Reinterpretation of the Starobinsky model

Takehiko Asaka,Kazunori Kohri,Satoshi Iso,Hikaru Kawai,Toshifumi Noumi,Takahiro Terada

doi:10.1093/ptep/ptw161

Abstract

The Starobinsky model of inflation, consistent with Planck 2015, has a peculiar form of the action, which contains the leading Einstein term $R$, the $R^2$ term with a huge coefficient, and negligible higher-order terms. We propose an explanation of this form based on compactification of extra dimensions. Once tuning of order $10^{-4}$ is accepted to suppress the linear term $R$, we no longer have to suppress higher-oder terms, which give nontrivial corrections to the Starobinsky model. We show our predictions of the spectral index, its runnings, and the tensor-to-scalar ratio. Finally, we discuss a possibility that quantum gravity may appear at the scale $\Lambda \gtrsim 5 \times 10^{15}$ GeV.

Highlights

The precise CMB observations favor the plateau-type inflaton potentials
We proposed a new interpretation of the Starobinsky model as a low-energy effective theory of a higher dimensional theory whose characteristic energy scale is denoted by Λ
With the tuning of |b1| 2 × 10−4, we obtain Starobinsky model augmented with higher order terms suppressed enough to be consistent with the Planck 2015 results

Summary

Introduction

The precise CMB observations favor the plateau-type inflaton potentials. the combined analysis of BICEP–Keck-Array–Planck resulted in a finite value of tensor-to-scalar ratio, r = 0.048+−00..003352 [1], Planck 2015 itself has not found any evidence of detecting it, r < 0.103 (Planck TT + lowP) [2]. The “next-to-natural” expectation would be that it is the reduced Planck scale MP, since there are no other scales in the theory In this case, the action is expanded by the Planck scale MP with order one coefficients, but the coefficient of the second term R2 must be somewhat very large (a2 ≃ 5 × 108). The action is expanded by the Planck scale MP with order one coefficients, but the coefficient of the second term R2 must be somewhat very large (a2 ≃ 5 × 108) This is the well-known peculiarity of the Starobinsky model, which we try to partially explain here. We have to suppress the coefficient of the linear term R by tuning of order 10−4, we do not have to suppress the higher order terms It leads to a Starobinsky-like model with interesting observational consequences. We predict inflationary observables, and obtain the lower bound on the fundamental scale of the underlying higher dimensional theory

Starobinsky-like model from extra dimensions

Implications for inflationary observables

Discussion