Power-law Inflation in the f (R) Gravity

We investigate a form off (R) = R-1+(delta)/R-c(delta) 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+epsilon/R-c(delta) 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 delta parameter very close to one (delta = 0.98), while the reheating temperature T-re similar to 10(16) GeV at delta = 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.

Automated summary

This study investigates a model with the form (R) = R-1+(delta)/R-c(delta) and examines its viability for inflation in the Jordan and Einstein frames. The model is extended to f (R) = R + R1+epsilon/R-c(delta) in an attempt to address the issues of the previous model. The analysis of slow roll parameters and power spectrum indices suggests that the model aligns closely with recent observational data and is consistent with standard inflationary approaches and observations.