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

## Abstract

**:**

## 1. Clifford Algebra of Space ${\mathbf{Cl}}_{\mathbf{3},\mathbf{0}}$

## 2. Physical Relativity and Uniform Acceleration in Two Dimensions of $\mathbf{Cen}\left({\mathbf{Cl}}_{\mathbf{3},\mathbf{0}}\right)$

## 3. The Scale Factor and AdS Model for ${\mathbf{Cl}}_{\mathbf{3},\mathbf{0}}$

## 4. Clifford Algebra of Anti-Space ${\mathbf{Cl}}_{\mathbf{0},\mathbf{3}}$

## 5. Observed Cosmological Model via Measured Deceleration Parameter

## 6. Discussion

## 7. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

- Vilenkin, A. Cosmological constant problems and their solutions. arXiv
**2001**, arXiv:hep-th/0106083. [Google Scholar] - Weinberg, S. The cosmological constant problem. Rev. Mod. Phys.
**1989**, 61, 1. [Google Scholar] [CrossRef] - Kritov, A. Unified Two Dimensional Spacetime for the River Model of Gravity and Cosmology. Prog. Phys.
**2019**, 15, 163–170. [Google Scholar] - Ablamowicz, E.; Baylis, W.E.; Sobczyk, G. Lectures on Clifford (Geometric) Algebras and Applications; Springer Science + Business Media LLC.: Berlin, Germany, 2003. [Google Scholar]
- Clifford, W.K. Mathematical Papers by William Kingdon Clifford; Tucker, R., Ed.; Macmillan & Co: London, UK, 1882; pp. 266–276. [Google Scholar]
- Clifford, W.K. On the Classification of Geometric Algebras, paper XLIII. In Mathematical Papers of W. K. Clifford; Tucker, R., Ed.; Macmillan & Co: London, UK, 1882. [Google Scholar]
- Lounesto, P. Clifford Algebras and Spinors, 2nd ed.; Cambridge University Press: Cambridge, UK, 2001. [Google Scholar]
- Porteus, I. Clifford Algebras and the Classical Groups; Cambridge University Press: Cambridge, UK, 2005; p. 137. [Google Scholar]
- Hamilton, J. Dwaune The uniformly accelerated reference frame. Am. J. Phys.
**1978**, 46, 83–89. [Google Scholar] [CrossRef] - Møller, C. The Theory of Relativity; Oxford Clarendon Press: Oxford, UK, 1955; p. 75. [Google Scholar]
- Rindler, W. Essential Relativity Special, General, and Cosmological, Revised, 2nd ed.; Springer: New York, NY, USA, 1986; p. 156. [Google Scholar]
- Kritov, A. From the FLRW to the Gravitational Dynamics. Prog. Phys.
**2019**, 15, 145–147. [Google Scholar] - Christillin, P.; Morchio, G. Relativistic Newtonian gravitation. arXiv
**2019**, arXiv:1707.05187. [Google Scholar] - Kritov, A. Approach to the Schwarzschild Metric with SL(2,R) Group Decomposition. Prog. Phys.
**2020**, 16, 139–142. [Google Scholar] - Mitra, A. Interpretational conflicts between the static and non-static forms of the de Sitter metric. Sci. Rep.
**2012**, 2, 923. [Google Scholar] [CrossRef] [PubMed][Green Version] - Rosenfeld, B.A.; Wiebe, B. Geometry of Lie Groups; Springer: New York, NY, USA, 1997. [Google Scholar]
- Rosenfeld, B.A. Non-Euclidean Geometry; State Publishing House of Technical and Theoretical Literature: Moscow, Russia, 1955. (In Russian) [Google Scholar]
- Silberstein, L. Quaternionic Form of Relativity. Philos. Mag.
**1912**, 23, 790–809. [Google Scholar] [CrossRef][Green Version] - Deltete, R.J.; Guy, R.A. Emerging from imaginary time. Synthese
**1996**, 108, 185–203. [Google Scholar] [CrossRef] - Hartle, J.B.; Hawking, S.W. Wave function of the Universe. Phys. Rev. D
**1983**, 28, 2960. [Google Scholar] [CrossRef] - Sazhin, M.V.; Sazhina, O.S.; Chadayammuri, U. The Scale Factor in the Universe with Dark Energy. arXiv
**2011**, arXiv:1109.2258v1. [Google Scholar] [CrossRef][Green Version] - Xu, L.; Zhang, C.; Chang, B.; Liu, H. Reconstruction of Deceleration Parameters from Recent Cosmic Observations. arXiv
**2007**, arXiv:astro-ph/0701519v2. [Google Scholar] - Mamon, A.A. Constraints on a generalized deceleration parameter from cosmic chronometers. arXiv
**2018**, arXiv:1702.04916v2. [Google Scholar] [CrossRef][Green Version] - Gu, Y.Q. Space-Time Geometry and Some Applications of Clifford Algebra in Physics. Adv. Apppl. Clifford Algebr.
**2018**, 28. [Google Scholar] [CrossRef]

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**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