Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Horizon Radius of Spacetime Curvature

Version 1 : Received: 14 May 2020 / Approved: 15 May 2020 / Online: 15 May 2020 (09:49:54 CEST)
Version 2 : Received: 18 May 2020 / Approved: 18 May 2020 / Online: 18 May 2020 (11:37:59 CEST)
Version 3 : Received: 12 June 2020 / Approved: 12 June 2020 / Online: 12 June 2020 (14:30:54 CEST)
Version 4 : Received: 25 August 2020 / Approved: 25 August 2020 / Online: 25 August 2020 (13:50:33 CEST)
Version 5 : Received: 23 September 2020 / Approved: 23 September 2020 / Online: 23 September 2020 (10:41:14 CEST)
Version 6 : Received: 7 October 2020 / Approved: 8 October 2020 / Online: 8 October 2020 (09:43:17 CEST)
Version 7 : Received: 12 October 2020 / Approved: 13 October 2020 / Online: 13 October 2020 (09:38:38 CEST)

How to cite: Al-Fadhli, M. Horizon Radius of Spacetime Curvature . Preprints 2020, 2020050250 (doi: 10.20944/preprints202005.0250.v1). Al-Fadhli, M. Horizon Radius of Spacetime Curvature . Preprints 2020, 2020050250 (doi: 10.20944/preprints202005.0250.v1).


The necessity of the dark energy and dark matter in the present universe could be a consequence of the antimatter elimination assumption in the early universe. In this research, I derive a new model to obtain the potential cosmic topology and the horizon radius of spacetime curvature utilising a new construal of the geometry of space inspired by large-angle correlations of the cosmic microwave background (CMB). I utilise the Big Bounce theory to tune the initial conditions of the curvature density, and to avoid the Big Bang singularity and inflationary constraints. The mathematical derivation of a positively curved universe governed by only gravity revealed horizon solutions. Although the positive horizon is conventionally associated with the evolution of the matter universe, the negative horizon solution could imply additional evolution in the opposite direction. This possibly suggests that the matter and antimatter could be evolving in opposite directions as distinct sides of the universe such as visualised Sloan Digital Sky Survey Data. Using this model, we found a decelerated stage of expansion during the first 10 Gyr, which is followed by a second stage of accelerated expansion; potentially matching the tension in Hubble parameter measurements. In addition, the model predicts a final time-reversal stage of spatial contraction leading to the Big Crunch of a cyclic universe. The predicted density is 1.14. Other predictions are (1) a calculable flow rate of the matter side towards the antimatter side at the accelerated stage; conceivably explaining the dark flow observation, (2) a time-dependent spacetime curvature over horizon evolution, which could influence the galactic rotational speed; possibly explaining the high speed of stars, and (3) evolvable spacetime internal voids at the accelerated stage, which could contribute in continuously increasing the matter and antimatter densities elsewhere in both sides respectively. These findings may indicate the existence of the antimatter as a distinct side, which influences the evolution of the universe instead of the dark energy or dark matter.

Subject Areas

cosmology; horizon; antimatter; accelerated expansion; time-reversal

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