theory. Our study reveals that, within the $f(Q)$ gravity framework, it is crucial to assume that matter fields are independent of the connection, as any dependence would lead to unphysical results. |
| title | Polarization modes of gravitational waves in general symmetric teleparallel gravity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2505.13298 |