Inflation in an R 2 -Corrected f(R) gravity model

Abstract

We conducted an analysis of the inflationary scenario within the f(R) gravity framework, focusing on the Gogoi-Goswami model defined by the parameters α > 0, β > 0, and the characteristic curvature constant R_c. This model exhibits a potential in the Einstein frame characterized by V ∝ φ p . The spectral index for this model is given by n_s = 1 − (p + 2)/2N, while the tensor-to-scalar ratio is r = 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 for p when 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 x₀ = R₀/R_c «1 (with R0 representing the scalar curvature during the late-time accelerated expansion), α_max = O(1), and introducing a parameter γ related to the R² term within the range −0.024600 < γ < 0. The parameter x₀ establishes a connection between α and β via the de Sitter solution of the model. Additionally, the parameter Rc can be estimated similarly to that in the Starobinsky model, as R_c ~ (1.3 × 10⁻⁵ /κ)² .