Brane assisted quintessential inflation with transient acceleration
  A simple model of quintessential inflation with the modified exponential potential exp(-\alpha \phi) [A + (\phi-\phi_0)^2] is analyzed in the braneworld context. Considering reheating via instant preheating, it is shown that the evolution of the scalar field \phi from inflation to the present epoch is consistent with the observational constraints in a wide region of the parameter space. The model exhibits transient acceleration at late times for 0.96 < A \alpha^2 < 1.26 and 271 < \phi_0 \alpha < 273, while permanent acceleration is obtained for 2.3 10^{-8} < A \alpha^2 < 0.98 and 255 < \phi_0 \alpha < 273. The steep parameter \alpha is constrained to be in the range 5.3 < \alpha < 10.8. 
M.C. Bento, R. Gonzalez Felipe, N.M.C. Santos