Radiative Corrections in Supergravity Models of Inflation

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 Kähler 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.

Figures (11)

• Figure 1: The scalar potential $V(\phi)$ in the HRR model, shown at tree level (blue solid line) and including one-loop corrections (green dashed line).
• Figure 2: The one-loop corrected Kähler metric as a function of the scalar field $\phi$. We have set $\mu=M$ with $M=1.3\times 10^{-8}$, and take $\bar{\phi}=\phi$.
• Figure 3: One-loop induced shifts in $\lambda_{2,3}$ as a function of $\phi$. Solid curves: $\lambda=1$, dashed curves: $\lambda = 0.999995$.
• Figure 4: The one-loop Kähler metric $K^{(1)}_{\Phi\bar{\Phi}}$ as a function of $\phi$. We fix $M=1.3\times 10^{-5}$, and $\lambda=1$ and set $S=0$ and $\text{Im}\,\phi=0$.
• Figure 5: The coupling variations $\tilde{\lambda}$, $\tilde{M}$ as functions of $\phi$.