Non-commutative DKP equation and pair creation in curved space-time

TL;DR

This paper investigates how non-commutativity affects the DKP equation in curved space-time, revealing that non-commutativity reduces particle density and increases pair creation rates as the non-commutative parameter decreases.

Contribution

It introduces a first-order non-commutative correction to the DKP equation in curved space-time and analyzes its impact on boson pair creation from vacuum.

Findings

Non-commutative density of particles decreases with increasing non-commutativity parameter.

Particle creation rate increases as the non-commutativity parameter decreases.

The study links non-commutativity to quantum mechanical behavior in curved space-time.

Abstract

This study is about the application of the non-commutativity on the DKP equation up to first order in $\theta $ for the process of pair-creation of bosons from vacuum in (1+1) curved space-time. The density of particles created in the vacuum can be calculated with the help of the Bogoliubov transformations. The non-commutative density of created particles is found to decrease as $\frac{1% }{\sqrt{\theta }}\sim \Lambda _{NC},$, so that the rate of particle creation increases whenever a non-commutativity parameter is small and this corresponds to the spirit of quantum mechanics.