(Pre)-Inflationary Dynamics with Starobinsky Potential in Noncommutative Effective LQC

TL;DR

This paper explores the early universe's inflationary behavior using the Starobinsky potential within noncommutative loop quantum cosmology, analyzing different energy regimes and comparing with previous models.

Contribution

It introduces a numerical and dynamical systems analysis of the Starobinsky potential in noncommutative effective LQC, extending prior work beyond quadratic potentials.

Findings

Different initial conditions lead to varied inflationary dynamics.

The noncommutative parameter influences the evolution of the scalar field.

Results show qualitative agreement with previous quadratic potential studies.

Abstract

In this work, we investigate the (pre)-inflationary dynamics of a flat, homogeneous, and isotropic universe governed by the Starobinsky potential within the framework of noncommutative effective loop quantum cosmology. The field equations are solved numerically for various initial conditions and different values of the noncommutative parameter. We analyze the background dynamics for three representative regimes -- the extreme kinetic-energy domination, kinetic-energy domination, and potential-energy domination. A complementary analysis is performed from the viewpoint of dynamical systems, highlighting the qualitative features of the scalar field evolution. Finally, a discussion comparing our results with previous studies employing the chaotic (quadratic) potential in the same formalism is presented.