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The equivalence between Einstein and Jordan frames: a study based on the inflationary magnetogenesis model.

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Title: The equivalence between Einstein and Jordan frames: a study based on the inflationary magnetogenesis model.
Authors: Wang, Hang1 (AUTHOR) wang-hang@dlmu.edu.cn, Liu, Shuang1 (AUTHOR) 1120240893shuangliu@dlmu.edu.cn, Li, Yu1 (AUTHOR) leeyu@dlmu.edu.cn, Wang, Yao-Chuan1 (AUTHOR) ycwang@dlmu.edu.cn
Source: International Journal of Modern Physics D: Gravitation, Astrophysics & Cosmology. Jan2026, Vol. 35 Issue 2, p1-19. 19p.
Subjects: Magnetic fields, Frames of reference (Relativity), Frequency spectra, Energy density, Inflationary universe, Cosmic magnetic fields, Einstein, Albert, 1879-1955
Abstract: 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. And we compared our findings with the results derived from the analysis of observational data by other researchers and found them to be consistent. 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. Finally, we discuss the validity of our conclusions for other f (R) gravity theories. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Modern Physics D: Gravitation, Astrophysics & Cosmology is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 190956492
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: The equivalence between Einstein and Jordan frames: a study based on the inflationary magnetogenesis model.
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  Data: <searchLink fieldCode="AR" term="%22Wang%2C+Hang%22">Wang, Hang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wang-hang@dlmu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Liu%2C+Shuang%22">Liu, Shuang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> 1120240893shuangliu@dlmu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Li%2C+Yu%22">Li, Yu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> leeyu@dlmu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Yao-Chuan%22">Wang, Yao-Chuan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ycwang@dlmu.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Modern+Physics+D%3A+Gravitation%2C+Astrophysics+%26+Cosmology%22">International Journal of Modern Physics D: Gravitation, Astrophysics & Cosmology</searchLink>. Jan2026, Vol. 35 Issue 2, p1-19. 19p.
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  Data: <searchLink fieldCode="DE" term="%22Magnetic+fields%22">Magnetic fields</searchLink><br /><searchLink fieldCode="DE" term="%22Frames+of+reference+%28Relativity%29%22">Frames of reference (Relativity)</searchLink><br /><searchLink fieldCode="DE" term="%22Frequency+spectra%22">Frequency spectra</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+density%22">Energy density</searchLink><br /><searchLink fieldCode="DE" term="%22Inflationary+universe%22">Inflationary universe</searchLink><br /><searchLink fieldCode="DE" term="%22Cosmic+magnetic+fields%22">Cosmic magnetic fields</searchLink><br /><searchLink fieldCode="DE" term="%22Einstein%2C+Albert%2C+1879-1955%22">Einstein, Albert, 1879-1955</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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. And we compared our findings with the results derived from the analysis of observational data by other researchers and found them to be consistent. 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. Finally, we discuss the validity of our conclusions for other f (R) gravity theories. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Modern Physics D: Gravitation, Astrophysics & Cosmology is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1142/S0218271825500944
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      – Code: eng
        Text: English
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        PageCount: 19
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      – SubjectFull: Magnetic fields
        Type: general
      – SubjectFull: Frames of reference (Relativity)
        Type: general
      – SubjectFull: Frequency spectra
        Type: general
      – SubjectFull: Energy density
        Type: general
      – SubjectFull: Inflationary universe
        Type: general
      – SubjectFull: Cosmic magnetic fields
        Type: general
      – SubjectFull: Einstein, Albert, 1879-1955
        Type: general
    Titles:
      – TitleFull: The equivalence between Einstein and Jordan frames: a study based on the inflationary magnetogenesis model.
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            NameFull: Wang, Hang
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            NameFull: Liu, Shuang
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            NameFull: Li, Yu
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            NameFull: Wang, Yao-Chuan
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            – D: 30
              M: 01
              Text: Jan2026
              Type: published
              Y: 2026
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              Value: 35
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            – TitleFull: International Journal of Modern Physics D: Gravitation, Astrophysics & Cosmology
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