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. Consider
ing 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 $omega ^{ast }$. 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 $alpha geq 1$ to be consistent with $Planck$s data, while the ratio $r$ is in agreement with observation for $ alpha leq 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 $0.8leq alphaleq 1.1$, and conclude that $T_{re}$ and $N_{re}$ require $alpha leq 1$, while for $N_{pre}$ the condition $alpha leq 0.9$ must be satisfied, to be compatible with $Planck$s results.
We propose a new unified model that describes~dark energy and dark matter in the context of $f(R,phi )$ gravity using a massive scalar field in five dimensions. The scalar field is considered in the bulk that surrounds the 3-brane in branworld model.
We show that for a specific choice of the $% f(R,phi )$ function, we can describe the Einstein gravitation in 4-dimensional space-time. We obtain a relationship between the speed of the universes expansion and the speed of the bulks expansion. We also propose that the dark matter is represented by the scalar field mass and that the dark energy is a kinetic energy of this field. Finally, we show that, according to conditions, one can obtain the percentages of density of dark matter and the density of ordinary matter.
We are interested on studing various inflationary spectrum perturbation parameters in the context of the Randall-Sandrum type 2 Braneworld model. We consider in particular three types of potentials. We apply the slow-roll approximation in the high en
ergy limit to constraint the parameter potentials by confronting our results to recent WMAP7 observations. We show that, for some values of the e-folding number N; the monomial potential provides the best fit results to observations data.
We study a new inflation potential in the framework of the Randall-Sundrum type 2 Braneworld model. Using the technic developped in(Phys. Rev. D75, 123504 (2007).1), we consider both an monomial and a new inflation potentials and apply the Slow-Roll
approximation in high energy limit, to derive analytical expression of relevant perturabtion spectrum. We show that for some values of the parameter n of the potential, we obtain an perturbation spectrum wich present a good agreement with recent WMAP5 observations.
