Gravity Rainbow Effects on Higher Curvature Modification of R2 inflation

TL;DR

This paper explores extensions of R^2 inflation within gravity's rainbow framework, analyzing how added curvature terms and rainbow parameters influence inflationary observables and compatibility with Planck data.

Contribution

It introduces new higher curvature terms into R^2 inflation in gravity's rainbow and studies their effects on inflationary predictions and observational constraints.

Findings

The tensor-to-scalar ratio r can reach up to 0.01 under certain conditions.

Inflationary observables depend on rainbow parameters and curvature coefficients.

The model remains consistent with Planck 2018 data for specific parameter ranges.

Abstract

In this work, we study several extensions of the higher curvature modification of $R^{2}$ inflation in the context of gravity's rainbow. We modify the $(R+R^{2})$ model by adding an $f_{1}R^3$-term, an $f_{2}R^4$-term, and an $f_{3}R^{3/2}$-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 $\tilde{f}=1+\left(\frac{H}{M}\right)^{\lambda }$ with $\lambda$ being a rainbow parameter and $M$ a mass-dimensional parameter. We demonstrate that the power spectrum of curvature perturbation relies on the dimensionless coefficient $f_{i},\,i=1,2,3$, a rainbow parameter $\lambda$ and a ratio $H/M$. Likewise, the scalar spectral index $n_s$ is affected by both $f_{i}$ and the rainbow parameter. Moreover, the tensor-to-scalar ratio $r$ is solely determined by the rainbow parameter. Interestingly, by ensuring that $n_s$ aligns with the Planck collaboration's findings at the $1\sigma$ confidence level, the tensor-to-scalar ratio could reach up to $r\sim 0.01$, which is possibly measurable for detection in forthcoming Stage IV CMB ground experiments and is certainly feasible for future dedicated space missions.