Softening of gravitational effect on noncommutative spacetime

Abstract

A noncommutative gravitational theory constructed by applying Moyal deformation quantization and the Seiberg–Witten map to teleparallel gravity shows that gravity acts repulsively in an extreme region where its quantum effects become prominent. The problems involved with the order of products and the relationship between the metric and the Moyal product can be solved by assigning their roles, such that the former is responsible for the rule of the inner product and the latter is in charge of tensor and field noncommutativity. As a result, it is found that the cosmic evolution of the very early stage of the universe was modified as if the noncommutative effect works similarly to a cosmological constant. Furthermore it was clarified that the degree of gravitational redshift of a spherically symmetric space with central mass becomes smaller, which means the attractive force is effectively weakened. Such consequences indicate that in the noncommutative spacetime, the gravitational interaction is softened compared to the classical gravity.