From R2 gravity to no-scale supergravity

John Ellis,Keith A Olive,Dimitri V Nanopoulos

doi:10.1103/physrevd.97.043530

Abstract

We show that $R^2$ gravity coupled conformally to scalar fields is equivalent to the real bosonic sector of SU(N,1)/SU(N)$\times$U(1) no-scale supergravity, where the conformal factor can be identified with the K\"ahler potential, and we review the construction of Starobinsky-like models of inflation within this framework.

Highlights

The singularity-free cosmological model which incorporates inflation [1], and that in which quantum perturbations were first calculated [2], was that based on R þ R2 gravity
We show that R2 gravity coupled conformally to scalar fields is equivalent to the real bosonic sector of SUðN; 1Þ=SUðNÞ × Uð1Þ no-scale supergravity, where the conformal factor can be identified with the Kähler potential, and we review the construction of Starobinsky-like models of inflation within this framework
Almost four decades later, the perturbation spectrum calculated in this pioneering model of inflation remains in excellent agreement with the growing wealth of measurements of the cosmic microwave background (CMB) radiation and data on a large-scale structure [3], whereas many more junior models have fallen by the wayside

Summary

INTRODUCTION

The singularity-free cosmological model which incorporates inflation [1], and that in which quantum perturbations were first calculated [2], was that based on R þ R2 gravity. Imagine our surprise when we discovered that a simple model of an inflaton field coupled to SUð1; 1Þ=Uð1Þ no-scale supergravity [16] could yield an effective scalar potential that is identical to that obtained in the original R þ R2 model after a conformal transformation [17], a realization that had been reached in 1987 [18], though without making the connection to cosmological inflation. This convergence between R þ R2 gravity and no-scale supergravity was very intriguing [19], but the nature of any deeper connection remained obscure. This identification reinforces the connection between R2 gravity and no-scale supergravity that emerged in [17] (see [21]), and was developed further in [22,23,24,25,26,27,28,29,30]

R2 GRAVITY AND A DE SITTER UNIVERSE

THE STAROBINSKY MODEL OF INFLATION

GENERALIZATION WITH ADDITIONAL CONFORMALLY COUPLED FIELDS

INTRODUCING A STAROBINSKY-LIKE INFLATIONARY POTENTIAL

VIII. SUMMARY