Noncommutative minisuperspace, gravity-driven acceleration and kinetic inflation

TL;DR

This paper introduces a noncommutative extension of Brans-Dicke cosmology, revealing how noncommutativity influences inflationary dynamics and provides a natural graceful exit from acceleration, offering new insights into early universe behavior.

Contribution

It develops a noncommutative Brans-Dicke model and demonstrates its impact on inflation and cosmic acceleration, extending prior commutative theories with novel dynamical features.

Findings

Noncommutative parameter modifies scale factor and scalar field dynamics.

Inflationary solutions are achievable with small noncommutative parameters.

The model naturally includes a graceful exit from acceleration to deceleration.

Abstract

In this paper, we introduce a noncommutative version of the Brans-Dicke (BD) theory and obtain the Hamiltonian equations of motion for a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker universe filled with a perfect fluid. We focus on the case where the scalar potential as well as the ordinary matter sector are absent. Then, we investigate gravity-driven acceleration and kinetic inflation in this noncommutative BD cosmology. In contrast to the commutative case, in which the scale factor and BD scalar field are in a power-law form, in the noncommutative case the power-law scalar factor is multiplied by a dynamical exponential warp factor. This warp factor depends on the noncommutative parameter as well as the momentum conjugate associated to the BD scalar field. We show that the BD scalar field and the scale factor effectively depend on the noncommutative parameter. For very small values of this parameter, we obtain an appropriate inflationary solution, which can overcome problems within BD standard cosmology in a more efficient manner. Furthermore, a graceful exit from an early acceleration epoch towards a decelerating radiation epoch is provided. For late times, due to the presence of the noncommutative parameter, we obtain a zero acceleration epoch, which can be interpreted as the coarse-grained explanation.