The Hyperboloidal Universe

Christopher Laforet

doi:10.20944/preprints202201.0301.v12

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preprints.org > physical sciences > astronomy and astrophysics > doi: 10.20944/preprints202201.0301.v12

Preprint Article Version 12 Preserved in Portico This version is not peer-reviewed

The Hyperboloidal Universe

Christopher Laforet

Version 1 : Received: 18 January 2022 / Approved: 20 January 2022 / Online: 20 January 2022 (11:11:44 CET)
Version 2 : Received: 28 January 2022 / Approved: 31 January 2022 / Online: 31 January 2022 (12:56:14 CET)
Version 3 : Received: 16 March 2022 / Approved: 17 March 2022 / Online: 17 March 2022 (10:54:26 CET)
Version 4 : Received: 20 March 2022 / Approved: 21 March 2022 / Online: 21 March 2022 (08:59:59 CET)
Version 5 : Received: 1 May 2022 / Approved: 4 May 2022 / Online: 4 May 2022 (12:51:42 CEST)
Version 6 : Received: 15 May 2022 / Approved: 16 May 2022 / Online: 16 May 2022 (12:17:54 CEST)
Version 7 : Received: 20 May 2022 / Approved: 23 May 2022 / Online: 23 May 2022 (10:35:10 CEST)
Version 8 : Received: 30 May 2022 / Approved: 31 May 2022 / Online: 31 May 2022 (09:11:40 CEST)
Version 9 : Received: 18 July 2022 / Approved: 19 July 2022 / Online: 19 July 2022 (10:32:16 CEST)
Version 10 : Received: 30 August 2022 / Approved: 31 August 2022 / Online: 31 August 2022 (14:35:15 CEST)
Version 11 : Received: 28 September 2022 / Approved: 29 September 2022 / Online: 29 September 2022 (10:04:38 CEST)
Version 12 : Received: 20 October 2022 / Approved: 21 October 2022 / Online: 21 October 2022 (11:18:22 CEST)
Version 13 : Received: 29 December 2022 / Approved: 4 January 2023 / Online: 4 January 2023 (12:00:14 CET)
Version 14 : Received: 7 January 2023 / Approved: 9 January 2023 / Online: 9 January 2023 (11:01:51 CET)
Version 15 : Received: 12 February 2023 / Approved: 13 February 2023 / Online: 13 February 2023 (16:12:56 CET)
Version 16 : Received: 10 March 2023 / Approved: 13 March 2023 / Online: 13 March 2023 (09:47:07 CET)
Version 17 : Received: 21 July 2023 / Approved: 21 July 2023 / Online: 24 July 2023 (08:08:52 CEST)
Version 18 : Received: 17 March 2024 / Approved: 19 March 2024 / Online: 19 March 2024 (12:58:11 CET)
Version 19 : Received: 12 June 2024 / Approved: 13 June 2024 / Online: 13 June 2024 (09:35:50 CEST)
Version 20 : Received: 5 July 2024 / Approved: 8 July 2024 / Online: 9 July 2024 (07:06:37 CEST)

How to cite: Laforet, C. The Hyperboloidal Universe. Preprints 2022, 2022010301. https://doi.org/10.20944/preprints202201.0301.v12 Laforet, C. The Hyperboloidal Universe. Preprints 2022, 2022010301. https://doi.org/10.20944/preprints202201.0301.v12

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MDPI and ACS Style

Laforet, C. The Hyperboloidal Universe. Preprints 2022, 2022010301. https://doi.org/10.20944/preprints202201.0301.v12

APA Style

Laforet, C. (2022). The Hyperboloidal Universe. Preprints. https://doi.org/10.20944/preprints202201.0301.v12

Chicago/Turabian Style

Laforet, C. 2022 "The Hyperboloidal Universe" Preprints. https://doi.org/10.20944/preprints202201.0301.v12

Abstract

This paper investigates a relativistic model of the Universe in which the geometry describes a 4D version of the 2-sheeted hyperboloid that is isotropic, homogeneous in space at a given time and inhomogeneous in time. The internal Schwarzschild metric is used for this model, which is justified by the fact that spherically-symmetric empty spaces in the Universe are effectively surrounded by a shell of infinite mass (the surrounding Universe). Thus the metric for the empty spaces must be described by the Schwarzschild metric according to Birkhoff’s theorem. Since the shell’s mass is infinite, the external solution cannot describe this spacetime and therefore the internal Schwarzschild solution must be the correct metric for this spacetime. The model predicts both a Universe and Anti-Universe moving in opposite directions of time undergoing an expansion phase, followed by a collapsing phase. Using only the current coordinate age of the Universe and transition redshift, it predicts the accelerated expansion and it is shown that its Hubble diagram fits currently available supernova and quasar data as well as predicting a Hubble constant H₀ ≈ 71.6km/s/M pc. The angular term of the metric describes time dilation caused by the relativistic kinematic precession effect known as Thomas Precession which can be interpreted as spin about the time dimension. This precession results in novel Coriolis accelerations that affect the trajectories of both massive and massless particles in the Universe. The model also makes two novel predictions: that the early Universe should have structures older than expected due to an increased amount of proper time relative to coordinate time in that era and that the background Universe should appear brighter than current models predict.

Keywords

Cosmology; Black holes; Dark Energy; Schwarzschild metric

Subject

Physical Sciences, Astronomy and Astrophysics

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: 21 October 2022
Commenter: Christopher Laforet
Commenter's Conflict of Interests: Author

Comment: Finally pinned down the justification for using the internal Schwarzschild metric for the model by noting that the pockets of spherically-symmetric vacua in the Universe are effectively surrounded by a shell of infinite mass. Because it is a spherically symmetric vacuum, it must be described by the Schwarzschild metric, but since the mass of the shell is infinite, we cannot use the external metric to describe that spacetime. Therefore, the internal metric must be the description for the vacuum of the Universe. Also updated the abstract.

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