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

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.