Big-bounce and future time singularity resolution in Bianchi I: the projective invariant Nieh-Yan case

Abstract

We extend the notion of the Nieh-Yan invariant to generic metric-affine geometries, where both torsion and nonmetricity are taken into account. Notably, we show that the properties of projective invariance and topologicity can be independently accommodated by a suitable choice of the parameters featuring this new Nieh-Yan term. We then consider a special class of modified theories of gravity able to promote the Immirzi parameter to a dynamical scalar field coupled to the Nieh-Yan form, and we discuss in more detail the dynamics of the effective scalar tensor theory stemming from such a revised theoretical framework. We focus, in particular, on cosmological Bianchi I models and we derive classical solutions where the initial singularity is safely removed in favor of a big-bounce, which is ultimately driven by the non-minimal coupling with the Immirzi field. These solutions, moreover, turn out to be characterized by finite time singularities, but we show that such critical points do not spoil the geodesic completeness and wave regularity of these space-times.

Constraints on the Nieh-Yan modified teleparallel gravity with gravitational waves

“…The cosmological perturbations and parametrized post-Newtonian limit in this theory have also been explored recently in [53,54,56]. Some other parity vio-lating theories in the framework of teleparallel gravity or with Nieh-Yan term have also been considered in [58][59][60][61].…”

Induced gravitational topological term and the Einstein-Cartan modified theory

“…It is worth mentioning that these invariants allow to break CPT, and in certain cases Lorentz symmetry [12]. In a scenario involving non-trivial torsion, it is possible to construct another topological invariant which is the Nieh-Yan term [14,15]. Both topological invariants, Pontryagin and Nieh-Yan terms, will be studied in the present paper.…”