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

Faculty of Physics Moscow, Lomonosov Moscow State University, 119991 Moscow, Russia
Academic Editor: Jaime Haro Cases
Symmetry 2021, 13(3), 366; https://doi.org/10.3390/sym13030366
Received: 16 January 2021 / Revised: 14 February 2021 / Accepted: 19 February 2021 / Published: 24 February 2021
(This article belongs to the Section Physics and Symmetry/Asymmetry)
This paper presents a novel approach to the cosmological constant problem by the use of the Clifford algebras of space Cl3,0 and anti-space Cl0,3 with a particular focus on the paravector representation, emphasizing the fact that both algebras have a 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 3H0c. 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 Cl3,0 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 Cl0,3 leads to the de Sitter model with the positive cosmological term and the exact form of the scale factor used in modern cosmology. View Full-Text
Keywords: cosmological constant problem; Clifford algebras; Cl(3,0); Cl(0,3); two-dimensional spacetime; time-volume coordinates; uniform acceleration 3Hc; Rindler coordinates; FLRW metric; scale factor; AdS and de Sitter models cosmological constant problem; Clifford algebras; Cl(3,0); Cl(0,3); two-dimensional spacetime; time-volume coordinates; uniform acceleration 3Hc; Rindler coordinates; FLRW metric; scale factor; AdS and de Sitter models
MDPI and ACS Style

Kritov, A. Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates. Symmetry 2021, 13, 366. https://doi.org/10.3390/sym13030366

AMA Style

Kritov A. Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates. Symmetry. 2021; 13(3):366. https://doi.org/10.3390/sym13030366

Chicago/Turabian Style

Kritov, Alexander. 2021. "Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates" Symmetry 13, no. 3: 366. https://doi.org/10.3390/sym13030366

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