Deformed spaces and loop cosmology

TL;DR

This paper introduces a deformed algebraic framework that reproduces non-singular bouncing solutions in loop quantum cosmology, connecting it to Snyder space and $ppa$-Poincare9 symmetries, and proposes a generalized uncertainty principle.

Contribution

It presents a novel deformed minisuperspace algebra that unifies loop quantum cosmology, Snyder space, and braneworld models, and introduces a generalized uncertainty principle.

Findings

Reproduces bouncing solutions of loop quantum cosmology

Connects deformed algebra to Snyder space and $ppa$-Poincare9

Proposes a generalized uncertainty principle for cosmology

Abstract

The non-singular bouncing solution of loop quantum cosmology is reproduced by a deformed minisuperspace Heisenberg algebra. This algebra is a realization of the Snyder space, is almost unique and is related to the $\kappa$-Poincar\'e one. Since the sign of the deformation parameter it is not fixed, the Friedmann equation of braneworlds theory can also be obtained. Moreover, the sign is the only freedom in the picture and these frameworks are the only ones which can be reproduced by our deformed scheme. A generalized uncertainty principle for loop quantum cosmology is also proposed.