Gravity’s rainbow effects on higher curvature modification of $$R^{2}$$ R 2 inflation

Abstract

Abstract In this work, we study several extensions of the higher curvature modification of $$R^{2}$$ R 2 inflation in the context of gravity’s rainbow. We modify the $$(R+R^{2})$$ ( R + R 2 ) model by adding an $$f_{1}R^3$$ f 1 R 3 -term, an $$f_{2}R^4$$ f 2 R 4 -term, and an $$f_{3}R^{3/2}$$ 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 $${\tilde{f}}=1+\left( \frac{H}{M}\right) ^{\lambda }$$ f ~ = 1 + H M λ with $$\lambda $$ 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 $$f_{i},\,i=1,2,3$$ f i , i = 1 , 2 , 3 , a rainbow parameter $$\lambda $$ λ and a ratio H/M. Likewise, the scalar spectral index $$n_s$$ n s is affected by both $$f_{i}$$ f i and the rainbow parameter. Moreover, the tensor-to-scalar ratio r is solely determined by the rainbow parameter. Interestingly, by ensuring that $$n_s$$ n s aligns with the Planck collaboration’s findings at the $$1\sigma $$ 1 σ confidence level, the tensor-to-scalar ratio could reach up to $$r\sim 0.01$$ 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.