Gravity Rainbow Effects on Higher Curvature Modification of R2 inflation

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.

v3: 21 pages, 4 figures. references added, texts modified, results unchanged. Version published in EPJC. arXiv admin note: text overlap with arXiv:2404.14766

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Cited by in corpus (2)

• Inflation in Myrzakulov $F(R,T)$ Gravity: A Comparative Study in Metric, Symmetric Teleparallel, and Weitzenböck Formalisms
• Gravitational baryogenesis in $F(R)$ gravity's rainbow