Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates

Version 1 : Received: 24 January 2021 / Approved: 26 January 2021 / Online: 26 January 2021 (15:55:06 CET)
Version 2 : Received: 3 February 2021 / Approved: 5 February 2021 / Online: 5 February 2021 (10:13:00 CET)

A peer-reviewed article of this Preprint also exists.

Kritov, A. Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates. Symmetry 2021, 13, 366. Kritov, A. Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates. Symmetry 2021, 13, 366.

Journal reference: Symmetry 2021, 13, 366
DOI: 10.3390/sym13030366

Abstract

The recently proposed model of the "unified two-dimensional spacetime"[18] shows substantial conformity to Clifford algebras Cl3,0 and Cl0,3. As shown, such two-dimensional spacetime of time and volume corresponds to two Clifford coordinates given by a center of the respective algebra. In the application to comoving frame, the model results in the exact form of the scale factor of the FLRW metric of modern cosmology. This paper formulates and formalizes the approach using Clifford algebras. The study concludes that the Clifford algebra of space (APS)Cen(Cl3,0) has an intrinsic correspondence with the anti-de Sitter (AdS) flat universe and the negative cosmological term that results in an oscillating model of the universe. The approach with anti-Euclidean Clifford algebra Cen(Cl0,3) leads to the de Sitter model with a positive cosmological term. As reviewed, the Clifford algebra has isomorphic algebras and Lie groups corresponding to different from Minkowski spacetime, such as SO(4); therefore, further study may be required regarding their relation to gravitation.

Subject Areas

Clifford algebras Cl(3,0) and Cl(0,3); center of Cl(3); two dimensional spacetime of time-volume; constant uniform acceleration; Rindler coordinates; FLRW metric; scale factor; AdS and de Sitter models

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