Spin-2 fields from torsion: Dark energy and bouncing cosmology

Abstract

We study a modified theory of gravitation built on a restricted Riemann–Cartan space-time, characterized by reduction in the number of degrees of freedom of torsion. The dynamics is defined by the Einstein–Cartan action of the Einstein–Cartan–Sciama–Kibble (ECSK) theory, while the kinematical structure is defined in such a way that the general-relativistic kinematics is recovered in the associated Riemannian space-time. In this case, the torsion is automatically decomposed into two spin-2 fields with energies of opposite sign. Investigated is the special case where these spin-2 fields are “sterile” (i.e., only interact with other matter fields through gravitation) and have their number of degrees of freedom further reduced to only one. When these fields are furnished with a conservative self-interaction potential, the spatially homogeneous and isotropic cosmological solution obtained via numerical integration of the field equations exhibits accelerated expansion compatible with the current observational data, while the equation of state of both spin-2 fields have values confined in the interval between −1 and −1/3 during the whole cosmic history. Moreover, the present model exhibits nonsingular (bouncing) cosmological solutions.