  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 $\omega ^{\ast }$. 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 $0.8\leq \alpha\leq 1.1$\, 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.
