Modified Starobinsky Inflation

Starobinsky has suggested an inflation model which is obtained from the vacuum Einstein's equations modified by the one-loop corrections due to quantized matter fields. Although the one-loop gravitational action is not known for a general FRW background, it can be obtained in a de Sitter space to give $\Mp^2 R + \alpha R^2 + \beta R^2 \ln (R/M^2)$. Thus, one needs to investigate the inflationary behavior of this model compared to the Starobinsky model (i.e. $\beta = 0$). The coefficient $\alpha$ can be changed by varying the renormalization scale $M^2$ and $\beta$ is obtained from the quantum anomaly which is related to the numbers of quantum fields. It has been assumed that $\alpha \gg \beta$. We investigate the viable values of $\alpha$ and $\beta$ based on the CMB observation. We also scrutinize the reheating process in this model.