A Symmetry of the Einstein–Friedmann Equations for Spatially Flat, Perfect Fluid, Universes
Abstract
:1. Introduction
2. The Symmetry Transformation
3. A Group of Symmetry Transformations
4. Symmetry of the Solutions
5. Conclusions
Funding
Conflicts of Interest
References
- Chimento, L.P. Symmetry and inflation. Phys. Rev. D 2002, 65, 063517. [Google Scholar] [CrossRef]
- Aguirregabiria, J.M.; Chimento, L.P.; Jakubi, A.; Lazkoz, R. Symmetries leading to inflation. Phys. Rev. D 2003, 67, 083518. [Google Scholar] [CrossRef] [Green Version]
- Chimento, L.P.; Lazkoz, R. On the link between phantom and standard cosmologies. Phys. Rev. Lett. 2003, 91, 211301. [Google Scholar] [CrossRef] [Green Version]
- Dabrowski, M.P.; Stachowiak, T.; Szydlowski, M. Phantom cosmologies. Phys. Rev. D 2003, 68, 103519. [Google Scholar] [CrossRef] [Green Version]
- Aguirragabiria, J.M.; Chimento, L.P.; Lazkoz, R. Phantom k-essence cosmologies. Phys. Rev. D 2004, 70, 023509. [Google Scholar] [CrossRef]
- Calcagni, G. Patch dualities and remarks on nonstandard cosmologies. Phys. Rev. D 2005, 71, 023511. [Google Scholar] [CrossRef] [Green Version]
- Szydlowski, M.; Godlowski, W.; Wojtak, R. Equation of state for Universe from similarity symmetries. Gen. Relativ. Gravit. 2006, 38, 795. [Google Scholar] [CrossRef] [Green Version]
- Chimento, L.P.; Lazkoz, R. Duality extended Chaplygin cosmologies with a big rip. Class. Quantum Grav. 2006, 23, 3195–3204. [Google Scholar] [CrossRef]
- Chimento, L.P.; Zimdhal, W. Duality invariance and cosmological dynamics. Int. J. Mod. Phys. D 2008, 17, 2229–2254. [Google Scholar] [CrossRef] [Green Version]
- Chimento, L.P.; Pavon, D. Dual interacting cosmologies and late accelerated expansion. Phys. Rev. D 2006, 73, 063511. [Google Scholar] [CrossRef] [Green Version]
- Dąbrowski, M.P.; Kiefer, C.; Sandhöfer, B. Sandhoefer, Quantum Phantom Cosmology. Phys. Rev. D 2006, 74, 044022. [Google Scholar] [CrossRef] [Green Version]
- Cai, Y.-F.; Li, H.; Piao, Y.-S.; Zhang, X. Duality invariance and cosmological dynamics. Phys. Lett. B 2007, 646, 141. [Google Scholar]
- Chimento, L.P.; Devecchi, F.P.; Forte, M.I.; Kremer, G.M. Phantom cosmologies and fermions. Class. Quantum Grav. 2008, 25, 085007. [Google Scholar] [CrossRef] [Green Version]
- Cataldo, M.; Chimento, L.P. Form invariant transformations between n-dimensional flat Friedmann-Robertson-Walker cosmologies. Int. J. Mod. Phys. D 2008, 17, 1981–1989. [Google Scholar] [CrossRef] [Green Version]
- Capozziello, S.; Piedipalumbo, E.; Rubano, C.; Scudellaro, P. Noether symmetry approach in phantom quintessence cosmology. Phys. Rev. D 2009, 80, 104030. [Google Scholar] [CrossRef] [Green Version]
- Wang, J.; Lan, T.; Yang, S.-P. Cosmic Duality and Statefinder Diagnosis of Spinor Quintom. J. Theor. Phys. 2012, 1, 62–75. [Google Scholar]
- Capozziello, S.; Faraoni, V. Beyond Einstein Gravity; Springer: New York, NY, USA, 2010. [Google Scholar]
- Cai, Y.-F.; Saridakis, E.N.; Setare, M.R.; Xia, J.-Q. Quintom Cosmology: Theoretical implications and observations. Phys. Rep. 2010, 493, 1–60. [Google Scholar] [CrossRef] [Green Version]
- Pucheu, L.; Bellini, M. Phantom and inflation scenarios from a 5D vacuum through form-invariance transformations of the Einstein equations. Nuovo Cimento B 2010, 125, 851–859. [Google Scholar]
- Chimento, L.P.; Lazkoz, R.; Richarte, M.G. Inflation in the Dirac-Born-Infeld framework. Phys. Rev. D 2011, 83, 063505. [Google Scholar] [CrossRef] [Green Version]
- Faraoni, V. A symmetry of the spatially flat Friedmann equations with barotropic fluids. Phys. Lett. B 2011, 703, 228–231. [Google Scholar] [CrossRef] [Green Version]
- Rosu, H.C.; Khmelnytskaya, K.V. Shifted Riccati procedure: Application to conformal barotropic FRW cosmologies. SIGMA 2011, 7, 013. [Google Scholar] [CrossRef]
- Rosu, H.C.; Ojeda-May, P. Supersymmetry of FRW barotropic cosmologies. Int. J. Theor. Phys. 2006, 45, 1191. [Google Scholar] [CrossRef] [Green Version]
- Nowakoswki, M.; Rosu, H.C. Newtons`s Laws of motion in the form of a Riccati equation. Phys. Rev. E 2002, 65, 047602. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Wald, R.M. General Relativity; Chicago University Press: Chicago, IL, USA, 1984. [Google Scholar]
- Carroll, S.M. Spacetime and Geometry: An Introduction to General Relativity; Addison Wesley: San Francisco, CA, USA, 2004. [Google Scholar]
- Faraoni, V. Analogy between freezing lakes and the cosmic radiation era. 2020, submitted. 2020. submitted. [Google Scholar]
© 2020 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 (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Faraoni, V. A Symmetry of the Einstein–Friedmann Equations for Spatially Flat, Perfect Fluid, Universes. Symmetry 2020, 12, 147. https://doi.org/10.3390/sym12010147
Faraoni V. A Symmetry of the Einstein–Friedmann Equations for Spatially Flat, Perfect Fluid, Universes. Symmetry. 2020; 12(1):147. https://doi.org/10.3390/sym12010147
Chicago/Turabian StyleFaraoni, Valerio. 2020. "A Symmetry of the Einstein–Friedmann Equations for Spatially Flat, Perfect Fluid, Universes" Symmetry 12, no. 1: 147. https://doi.org/10.3390/sym12010147