The equivalence between Einstein and Jordan frames: a study based on the inflationary magnetogenesis model
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916707475390464 |
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| author | Wang, Hang Liu, Shuang Li, Yu Wang, Yao-chuan |
| author_facet | Wang, Hang Liu, Shuang Li, Yu Wang, Yao-chuan |
| contents | The equivalence of the Jordan and Einstein frames has been a subject of considerable interest in the field. In this paper, within the context of $f(R)$ gravity, we explore the inflationary magnetogenesis model, focusing on the magnetic field energy density and its spectrum in both the Jordan and Einstein frames to elucidate the equivalence between these two reference frames. Our analysis reveals that during the inflationary epoch, while the magnetic field exhibits a scale-invariant spectrum in the Einstein frame, it demonstrates a blue spectrum in the Jordan frame. Additionally, we investigate the post-inflationary evolution of the magnetic field's energy density in both frames, uncovering that for scale-invariant spectra in the Einstein frame during inflation, the magnetic field transitions to a blue spectrum, whereas in the Jordan frame, it evolves into a red spectrum. We also establish the conditions under which both frames may exhibit scale-invariant spectra simultaneously during the inflationary period. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_18005 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The equivalence between Einstein and Jordan frames: a study based on the inflationary magnetogenesis model Wang, Hang Liu, Shuang Li, Yu Wang, Yao-chuan Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology The equivalence of the Jordan and Einstein frames has been a subject of considerable interest in the field. In this paper, within the context of $f(R)$ gravity, we explore the inflationary magnetogenesis model, focusing on the magnetic field energy density and its spectrum in both the Jordan and Einstein frames to elucidate the equivalence between these two reference frames. Our analysis reveals that during the inflationary epoch, while the magnetic field exhibits a scale-invariant spectrum in the Einstein frame, it demonstrates a blue spectrum in the Jordan frame. Additionally, we investigate the post-inflationary evolution of the magnetic field's energy density in both frames, uncovering that for scale-invariant spectra in the Einstein frame during inflation, the magnetic field transitions to a blue spectrum, whereas in the Jordan frame, it evolves into a red spectrum. We also establish the conditions under which both frames may exhibit scale-invariant spectra simultaneously during the inflationary period. |
| title | The equivalence between Einstein and Jordan frames: a study based on the inflationary magnetogenesis model |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2504.18005 |