Cosmology with polynomial potentials of the fourth degree in Einstein–Cartan theory

Abstract

Exact general solutions to the Einstein–Cartan equations are obtained for spatially flat isotropic and homogeneous cosmologies with a nonminimally coupled scalar field that has polynomial potentials of the fourth degree V(Φ). An analogous problem is investigated in Einstein's theory of general relativity. Some effects of torsion are elucidated. A comparative analysis of the cosmological models with and without V(Φ) is carried out in the context of the Einstein–Cartan theory. The role of the scalar field potential in the dynamics of models is discussed.

Stiff Fluid in Accelerated Universes with Torsion

“…In order to elucidate the role of the stiff fluid in the Einstein-Cartan cosmology, we should carry out a comparative analysis of the corresponding cosmological models obtained in this paper and those in [12] for "Scalar-torsion field" and in [13] for "Scalar-torsion field" + " (Φ). "…”

“…Different theoretical models of DE have been put forward (see, e.g., the reviews [7][8][9][10] and references therein). Among these models various modifications of general relativity (GR) were considered, the Einstein-Cartan theory (ECT) in particular [11][12][13]. This theory [14][15][16][17] is an extension of GR to a space time with torsion, and it reduces to GR when the torsion vanishes.…”

“…The exact general solutions for spatially flat FRW cosmologies with a nonminimally coupled scalar field that has polynomial potentials of the fourth degree (Φ) have been obtained in [13]. The main results for the material scalar field are as follows.…”

Nonminimally coupled scalar field and perfect fluid in Einstein–Cartan cosmology

“…It must be noted that the method of deriving exact solutions and their asymptotics has been demonstrated in detail in [13]. It is convenient to discuss separately the cases ξ > 0 and ξ < 0.…”

Wormholes and black universes without phantom fields in Einstein-Cartan theory

“…Moreover, the existence of bouncing cosmologies in the ECT [11] shows that torsion can replace "exotic" sources, violating the weak and null energy conditions (WEC and NEC). As is well known, such a violation is in GR a necessary condition for the existence of traversable wormholes [25].…”