Deformed Starobinsky model in gravity's rainbow

In the context of gravity's rainbow, we study the deformed Starobinsky model in which the deformations take the form $f(R)\sim R^{2(1-\alpha)}$, with $R$ the Ricci scalar and $\alpha$ a positive parameter. We show that the spectral index of curvature perturbation and the tensor-to-scalar ratio can be written in terms of $N,\,\lambda$ and $\alpha$, with $N$ being the number of {\it e}-foldings, $\lambda$ a rainbow parameter. We compare the predictions of our models with Planck data. With the sizeable number of {\it e}-foldings and proper choices of parameters, we discover that the predictions of the model are in excellent agreement with the Planck analysis. Interestingly, we obtain the upper limit and the lower limit of a rainbow parameter $\lambda$ and a positive constant $\alpha$, respectively.