Inflation from f(R) theories in gravity’s rainbow

Areef Waeming; Phongpichit Channuie

doi:10.1140/epjc/s10052-020-8387-7

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2020) 80: 802
https://doi.org/10.1140/epjc/s10052-020-8387-7

Regular Article - Theoretical Physics

Inflation from f(R) theories in gravity’s rainbow

Areef Waeming¹ and Phongpichit Channuie¹^,2^,3^,4^b

¹ School of Science, Walailak University, 80160, Nakhon Si Thammarat, Thailand
² College of Graduate Studies, Walailak University, 80160, Nakhon Si Thammarat, Thailand
³ Research Group in Applied, Computational and Theoretical Science (ACTS), Walailak University, 80160, Nakhon Si Thammarat, Thailand
⁴ Thailand Center of Excellence in Physics, Ministry of Higher Education, Science, Research and Innovation, 10400, Bangkok, Thailand

^b channuie@gmail.com

Received: 14 May 2020
Accepted: 23 August 2020
Published online: 1 September 2020

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: $f (R) = R + α {(R / M)}^{n}, f (R) = R + α R^{2} + β R^{2} log (R / M^{2})$ $f(R)=R+\alpha (R/M)^{n},\,f(R)=R+\alpha R^{2}+\beta R^{2}\log (R/M^{2})$ and the Einstein–Hu–Sawicki model with $n, α, β$ $n,\,\alpha ,\,\beta$ 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.

© The Author(s) 2020

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