Radiative Corrections in Supergravity Models of Inflation

TL;DR

This paper investigates radiative corrections in supergravity-based inflation models, identifying conditions under which these corrections are controlled, and highlighting models where quantum effects do not spoil the agreement with CMB observations.

Contribution

It derives conditions on the superpotential to keep radiative corrections small and analyzes specific no-scale supergravity models, including the Cecotti model, for their viability in inflation.

Findings

Radiative corrections can dominate at large inflaton values in some models.

Certain no-scale models maintain small corrections up to inflaton values of about 8 Planck units.

The Cecotti model preserves the agreement with Planck CMB data due to controlled quantum corrections.

Abstract

Supergravity provides the natural supersymmetric framework for early universe cosmology. A broad class of inflationary models in no-scale supergravity yields tree-level predictions for cosmic microwave background (CMB) observables that closely resemble those of the Starobinsky $R + R^2$ model. Using results from global supersymmetry and supergravity, we analyze radiative corrections in models with canonical and non-canonical kinetic terms, focusing particularly on Starobinsky-like no-scale supergravity models. We derive conditions on the superpotential that keep the gravitino mass finite during inflation and ensure that loop-induced corrections to the K\"ahler potential remain either finite or subdominant relative to the tree-level potential. We show that in some models, most notably the original no-scale supergravity model with a Wess-Zumino superpotential, radiative corrections grow at large inflaton field values and can dominate the inflationary dynamics, rendering unreliable the model predictions for CMB data. However, we identify a class of no-scale Starobinsky-like models, including the Cecotti model, in which radiative corrections remain very small for inflaton field values $\lesssim 8$ (in Planck units), preserving the agreement of the tree-level predictions with Planck CMB data.