Features of the primordial Universe in f(R)-gravity as viewed in the Jordan frame

Abstract

We analyze some features of the primordial Universe as viewed in the Jordan frame formulation of the f(R)-gravity when the potential term is negligible. We start formulating the Hamiltonian picture using the three-metric determinant as a basic variable and we outline that its conjugated momentum appears linearly only in the scalar constraint. We construct the formalism to characterize the dynamics of a generic inhomogeneous cosmological model and specialize it to describe behaviors of the Bianchi Universes, both on a classical and a quantum regime. We demonstrate that, when the potential term of the additional scalar mode is negligible near to the initial singularity, the Bianchi IX cosmology is no longer affected by the chaotic behavior, typical in the vacuum of the Einsteinian dynamics. In fact, the presence of the Kasner stability region and its attractive character are properly characterized. Finally, we investigate the canonical quantization of the Bianchi I model, using as time variable the non-minimally coupled scalar field and showing that the existence of a conserved current is outlined for the corresponding Wheeler–DeWitt equation. The behavior of a localized wave-packet for the isotropic Universe is also evolved, demonstrating that the singularity is still present in this revised quantum dynamics.