Creation of Non-minimal Coupled Particle in Asymptotic de-Sitter Background

A general form of quasi-de Sitter(dS) modes in a dynamical background is used to study the creation of particle during the inflation. Actually, by considering the general form of inflaton field equation as a function of the Hankel function index and by using the Planck 2015 constraint on spectral index, we obtain the possible new constraints for the values of coupling constant in the era with quasi-dS space-time. Then, we explicitly calculate the general form of expectation value of the created particles in terms of the Hankel function index and the conformal time. As an important result, we see that the number of created particles and the value of coupling constant can be dependent to the selection of the background space-time and it's dynamics. Our result is general and confirm the conventional special results for the Minkowski and dS background.