A Re-Examination Of Foundational Elements Of Cosmology
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908721487020032 |
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| author | Heisenberg, Lavinia |
| author_facet | Heisenberg, Lavinia |
| contents | This paper undertakes a conceptual re-examination of several foundational elements of cosmology through the lens of spacetime symmetries. A new derivation of the Friedmann-Lemaître-Robertson-Walker metric is obtained by a careful conceptual examination of rotations and translations on generic manifolds, followed by solving the rotational and translational Killing equations, yielding both the metric \emph{and} its translational generators for $k\in\{-1,0,1\}$ without any further assumptions. We then analyze how continuous symmetries are inherited by the Einstein tensor and the Hilbert energy-momentum tensor, proving two general propositions. Furthermore, we use the Maxwell and Kalb-Ramond fields to show that a homogeneous and isotropic energy-momentum tensor, in general, does \emph{not} give rise to field configurations which share these symmetries. In particular, the Kalb-Ramond field we derive is significantly more general than what is usually encountered in the cosmological context. Finally, we provide a rigorous but accessible, elementary, and transparent derivation of the scalar-vector-tensor decomposition from the linearized Einstein equations. Together, these results highlight the value of multiple complementary formulations of the same cosmological physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16934 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Re-Examination Of Foundational Elements Of Cosmology Heisenberg, Lavinia General Physics General Relativity and Quantum Cosmology This paper undertakes a conceptual re-examination of several foundational elements of cosmology through the lens of spacetime symmetries. A new derivation of the Friedmann-Lemaître-Robertson-Walker metric is obtained by a careful conceptual examination of rotations and translations on generic manifolds, followed by solving the rotational and translational Killing equations, yielding both the metric \emph{and} its translational generators for $k\in\{-1,0,1\}$ without any further assumptions. We then analyze how continuous symmetries are inherited by the Einstein tensor and the Hilbert energy-momentum tensor, proving two general propositions. Furthermore, we use the Maxwell and Kalb-Ramond fields to show that a homogeneous and isotropic energy-momentum tensor, in general, does \emph{not} give rise to field configurations which share these symmetries. In particular, the Kalb-Ramond field we derive is significantly more general than what is usually encountered in the cosmological context. Finally, we provide a rigorous but accessible, elementary, and transparent derivation of the scalar-vector-tensor decomposition from the linearized Einstein equations. Together, these results highlight the value of multiple complementary formulations of the same cosmological physics. |
| title | A Re-Examination Of Foundational Elements Of Cosmology |
| topic | General Physics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2512.16934 |