Kinetic inflation in deformed phase space Brans-Dicke cosmology

TL;DR

This paper introduces a deformed phase space Brans-Dicke cosmology that enables successful inflation without scalar potential or matter, resembling Starobinsky inflation, by employing a dynamical noncommutative deformation.

Contribution

It demonstrates that a dynamical phase space deformation in Brans-Dicke cosmology can overcome previous limitations and produce a viable inflationary epoch.

Findings

Achieves an adequate inflationary phase with graceful exit.

Reproduces conditions for inflation in both Jordan and Einstein frames.

Resembles the Starobinsky R^2 inflation model.

Abstract

In this paper, by establishing a Brans-Dicke (BD) cosmology by means of a deformed phase space, in the absence of any scalar potential, cosmological constant and ordinary matter, we show that it is feasible to overcome obstacles reported in the corresponding commutative (non-deformed) frameworks. More concretely, by applying the Hamiltonian formalism and introducing a dynamical deformation, between the momenta associated to the FLRW scale factor and the BD scalar field, we obtain the modified equations of motion. In particular, these equations reduce to their standard counterparts when the noncommutative (NC) parameter is switched off. By focusing on a specific branch of solutions, in contrast to standard frameworks (even with a varying BD coupling parameter), we show that we can obtain an adequate appropriate inflationary epoch possessing a suitable graceful exit. In other words, in the Jordan frame (JF), such branch of solutions properly satisfy the sufficient condition required for satisfactory inflation, which is equivalent to get an inflationary phase in the conformal Einstein frame (EF) without branch change. Concerning the cosmological dynamics, we further show that our NC framework bears close resemblance to the $R^2$ (Starobinsky) inflationary model.