Submitted:
03 February 2021
Posted:
05 February 2021
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Abstract
The paper briefly reviews the Clifford algebras of space Cl(3,0) and anti-space Cl(0,3) with a particular focus on the paravector representation, emphasizing the fact that both algebras have an isomorphic center represented just by two coordinates. Since the paravector representation allows assigning the scalar element of grade 0 to the time coordinate, we consider the relativity in such two-dimensional spacetime for a uniformly accelerated frame with the constant acceleration 3Hc. Using the Rindler coordinate transformations in two-dimensional spacetime and then applying it to Minkowski coordinates, we obtain the FLRW metric, which in the case of the Clifford algebra of space Cl(3,0) corresponds to the anti-de Sitter (AdS) flat (k=0) case, the negative cosmological term and an oscillating model of the universe. The approach with anti-Euclidean Clifford algebra Cl(0,3) leads to the de Sitter model with the positive cosmological term and the exact form of the scale factor used in modern cosmology.
Keywords:
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
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
