Noncommutative Corrections to the Robertson-Walker metric

TL;DR

This paper derives first-order noncommutative corrections to the Robertson-Walker metric, revealing potential singularity resolution and bouncing cosmology features through a modified, isotropic inhomogeneous spacetime structure.

Contribution

It introduces a novel application of noncommutative gravity to cosmology, showing how noncommutativity can alter singularity behavior in the Robertson-Walker metric.

Findings

Noncommutative corrections lead to an isotropic inhomogeneous metric.

Singularity at t=0 can be replaced by a non-singular structure.

Possible emergence of bouncing cosmology scenarios.

Abstract

Upon applying Chamseddine's noncommutative deformation of gravity we obtain the leading order noncommutative corrections to the Robertson-Walker metric tensor. We get an isotropic inhomogeneous metric tensor for a certain choice of the noncommutativity parameters. Moreover, the singularity of the commutative metric at $t=0$ is replaced by a more involved space-time structure in the noncommutative theory. In a toy model we construct a scenario where there is no singularity at $t=0$ at leading order in the noncommutativity parameter. Although singularities may still be present for nonzero $t$, they need not be the source of all time-like geodesics and the result resembles a bouncing cosmology.