Inflation and the principle of equivalence
A formal, mathematical statement of the principle of equivalence in general relativity is that one must always be able to find – at each location within a curved spacetime – the local free-falling frame against which one can measure the acceleration-induced time dilation and degree of curvature rela...
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De Gruyter
2024-11-01
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| Series: | Open Physics |
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| Online Access: | https://doi.org/10.1515/phys-2024-0077 |
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| author | Melia Fulvio |
| author_facet | Melia Fulvio |
| author_sort | Melia Fulvio |
| collection | DOAJ |
| description | A formal, mathematical statement of the principle of equivalence in general relativity is that one must always be able to find – at each location within a curved spacetime – the local free-falling frame against which one can measure the acceleration-induced time dilation and degree of curvature relative to flat spacetime. In this article, we use this theorem to prove that a de Sitter expansion, required during cosmic inflation, does not satisfy this condition and is therefore inconsistent with the PoE. To emphasize the importance – and reality – of this outcome, we contrast it with the analogous derivation for the Schwarzschild metric, which instead satisfies this requirement completely. We point out that this failure by de Sitter results from its incorrect handling of the Friedmann–Lemaître–Robertson–Walker (FLRW) lapse function, gtt{g}_{{\rm{tt}}}. Our conclusion calls into question whether a period of inflated expansion could have even been possible in the context of FLRW cosmologies, and is noteworthy in light of recent, high-precision measurements showing that inflation could not have solved the temperature horizon problem while simultaneously producing the observed primordial power spectrum. |
| format | Article |
| id | doaj-art-4617fb0d21f24aac8dfdbad58d40fdbd |
| institution | Kabale University |
| issn | 2391-5471 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Physics |
| spelling | doaj-art-4617fb0d21f24aac8dfdbad58d40fdbd2024-12-02T12:05:11ZengDe GruyterOpen Physics2391-54712024-11-012213475610.1515/phys-2024-0077Inflation and the principle of equivalenceMelia Fulvio0Department of Physics, The Applied Math Program and Department of Astronomy, The University of Arizona, AZ 85721, United States of AmericaA formal, mathematical statement of the principle of equivalence in general relativity is that one must always be able to find – at each location within a curved spacetime – the local free-falling frame against which one can measure the acceleration-induced time dilation and degree of curvature relative to flat spacetime. In this article, we use this theorem to prove that a de Sitter expansion, required during cosmic inflation, does not satisfy this condition and is therefore inconsistent with the PoE. To emphasize the importance – and reality – of this outcome, we contrast it with the analogous derivation for the Schwarzschild metric, which instead satisfies this requirement completely. We point out that this failure by de Sitter results from its incorrect handling of the Friedmann–Lemaître–Robertson–Walker (FLRW) lapse function, gtt{g}_{{\rm{tt}}}. Our conclusion calls into question whether a period of inflated expansion could have even been possible in the context of FLRW cosmologies, and is noteworthy in light of recent, high-precision measurements showing that inflation could not have solved the temperature horizon problem while simultaneously producing the observed primordial power spectrum.https://doi.org/10.1515/phys-2024-0077classical theories of gravitycosmological theoryearly universeinflationdark energy |
| spellingShingle | Melia Fulvio Inflation and the principle of equivalence Open Physics classical theories of gravity cosmological theory early universe inflation dark energy |
| title | Inflation and the principle of equivalence |
| title_full | Inflation and the principle of equivalence |
| title_fullStr | Inflation and the principle of equivalence |
| title_full_unstemmed | Inflation and the principle of equivalence |
| title_short | Inflation and the principle of equivalence |
| title_sort | inflation and the principle of equivalence |
| topic | classical theories of gravity cosmological theory early universe inflation dark energy |
| url | https://doi.org/10.1515/phys-2024-0077 |
| work_keys_str_mv | AT meliafulvio inflationandtheprincipleofequivalence |