Deformed Starobinsky model in gravity\u2019s rainbow

Phongpichit Channuie

doi:10.1140/epjc/s10052-019-7031-x

Abstract

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 and alpha being the Ricci scalar and a positive parameter, respectively. 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 e-foldings, lambda a rainbow parameter. We compare the predictions of our models with Planck data. With the sizeable number of 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.

Highlights

The prediction of a minimal measurable length of the order of Planck length in various theories of quantum gravity restricts the maximum energy that any particle can attain to the Planck energy
The 2018 recent release of the Planck cosmic microwave background (CMB) anisotropy measurements [6] determines the spectral index of scalar perturbations to be ns = 0.9649 ± 0.0042 at 68% CL and the 95% CL upper limit on the tensor-to-scalar ratio is further tightened by combining with the BICEP2/Keck Array BK14 data to obtain r0.002 < 0.064
We studied the deformed Starobinsky model in which the deformations take the form R2(1−α), with R and α being the Ricci scalar and a positive parameter, respectively [14]

Summary

Introduction

The prediction of a minimal measurable length of the order of Planck length in various theories of quantum gravity restricts the maximum energy that any particle can attain to the Planck energy. The geometry of the space-time in gravity’s rainbow depends on energy of the test particles. The gravity’s rainbow has been used for analyzing the effects of rainbow functions on the Starobinsky model of f (R) gravity [11] and other cosmological scenarios [48–51]. [14] studied quantum-induced marginal deformations of the Starobinsky gravitational action of the form R2(1−α), with R and α being the Ricci scalar and a positive parameter, respectively. We take a short recap of a cosmological linear perturbation in the context of the gravity’s rainbow generated during inflation and calculate the spectral index of scalar perturbation and the tensor-to-scalar ratio of the model in Sect. The (0, 0)-component of Eq (4) yields the following differential equation: 3F H2

H F κ2 f2

Cosmological perturbation in gravity’s rainbow revisited

Conclusion