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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2505.15838 |
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| _version_ | 1866918030713290752 |
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| author | Lee, Seokcheon |
| author_facet | Lee, Seokcheon |
| contents | In the Friedmann-Lemaître-Robertson-Walker metric, a varying speed of light (VSL) reflects a change in the clock rate across hypersurfaces, described by the lapse function. This variation is not a dynamical field evolution but a consequence of coordinate choice, as the cosmic time coincides with the proper time of comoving observers due to the Weyl postulate. From an action principle including $\tilde c$, we derive that $\tilde c$ does not have its dynamics but imposes a constraint on the scale factor $a(t)$, indicating that it is not an independent degree of freedom. This insight reframes the VSL concept as a manifestation of gauge freedom in general relativity, wherein physical laws remain invariant under smooth coordinate transformations. Here, gauge refers to the freedom of choosing the temporal coordinate (\textit{e.g.}, setting the lapse $N(t) \neq 1$), which determines how the speed of light appears in the cosmological equations. Recognizing $\tilde c$ as a coordinate-dependent quantity offers a new interpretation of cosmological time and observational tensions, such as the Hubble tension, without invoking new physical fields. This redefinition opens a novel theoretical pathway in interpreting cosmic expansion within a consistent relativistic framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15838 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting Varying Speed of Light in Cosmology: Insights from the Friedmann-Lemaître-Robertson-Walker Metric Lee, Seokcheon General Physics In the Friedmann-Lemaître-Robertson-Walker metric, a varying speed of light (VSL) reflects a change in the clock rate across hypersurfaces, described by the lapse function. This variation is not a dynamical field evolution but a consequence of coordinate choice, as the cosmic time coincides with the proper time of comoving observers due to the Weyl postulate. From an action principle including $\tilde c$, we derive that $\tilde c$ does not have its dynamics but imposes a constraint on the scale factor $a(t)$, indicating that it is not an independent degree of freedom. This insight reframes the VSL concept as a manifestation of gauge freedom in general relativity, wherein physical laws remain invariant under smooth coordinate transformations. Here, gauge refers to the freedom of choosing the temporal coordinate (\textit{e.g.}, setting the lapse $N(t) \neq 1$), which determines how the speed of light appears in the cosmological equations. Recognizing $\tilde c$ as a coordinate-dependent quantity offers a new interpretation of cosmological time and observational tensions, such as the Hubble tension, without invoking new physical fields. This redefinition opens a novel theoretical pathway in interpreting cosmic expansion within a consistent relativistic framework. |
| title | Revisiting Varying Speed of Light in Cosmology: Insights from the Friedmann-Lemaître-Robertson-Walker Metric |
| topic | General Physics |
| url | https://arxiv.org/abs/2505.15838 |