A study on the Friedmann-like Universe with torsion using Noether symmetry. (English) Zbl 1432.83045

Summary: This paper deals with the symmetry analysis of the Einstein Cartan Theory [E. Cartan, C. R. Acad. Sci., Paris 174, 593–595 (1922; JFM 48.0854.02); Ann. Sci. Éc. Norm. Supér. (3) 40, 325–412 (1923; JFM 49.0542.02)] which is an extension of the general relativity and it accounts for the spacetime torsion [S. Basilakos et al., “Noether symmetries and analytical solutions in \(f(T)\) cosmology: a complete study”, Phys. Rev. D (3) 88, No. 10, Artcile ID 103526, 12 p. (2013; doi:10.1103/PhysRevD.88.103526)]. We begin by applying Noether theorem [S. Capozziello et al., “Nöther symmetries in cosmology”, Riv. Nuovo Cimento 19, No. 4, 1–114 (1996; doi:10.1007/BF02742992)] to the Lagrangian of the FRW type cosmology with torsion and choose a point transformation: \((a,\phi,N)\to(u,v,W)\), such that one of the transformed variables is cyclic [S. Capozziello, M. De Laurentis and S. D. Odintsov, “Hamiltonian dynamics and Noether symmetries in extended gravity cosmology”, Eur. Phys. J. C, Part. Fields 72, Article No. 2068, 21 p. (2012; doi:10.1140/epjc/s10052-012-2068-0)] for the Lagrangian. Then using the conserved charge [Capozziello, De Laurentis and Odintsov, loc. cit.], which is obtained by applying Noether theorem, and the constant of motion, we get the solutions and conclude that due to the presence of torsion, the FRW type cosmology is in the de Sitter phase [D. Kranas et al., “Friedmann-like universes with torsion”, ibid. 79, Article No. 341, 12 p. (2019; doi:10.1140/epjc/s10052-019-6822-4)].


83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83F05 Relativistic cosmology
83C40 Gravitational energy and conservation laws; groups of motions
Full Text: DOI arXiv


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