Inflation in uplifted Supergravities

TL;DR

The paper addresses how to realize slow-roll inflation within uplifted N=1 supergravity models that incorporate a gauge invariant D-term uplifting from an anomalous U1. It analyzes the challenges posed by the eta problem and initial-condition sensitivity in the simplest realizations and then introduces a minimal extension by adding a neutral singlet chi, which enables a saddle point driven eternal topological inflation and a slow-roll phase toward a quasi Minkowski vacuum. The authors demonstrate, with a concrete parameter choice, that a three-field reduction yields an inflaton predominantly along chi_R, achieving a sufficiently long inflationary phase and a spectral index near n_s ≈ 0.95 while matching the observed amplitude, albeit with notable tuning of the superpotential parameters. Overall, the work provides a concrete string-inspired path to combine moduli stabilization, D-term uplift, and inflation within a gauge invariant framework, highlighting both the potential and the tuning required in modular inflation scenarios.

Abstract

We present a model of slow-roll inflation in the context of effective Supergravities arising from string theories. The uplifting of the potential (to generate dS or Minkowski vacua) is provided by the D-term associated to an anomalous U(1), in a fully consistent and gauge invariant formulation. We develop a minimal working model which incorporates eternal topological inflation and complies with observational constraints, avoiding the usual obstacles to implement successful inflation ("eta problem" and initial condition problem among others).

Figures (8)

• Figure 1: Plot of the scalar potential, as a function of $T_{\rm R}$, for the example shown in the text and $\rho_{\rm M}$ chosen as the value minimising the potential at each $T_{\rm R}$.
• Figure 2: Periodic structure of the potential along the relative phase $\varphi_{\rm np}$. The model is the same as in the previous figure and $(T_{\rm R},\rho_{\rm M}^2)$ have been fixed to their at the minimum.
• Figure 3: Effective potential as a function of $\chi_{\rm R}$
• Figure 4: Plot of the total number of e-folds of inflation, $N_e^{\rm tot}$, as a function of the initial condition for the inflaton quoted as the shift, $\delta \chi_R$, with respect to its value at the saddle point given by $\chi=0$. The dotted line indicates the 60 e-folds needed to make inflation successful.
• Figure 5: Cosmological evolution of the singlet $\chi_{\rm R}$, normalised to its minimum value, as a function of the number of e-folds, $N_e$.