Planck mass and Dilaton field as a function of the noncommutative parameter

TL;DR

This paper derives how noncommutative geometry modifies the Planck mass and space-time structure, using a deformed Bianchi type I metric and gauge gravity to second order in noncommutativity.

Contribution

It introduces a model connecting noncommutative parameters with modifications to the Einstein-Hilbert action and Planck mass.

Findings

Planck mass depends on the noncommutative parameter { heta}

Noncommutativity alters space-time topology and structure

Derived scalar curvature up to second order in noncommutativity

Abstract

A deformed Bianchi type I metric in noncommutative gauge gravity is obtained. The gauge potential (tetrad fields) and scalar curvature are determined up to the second order in the noncommutativity parameters. The noncommutativity correction to the Einstein-Hilbert action is deduced. We obtain the Planck mass, on noncommutative space-time as a function of the noncommutative parameter {\theta}, which implies that noncommutativity has modified the structure and topology of the space-time.