\(\kappa \)-deformed power spectrum and modified Unruh temperature

Abstract

We study the power spectrum of the uniformly accelerating scalar field, obeying the \(\kappa \)-deformed Klein–Gordon equation. From this we obtain the \(\kappa \)-deformed corrections to the Unruh temperature, valid up to first order in the \(\kappa \)-deformation parameter a. We also show that in the small acceleration limit, this expression for the Unruh temperature in \(\kappa \)-deformed space-time is in exact agreement with the one derived from the \(\kappa \)-deformed uncertainty relation. Finally, we obtain an upper bound on the deformation parameter a.