Symmetric Yang--Mills theory in FLRW universes
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911026689081344 |
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| author | Ertürk, Mahir Picanço, Gabriel |
| author_facet | Ertürk, Mahir Picanço, Gabriel |
| contents | In this work, we set up the theoretical framework and indicate future applications of symmetric Yang--Mills fields to cosmology. We analyze the coset space dimensional reduction scheme to construct pure Yang--Mills fields on spacetimes given as cylinders over cosets. Particular cases of foliations using $H^n$, dS$_n$ and AdS$_n$ slices as non-compact symmetric spaces are solved, compared to previous results in the literature, and generalized in a structured fashion. Coupling to general relativity in FLRW-type universes is introduced via the cosmological scale factor. For the hyperbolic slicing in 4D, the dynamics of the Einstein--Yang--Mills system is analytically solved and discussed. Finally, we generalize the analysis to warped foliations of the cylinders, which enlarge the range of possible spacetimes while also introducing a Hubble friction-like term in the equation of motion for the Yang--Mills field. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_13645 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symmetric Yang--Mills theory in FLRW universes Ertürk, Mahir Picanço, Gabriel High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics In this work, we set up the theoretical framework and indicate future applications of symmetric Yang--Mills fields to cosmology. We analyze the coset space dimensional reduction scheme to construct pure Yang--Mills fields on spacetimes given as cylinders over cosets. Particular cases of foliations using $H^n$, dS$_n$ and AdS$_n$ slices as non-compact symmetric spaces are solved, compared to previous results in the literature, and generalized in a structured fashion. Coupling to general relativity in FLRW-type universes is introduced via the cosmological scale factor. For the hyperbolic slicing in 4D, the dynamics of the Einstein--Yang--Mills system is analytically solved and discussed. Finally, we generalize the analysis to warped foliations of the cylinders, which enlarge the range of possible spacetimes while also introducing a Hubble friction-like term in the equation of motion for the Yang--Mills field. |
| title | Symmetric Yang--Mills theory in FLRW universes |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2304.13645 |