Preheating and reheating constraints in supersymmetric braneworld inflation

Abstract

We study the evolution of the Universe at early stages; we discuss also preheating in the framework of hybrid braneworld inflation by setting conditions on the coupling constants $\lambda$ and g for effective production of $\chi$-particles. Considering the phase between the time observable CMB scales crossed the horizon and the present time, we write reheating and preheating parameters $N_{re}$, $T_{re}$ and $N_{pre}$ in terms of the scalar spectral index $n_{s}$ and prove that, unlike the reheating case, the preheating duration does not depend on the values of the equation of state $\omega ^{*}$. We apply the slow-roll approximation in the high energy limit to constrain the parameters of D-term hybrid potential. We show also that some inflationary parameters, in particular, the spectral index $n_{s}$ demand that the potential parameter $\alpha$ is bounded as $\alpha \ge 1$ to be consistent with Planck’s data, while the ratio r is in agreement with observation for $\alpha \le 1$ considering high inflationary e-folds. We also propose an investigation of the brane tension effect on the reheating temperature. Comparing our results to recent CMB measurements, we study preheating and reheating parameters $N_{re}$, $T_{re}$ and $N_{pre}$ in the Hybrid D-term inflation model in the range $0.8\le \alpha \le 1.1$  and conclude that $T_{re}$ and $N_{re}$ require $\alpha \le 1$, while for $N_{pre}$ the condition $\alpha \le 0.9$ must be satisfied, to be compatible with Planck’s results.