F-term Inflation and RSII Brane Mode

Considering hybrid F-term inflation in RSII model and using the most recent data from Planck 2018 and in comparison with Planck 2015and WMAP 9-year , we can obtain some interesting constraints on main parameters of the model. Also, we attain convenient compatibility between this model and observational data. We show that this setup provides a successful hybrid inflation with high enough Reheating Temperature, T_R, to have a successful thermalization. After inflation, particles are created in the process of preheating. Inflaton field(s) oscillated and fermionic field(s) interacted with it in a non-perturbative regime of parametric resonance. We apply theory of fermionic preheating coupling to the inflaton, without expansion of the universe, to calculate the occupation number of created particles analytically, and some interesting results are achieved.