We study the possible existence of static traversable wormholes without invoking exotic matter in the framework of the Einstein-Cartan theory. A family of exact static, spherically symmetric wormhole solutions with an arbitrary throat radius, with flat or AdS asymptotic behavior, has been obtained with sources in the form of two noninteracting scalar fields with nonzero potentials. Both scalar fields are canonical (that is, satisfy the weak energy condition), one is minimally and the other nonminimally coupled to gravity, and the latter is a source of torsion.

We obtain a family of regular static, spherically symmetric solutions in Einstein-Cartan theory with an electromagnetic field and a nonminimally coupled scalar field with the correct sign of kinetic energy density. At different values of its parameters, the solution, being asymptotically flat at large values of the radial coordinate, describes (i) twice asymptotically flat symmetric wormholes, (ii) asymmetric wormholes with an AdS asymptotic at the "far end", (iii) regular black holes with an extremal horizon or two simple horizons, and (iv) black universes with a de Sitter asymptotic at the "far end". As in other black universe models, it is a black hole as seen by a distant observer, but beyond its horizon there is a nonsingular expanding universe. In all these cases, both the metric and the torsion are regular in the whole space.

Exact general solutions to the Einstein–Cartan equations are obtained for spatially flat isotropic and homogeneous cosmologies with a nonminimally coupled scalar field. It is shown that both singular and nonsingular models are possible. Exact general solutions of an analogous problem in the torsion-less case are derived. The role of torsion in the evolution of models is elucidated.

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.

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