The Reconstruction of Non-Minimal Derivative Coupling Inflationary Potentials

We derive the reconstruction formulae for the inflation model with the non-minimal derivative coupling term. If reconstructing the potential from the tensor-to-scalar ratio r, we could obtain the potential without using the high friction limit. As an example, we reconstruct the potential from the parameterization r=8 alpha/(N+beta)gamma, which is a general form of the alpha-attractor. The reconstructed potential has the same asymptotic behavior as the T- and E-model if we choose gamma=2 and alpha MUCH LESS-THAN1. We also discuss the constraints from the reheating phase by assuming the parameter wre of state equation during reheating is a constant. The scale of big-bang nucleosynthesis could put an upper limit on ns if wre=2/3 and a low limit on ns if wre=1/6.