A Simple Quintessence Model
  A simple model of quintessential inflation with the modified exponential potential $e^{-\alpha \phi} [A+(\phi-\phi_0)^2]$ 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 $5.3 \lesssim \alpha \lesssim 10.8$. 
M.C. Bento, R. Gonzalez Felipe and N.M.C. Santos