Beyond Starobinsky inflation

Yermek Aldabergenov,Sergey I Kruglov,Ryotaro Ishikawa,Sergei V Ketov

doi:10.1103/physrevd.98.083511

Abstract

A supergravity extension of the $(R+R^2)$ gravity with the additional (Born-Infeld) structure of a massive vector multiplet gives rise to the specific $F(R)$ gravity, whose structure is investigated in detail. The massive vector multiplet has inflaton (scalaron), goldstino and a massive vector field as its field components. The model describes Starobinsky inflation and allows us to extrapolate the $F(R)$ function beyond the inflationary scale (up to Planck scale). We observe some differences versus the $(R+R^2)$ gravity, and several breaking patterns of the well known correspondence between the $F(R)$ gravity and the scalar-tensor gravity.

Highlights

An ultimate theory of cosmological inflation should be based on quantum gravity and is yet to be constructed
A supergravity extension of the ðR þ R2Þ gravity with the additional (Born-Infeld) structure of a massive vector multiplet gives rise to the specific FðRÞ gravity, whose structure is investigated in detail
The function (23) is well defined for any values of R and implies three physical regimes: (i) the small curvature regime, where gravity is described by the standard Einstein-Hilbert action, (ii) the inflationary regime, where gravity is described by Starobinsky ðR þ R2Þ action (4), (iii) the high curvature regime, where gravity is again described by the Einstein-Hilbert action, though with the different MPl;effective 1⁄4 MPlð1 þ(la4rgge2r=)peffi3ffifffiβfffiffieÞc1=ti2v≤e

Summary

INTRODUCTION

An ultimate theory of cosmological inflation should be based on quantum gravity and is yet to be constructed. This is related to another open problem of finding an ultraviolet (UV) completion of any phenomenologically viable inflationary model. (iii) the kinetic terms of the vector supermultiplet should have the Born-Infeld (or Dirac-Born-Infeld) structure, inspired by superstrings and D-branes. This leads to the specific (modified) FðRÞ gravity model, whose peculiar structure is in the focus of our investigation in this paper. In the Appendix, we formulate the full supergravity theory in terms of superfields in curved superspace

BORN-INFELD STRUCTURE IN GRAVITY AND SUPERGRAVITY

STAROBINSKY INFLATION AND FðRÞ GRAVITY

M2Pl φÃ φend

BI-MODIFIED STAROBINSKY MODEL

SCALAR-TENSOR GRAVITY AND THE INFLATON SCALAR POTENTIAL

CONCLUSION