Cosmology of a Polynomial Model for de Sitter Gauge Theory Sourced by a Fluid
Abstract
:1. Introduction
2. De Sitter Gauge Theory
2.1. Lagrangian–Noether Machinery
2.2. Reduction in the Lorentz Gauges
3. Polynomial Models for DGT
3.1. Stelle–West Gravity
3.2. Polynomial dS Fluid
4. Cosmological Solutions
4.1. Field Equations for the Universe
4.2. The Vacuum Solution
4.3. The Material Solution
4.4. Comparison with Observations
5. Remarks
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Kibble, T.W.B. Lorentz invariance and the gravitational field. J. Math. Phys. 1961, 2, 212–221. [Google Scholar] [CrossRef] [Green Version]
- Sciama, D.W. On the analogy between charge and spin in general relativity. In Infeld Festschrift: Recent Developments in General Relativity. A Collection of Papers Dedicated to Leopold Infeld; Pergamon Press: Oxford, UK, 1962; pp. 415–439. [Google Scholar]
- Blagojević, M.; Hehl, F.W. (Eds.) Gauge Theories of Gravitation. A Reader with Commentaries; Imperial College Press: London, UK, 2013. [Google Scholar]
- Ponomarev, V.N.; Barvinsky, A.O.; Obukhov, Y.N. Gauge Approach and Quantization Methods in Gravity Theory; Nauka: Moscow, Russia, 2017; Available online: http://en.ibrae.ac.ru/pubtext/259/ (accessed on 10 September 2022).
- Mielke, E.W. Geometrodynamics of Gauge Fields; Springer International Publishing Switzerland: Cham, Switzerland, 2017. [Google Scholar] [CrossRef]
- Stelle, K.S.; West, P.C. De Sitter gauge invariance and the geometry of the Einstein–Cartan theory. J. Phys. A Math. Theor. 1979, 12, L205–L210. [Google Scholar] [CrossRef]
- Stelle, K.S.; West, P.C. Spontaneously broken de Sitter symmetry and the gravitational holonomy group. Phys. Rev. D 1980, 21, 1466–1488. [Google Scholar] [CrossRef]
- MacDowell, S.W.; Mansouri, F. Unified geometric theory of gravity and supergravity. Phys. Rev. Lett. 1977, 38, 739–742. [Google Scholar] [CrossRef]
- West, P.C. A geometric gravity Lagrangian. Phys. Lett. B 1978, 76, 569–570. [Google Scholar] [CrossRef]
- Westman, H.; Złośnik, T. Exploring Cartan gravity with dynamical symmetry breaking. Class. Quant. Grav. 2014, 31, 95004. [Google Scholar] [CrossRef] [Green Version]
- Magueijo, J.; Rodríguez-Vázquez, M.; Westman, H.; Złośnik, T. Cosmological signature change in Cartan Gravity with dynamical symmetry breaking. Phys. Rev. D 2014, 89, 63542. [Google Scholar] [CrossRef] [Green Version]
- Westman, H.; Złośnik, T. An introduction to the physics of Cartan gravity. Ann. Phys. 2015, 361, 330–376. [Google Scholar] [CrossRef] [Green Version]
- Alexander, S.; Cortês, M.; Liddle, A.; Magueijo, J.; Sims, R.; Smolin, L. The cosmology of minimal varying Lambda theories. Phys. Rev. D 2019, 100, 83507. [Google Scholar] [CrossRef]
- Pagels, H.R. Gravitational gauge fields and the cosmological constant. Phys. Rev. D 1984, 29, 1690–1698. [Google Scholar] [CrossRef]
- Westman, H.; Złośnik, T. Cartan gravity, matter fields, and the gauge principle. Ann. Phys. 2013, 334, 157–197. [Google Scholar] [CrossRef] [Green Version]
- Lu, J.-A. Energy, momentum and angular momentum conservation in de Sitter gravity. Class. Quantum Grav. 2016, 33, 155009. [Google Scholar] [CrossRef] [Green Version]
- Hehl, F.W.; von der Heyde, P.; Kerlick, G.D.; Nester, J.M. General relativity with spin and torsion: Foundations and prospects. Rev. Mod. Phys. 1976, 48, 393–416. [Google Scholar] [CrossRef] [Green Version]
- Hehl, F.W.; McCrea, J.D.; Mielke, E.W.; Ne’eman, Y. Metric-affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance. Phys. Rep. 1995, 258, 1–171. [Google Scholar] [CrossRef] [Green Version]
- Lu, J.-A.; Huang, C.-G. Kaluza–Klein-type models of de Sitter and Poincaré gauge theories of gravity. Class. Quantum Grav. 2013, 30, 145004. [Google Scholar] [CrossRef] [Green Version]
- Guo, H.-Y. The local de Sitter invariance. Kexue Tongbao (Chin. Sci. Bull.) 1976, 21, 31–34. [Google Scholar]
- Obukhov, Y.N. Poincaré gauge gravity: Selected topics. Int. J. Geom. Meth. Mod. Phys. 2006, 3, 95–138. [Google Scholar] [CrossRef]
- Westman, H.; Złośnik, T. Gravity, Cartan geometry, and idealized waywisers. arXiv 2012. [Google Scholar] [CrossRef]
- Brown, J.D. Action functionals for relativistic perfect fluids. Class. Quant. Grav. 1993, 10, 1579–1606. [Google Scholar] [CrossRef] [Green Version]
- Magueijo, J.; Złośnik, T. Parity violating Friedmann Universes. Phys. Rev. D. 2019, 100, 84036. [Google Scholar] [CrossRef]
- Planck Collaboration. Planck 2018 results. VI. Cosmological parameters. Astron. Astrophys. 2020, 641, A6. [Google Scholar] [CrossRef] [Green Version]
- Riess, A.G.; Filippenko, A.V.; Challis, P.; Clocchiatti, A.; Diercks, A.; Garnavich, P.M.; Gilliard, R.L.; Hogan, C.J.; Jsa, S.; Kirshner, R.P. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 1998, 116, 1009–1038. [Google Scholar] [CrossRef] [Green Version]
- Schmidt, B.; Suntzeff, N.B.; Phillips, M.M.; Schommer, R.A.; Clocchiatti, A.; Kirshner, R.P.; Garnavich, P.; Challis, P.; Leibundgut, B.; Spyromilio, J.; et al. The high-Z supernova search: Measuring cosmic deceleration and global curvature of the universe using type IA supernovae. Astrophys. J. 1998, 507, 46–63. [Google Scholar] [CrossRef]
- Perlmutter, S.; Aldering, G.; Goldhaber, G.; Knop, R.A.; Nugent, P.; Castro, P.G.; Deustua, S.; Fabbro, S.; Goobar, A.; Hook, I.M.; et al. Measurements of Omega and Lambda from 42 high redshift supernovae. Astrophys. J. 1999, 517, 565–586. [Google Scholar] [CrossRef]
- Prigogine, I.; Geheniau, J.; Gunzig, E.; Nardone, P. Thermodynamics and cosmology. Gen. Relativ. Gravit. 1989, 21, 767–776. [Google Scholar] [CrossRef]
- Calvão, M.O.; Lima, J.A.S.; Wagal, I. On the thermodynamics of matter creation in cosmology. Phys. Lett. A 1992, 162, 223–226. [Google Scholar] [CrossRef]
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Lu, J.-A. Cosmology of a Polynomial Model for de Sitter Gauge Theory Sourced by a Fluid. Physics 2022, 4, 1168-1179. https://doi.org/10.3390/physics4040076
Lu J-A. Cosmology of a Polynomial Model for de Sitter Gauge Theory Sourced by a Fluid. Physics. 2022; 4(4):1168-1179. https://doi.org/10.3390/physics4040076
Chicago/Turabian StyleLu, Jia-An. 2022. "Cosmology of a Polynomial Model for de Sitter Gauge Theory Sourced by a Fluid" Physics 4, no. 4: 1168-1179. https://doi.org/10.3390/physics4040076