Curving flat space-time by deformation quantization?

Abstract

We use a deformed differential structure to obtain a curved metric by a deformation quantization of the flat space-time. In particular, by setting the deformation parameters to be equal to physical constants, we obtain the Friedmann-Robertson-Walker (FRW) model for inflation and a deformed version of the FRW space-time. By calculating classical Einstein-equations for the extended space-time, we obtain non-trivial solutions. Moreover, in this framework, we obtain the Moyal-Weyl, i.e., a constant non-commutative space-time, as a consistency condition.