A Simple Quintessence Model

A simple model of quintessential inflation with the modified exponential potential $e^{-\alpha \varphi }[A+(\varphi -{\varphi }_0{)}^2]$ is analyzed in the braneworld context. Considering reheating via instant preheating, we conclude that the model exhibits transient acceleration at late times for $0.96 \lesssim A \alpha^2 \lesssim 1.26$and$271 \lesssim \phi_0 \alpha \lesssim 273$, while permanent acceleration is obtained for $2.3\times10^{-8} \lesssim A \alpha^2 \lesssim 0.98$and$255 \lesssim \phi_0 \alpha \lesssim 273$. The steep parameter $\alpha$ is constrained to be in the range $5.3 \lesssim \alpha \lesssim 10.8$.