Gravity’s rainbow effects on higher curvature modification of R² inflation

In this work, we study several extensions of the higher curvature modification of R² R 2 inflation in the context of gravity’s rainbow. We modify the (R+R²) ( R + R 2 ) model by adding an f₁R³ f 1 R 3 -term, an f₂R⁴ f 2 R 4 -term, and an f₃R3/2 f 3 R 3 / 2 -term to the original model. We calculate the inflationary observables and confront them using the latest observational bounds from Planck 2018 data. We assume the rainbow function of the form f̃=1+( H/M) λ f ~ = 1 + H M λ with λ λ being a rainbow parameter and M a mass-dimensional parameter. We demonstrate that the power spectrum of curvature perturbation relies on the dimensionless coefficient fᵢ,\,i=1,2,3 f i , i = 1 , 2 , 3 , a rainbow parameter λ λ and a ratio H / M . Likewise, the scalar spectral index nₛ n s is affected by both fᵢ f i and the rainbow parameter. Moreover, the tensor-to-scalar ratio r is solely determined by the rainbow parameter. Interestingly, by ensuring that nₛ n s aligns with the Planck collaboration’s findings at the 1σ 1 σ confidence level, the tensor-to-scalar ratio could reach up to r~ 0.01 r ∼ 0.01 , which is possibly measurable for detection in forthcoming Stage IV CMB ground experiments and is certainly feasible for future dedicated space missions.