Abstract

In this work, we study several extensions of the higher curvature modification of R² inflation in the context of gravity’s rainbow. We modify the (R+R²) model by adding an f<inf>1</inf>R³-term, an f<inf>2</inf>R⁴-term, and an f<inf>3</inf>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 f~=1+HM^λ with 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 f<inf>i</inf>,i=1,2,3, a rainbow parameter λ and a ratio H/M. Likewise, the scalar spectral index n<inf>s</inf> is affected by both f<inf>i</inf> and the rainbow parameter. Moreover, the tensor-to-scalar ratio r is solely determined by the rainbow parameter. Interestingly, by ensuring that n<inf>s</inf> aligns with the Planck collaboration’s findings at the 1σ confidence level, the tensor-to-scalar ratio could reach up to 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.