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.