Power-law Inflation in the f(R) Gravity

We investigate a form of f(R)=R1+δ/Rcδ and study the viability of the model for inflation in the Jordan and the Einstein frames. We have extended this form to f(R)=R+R1+δ/Rcδ in an attempt to solve the problems of the former model. This model is further analyzed by using the power spectrum indices of inflation and the reheating temperature. During the inflationary evolution, the model predicts a value of the δ parameter very close to one (δ = 0.98), while the reheating temperature Tre∼1016 GeV at δ = 0.98 is consistent with the standard approach to inflation and observations. We calculate the slow roll parameters for the minimally coupled scalar field within the framework of our models. It is found that the values of the scalar spectral index and tensor-to-scalar ratio are very close to the recent observational data, including those released by Planck. Further, we find the scalar spectral index and the tensor-to-scalar ratio are exactly the same in the first model because the Jordan and the Einstein frames are conformally equivalent. We also attempt to provide a constraint through the non-Gaussianity parameter.