Extended General Relativity for a Curved Universe

Mohammed B. Al-Fadhli

doi:10.20944/preprints202010.0320.v4

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preprints.org > physical sciences > particle and field physics > doi: 10.20944/preprints202010.0320.v4

Preprint Article Version 4 Preserved in Portico This version is not peer-reviewed

Extended General Relativity for a Curved Universe

Mohammed B. Al-Fadhli

Version 1 : Received: 15 October 2020 / Approved: 15 October 2020 / Online: 15 October 2020 (11:47:59 CEST)
Version 2 : Received: 18 October 2020 / Approved: 19 October 2020 / Online: 19 October 2020 (10:43:06 CEST)
Version 3 : Received: 5 November 2020 / Approved: 6 November 2020 / Online: 6 November 2020 (13:11:37 CET)
Version 4 : Received: 1 January 2021 / Approved: 4 January 2021 / Online: 4 January 2021 (11:21:08 CET)
Version 5 : Received: 17 June 2021 / Approved: 17 June 2021 / Online: 17 June 2021 (14:08:56 CEST)
Version 6 : Received: 18 November 2021 / Approved: 18 November 2021 / Online: 18 November 2021 (13:17:29 CET)
Version 7 : Received: 14 April 2022 / Approved: 14 April 2022 / Online: 14 April 2022 (12:28:49 CEST)
Version 8 : Received: 6 June 2022 / Approved: 6 June 2022 / Online: 6 June 2022 (12:05:33 CEST)
Version 9 : Received: 10 January 2023 / Approved: 12 January 2023 / Online: 12 January 2023 (02:02:53 CET)

How to cite: Al-Fadhli, M.B. Extended General Relativity for a Curved Universe. Preprints 2020, 2020100320. https://doi.org/10.20944/preprints202010.0320.v4 Al-Fadhli, M.B. Extended General Relativity for a Curved Universe. Preprints 2020, 2020100320. https://doi.org/10.20944/preprints202010.0320.v4

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MDPI and ACS Style

Al-Fadhli, M.B. Extended General Relativity for a Curved Universe. Preprints 2020, 2020100320. https://doi.org/10.20944/preprints202010.0320.v4

APA Style

Al-Fadhli, M.B. (2021). Extended General Relativity for a Curved Universe. Preprints. https://doi.org/10.20944/preprints202010.0320.v4

Chicago/Turabian Style

Al-Fadhli, M.B. 2021 "Extended General Relativity for a Curved Universe" Preprints. https://doi.org/10.20944/preprints202010.0320.v4

Abstract

The recent Planck Legacy release revealed the presence of an enhanced lensing amplitude in the cosmic microwave background (CMB). Notably, this amplitude is higher than that estimated by the lambda cold dark matter model (ΛCDM), which endorses the positive curvature of the early Universe with a confidence level greater than 99%. Although General Relativity (GR) performs accurately in the local/present Universe where spacetime is almost flat, its lost boundary term, incompatibility with quantum mechanics and the necessity of dark matter and dark energy might indicate its incompleteness. By utilising the Einstein–Hilbert action, this study presents extended field equations considering the pre-existing/background curvature and the boundary contribution. The extended field equations consist of Einstein field equations with a conformal transformation feature in addition to the boundary term, which could remove singularities from the theory and facilitate its quantisation. The extended equations have been utilised to derive the evolution of the Universe with reference to the scale factor of the early Universe and its radius of curvature.

Keywords

General Relativity; Curved Universe

Subject

Physical Sciences, Particle and Field Physics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Comments (1)

Comment 1

Received: 4 January 2021
Commenter: Mohammed Al-Fadhli
Commenter's Conflict of Interests: Author

Comment: Dear Editor,

I hope you are doing very well

This version includes the utilisation of the extended field equations to model the Universe's evolution

A very happy new year with best wishes

Kindest regards,
Mohammed

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