Supersymmetric Moduli Stabilization and High-Scale Inflation

TL;DR

The paper addresses the back-reaction of a supersymmetrically stabilized modulus on F-term inflation in supergravity by deriving corrections to the inflaton potential as a series in the ratio $H/m_ρ$. Using a general setup with a modulus Kähler potential $K_{mod}=-\kappa \log(ρ+ρ̄)$ and a racetrack-type $W_{mod}(ρ)$ yielding a SUSY Minkowski minimum, the authors show how the modulus displacement $δρ$ shifts the inflaton dynamics and generates corrections of order $1/m_ρ$ and $1/m_ρ^2$. In hybrid inflation, the leading correction is linear in the inflaton and can render the spectral index compatible with Planck for suitable $m_ρ$; in chaotic inflation the leading effect appears at $O(1/m_ρ^2)$ due to suppression of the inflaton superpotential, with potentially large implications for CMB observables at high inflation scales. The findings imply that high-scale inflation with stabilized extra dimensions generically requires modulus masses near the GUT scale, aligning the inflationary energy scale with the stability of the extra dimensions and constraining model-building in string-inspired cosmology.

Abstract

We study the back-reaction of moduli fields on the inflaton potential in generic models of F-term inflation. We derive the moduli corrections as a power series in the ratio of Hubble scale and modulus mass. The general result is illustrated with two examples, hybrid inflation and chaotic inflation. We find that in both cases the decoupling of moduli dynamics and inflation requires moduli masses close to the scale of grand unification. For smaller moduli masses the CMB observables are strongly affected.