Eur. Phys. J. Plus (2021) 136: 888
https://doi.org/10.1140/epjp/s13360-021-01887-x

Regular Article

Preheating and reheating constraints in supersymmetric braneworld inflation

¹ Physics and Quantum Technology Team, LPMC, Ben M’sik Faculty of Sciences, Casablanca Hassan II University, Casablanca, Morocco
² LPHE-MS Laboratory Department of Physics, Faculty of Science, Mohammed V University in Rabat, Rabat, Morocco

^a k.elbourakadi@yahoo.com

Received: 20 May 2021
Accepted: 19 August 2021
Published online: 28 August 2021

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 $N_{\mathit{re}}$, $T_{\mathit{re}}$ and $N_{\mathit{pre}}$ 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 ${\omega }^{\ast }$. 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 $N_{\mathit{re}}$, $T_{\mathit{re}}$ and $N_{\mathit{pre}}$ in the Hybrid D-term inflation model in the range $0.8\le \alpha \le 1.1$  and conclude that $T_{\mathit{re}}$ and $N_{\mathit{re}}$ require $\alpha \le 1$, while for $N_{\mathit{pre}}$ the condition $\alpha \le 0.9$ must be satisfied, to be compatible with Planck’s results.