# Noncommutative Friedmann Equations in Effective LQC

## TL;DR

This paper develops a noncommutative extension of Friedmann equations within effective loop quantum cosmology, revealing preserved bounce behavior and potential inflationary effects due to noncommutativity.

## Contribution

It introduces a noncommutative framework in effective LQC, deriving new equations and solutions, and explores implications for inflation and cosmological dynamics.

## Key findings

- Bounce is preserved with unchanged energy density.
- Noncommutativity induces an effective potential in the modified equations.
- Inflationary era possibilities are investigated due to noncommutative effects.

## Abstract

In this work we construct a noncommutative version of the Friedmann equations in the framework of effective loop quantum cosmology, extending and applying the ideas presented in a previous proposal by some of the authors. The model under consideration is a flat FRW spacetime with a free scalar field. First, noncommutativity in the momentum sector is introduced. We establish the noncommutative equations of motion and obtain the corresponding exact solutions. Such solutions indicate that the bounce is preserved, in particular, the energy density is the same as in standard LQC. We also construct a noncommutative version of the modified Friedmann equations and argue that, as a consequence of noncommutativity, an effective potential arises. This, in turn, leads us to investigate the possibility of an inflationary era. Finally, we obtain the Friedmann and the Raychaudhuri equations when implementing noncommutativity in the configuration sector. In this case, no effective potential is induced.