Ultraviolet completion of Starobinsky inflation

TL;DR

This paper develops an $N=1$ supergravity framework for $F(R)$ gravity, including the Starobinsky model, and connects it to string theory, addressing initial conditions and swampland constraints.

Contribution

It constructs a supergravity action with an $F(R)$ structure, linking it to string theory and addressing initial conditions within effective field theory.

Findings

Constructed an $N=1$ supergravity action with $F(R)$ gravity.

Reduced the scalar potential to that of $F(R)$ gravity by setting certain fields to zero.

Provided a string theory example consistent with the model and swampland conjectures.

Abstract

We construct an $N=1$ supergravity action whose bosonic part contains an arbitrary function of the scalar curvature, the so-called $F(R)$ gravity. As in $R+R^2$ supergravity, it can be described in terms of two chiral superfields of no-scale supergravity: one contains the scalaron which plays the role of the Starobinsky inflaton and the other contains the goldstone fermion of spontaneously broken supersymmetry during the inflation plateau. Its (complex) scalar component acquires a non-tachyonic mass in the presence of the string dilaton and can be set to zero, together with the pseudoscalar partner of the scalaron, so that the scalar potential is reduced to the one of $F(R)$ gravity. In a perturbative expansion in powers of $R$, one obtains a small deformation of the Starobinsky cosmological model that solves the problem of initial conditions within the validity of the effective field theory, below the scale of tower of states predicted by the swampland distance conjecture. We also show that a particular example of an underlying microscopic theory with such properties is provided by a four-dimensional heterotic string model containing the Standard Model of particle physics.