Inflation from $f(R)$ theories in gravity's rainbow

Abstract

In this work, we study the $f(R)$ models of inflation in the context of gravity's rainbow theory. We choose three types of $f(R)$ models: $f(R)=R+\alpha (R/M{)}^n,f(R)=R+\alpha R^2+\beta R^2\log (R/M^2)$ and the Einstein-Hu-Sawicki model with $n,\alpha ,\beta$ being arbitrary real constants. Here $R$ and $M$ are the Ricci scalar and mass scale, respectively. For all models, the rainbow function is written in the power-law form of the Hubble parameter. We present a detailed derivation of the spectral index of curvature perturbation and the tensor-to-scalar ratio and compare the predictions of our results with the latest Planck 2018 data. With the sizeable number of e-foldings and proper choices of parameters, we discover that the predictions of all $f(R)$ models present in this work are in excellent agreement with the Planck analysis.

arXiv commentv1: 29 pages, many figures. arXiv admin note: text overlap with arXiv:1903.05996

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• Classical and quantum cosmology of $f(R)$ gravity's rainbow in Schutz's formalism
• Gravity Rainbow Effects on Higher Curvature Modification of R2 inflation
• Generalized Hidden Conformal Symmetry in Quadratic $f(T)$ Gravity
• Observational Constraints on Asymptotic Safety Inflation in Gravity Rainbow
• Gravitational baryogenesis in $F(R)$ gravity's rainbow
• Exact Analytical Taub-NUT like Solution in f(T) Gravity
• Primordial black holes formation in inflationary $F(R)$ models with scalar fields
• New Rotating Black Hole Solutions With Imperfect Fluid Energy-Momentum Tensor In $f(R)$ Gravity