Inflation in an R2-corrected f(R) gravity model

We conducted an analysis of the inflationary scenario within thef(R) gravity framework, focusing on the Gogoi-Goswami model defined by the parameters alpha > 0, beta > 0, and the characteristic curvature constant R-c. This model exhibits a potential in the Einstein frame characterized by V proportional to phi(p). The spectral index for this model is given by n(s)= 1 - (p + 2)/2N, while the tensor-to-scalar ratio isr = 4p/N, where N denotes the e-folding number at horizon crossing. Although this model aligns with the Planck 2018 observational data within a narrow range, specifically 1.10 <= p <= 1.25 for N = 50, it becomes increasingly difficult to find an appropriate value pforwhen N >= 54. To overcome this limitation, we propose incorporating an R-2 correction term from the Starobinsky model to enhance the inflationary predictions. Our analysis indicates that this correction improves the model's performance when optimal parameters are selected, specifically by setting x(0) = R-0/R-c<< 1 (with R-0 representing the scalar curvature during the late-time accelerated expansion), alpha(max) = O(1), and introducing a parameter gamma related to the R-2 term within the range-0.024600 < gamma < 0. The parameter x(0) establishes a connection between alpha and beta via the de Sitter solution of the model. Additionally, the parameter R-c can be estimated similarly to that in the Starobinsky model, as R-c similar or equal to(1.3 x 10(-5)/kappa)(2).