A study on the Friedmann-like Universe with torsion using Noether symmetry

This paper deals with the symmetry analysis of the Einstein Cartan Theory [E. Cartan, C. R. Acad. Sci. (Paris) 174, 593 (1922); E. Cartan, Ann. Sci. Ec. Norm. Super 40, 325 (1923)] which is an extension of the general relativity and it accounts for the spacetime torsion [S. Basilakos et al., Phys. Rev. D 88, 103526 (2013)]. We begin by applying Noether theorem [S. Capozziello, La Rivista del Nuovo Cimento (1978-1999) 19(4), 1 (1996)] to the Lagrangian of the FRW type cosmology with torsion and choose a point transformation: (a,ϕ,N) → (u,v,W), such that one of the transformed variables is cyclic [S. Capozziello, M. De Laurentis and S. D. Odintsov, Eur. Phys. J. C 72, 2068 (2012)] for the Lagrangian. Then using the conserved charge [S. Capozziello, M. De Laurentis and S. D. Odintsov, Eur. Phys. J. C 72, 2068 (2012)], 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, C. G. Tsagas, J. D. Barrow and D. Iosifidis, Eur. Phys. J. C 79, 341 (2019)].