Noncommutative corrections to the Robertson-Walker metric

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 timelike geodesics and the result resembles a bouncing cosmology.