Curving Flat Space-Time by Deformation Quantization?

TL;DR

This paper introduces a method to derive curved space-time metrics from flat space-time using deformation quantization, leading to models like FRW and non-commutative space-times with solutions to Einstein's equations.

Contribution

It presents a novel approach to generate curved metrics via deformation quantization, connecting flat space-time to cosmological models and non-commutative geometries.

Findings

Derived FRW inflation model from deformation parameters.

Obtained non-trivial Einstein solutions in deformed space-time.

Established conditions for constant non-commutative space-time.

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, by a consistency condition.