Particle Creation and Excited-de Sitter Modes

Recently, in Ref.\cite{moh1}, we introduced exited-de Sitter modes to study the power spectrum which was finite in Krein space quantization and the trans-Plankian corrections due to the exited modes were non-linear. It was shown that the de Sitter limit of corrections reduces to what obtained via the several previous conventional methods, moreover, with such modes the space-time symmetry becomes manifest. In this paper, inspired by Krein method and using exited-de Sitter modes as the fundamental initial states during the inflation, we calculate particle creation in the spatially flat Robertson-Walker space-time. It is shown that in de Sitter and Minkowski space-time in the far past time limit, our results coincides to the standard results.