F-term Hybrid Inflation in Effective Supergravity Theories

TL;DR

The paper develops F-term driven hybrid inflation within effective no-scale SUGRA theories motivated by string theory, using a generalized Heisenberg symmetry to keep the inflaton mass small during inflation. By stabilizing the modulus ρ and the dilaton S through nonperturbative corrections, the inflationary potential can be kept at a controlled, low height, with $V(\rho_0,S_0) = \epsilon m_{3/2}^2 \tilde M_P^2$ and $\epsilon \ll 1$, while the inflaton remains massless at tree level. The authors present a concrete NMSSM-based realization in which the superpotential tilde{W} = $\lambda N H_1 H_2 - k\phi N^2$ yields hybrid inflation with an ultralight inflaton ($\sim$ eV) and $V(0)^{1/4} \sim 10^8$ GeV, addressing the $\mu$ problem and strong CP via a $U(1)_{PQ}$ symmetry and a small coupling $k \sim 10^{-10}$, enabling a cosmological constant cancellation at the minimum. The framework thus provides a realistic, string-motivated mechanism for F-term inflation with controlled radiative corrections and potential observational signatures, notably a nearly scale-invariant spectrum with $n \approx 1$.

Abstract

We show that a particular class of effective low energy supergravity theories motivated by string theory can provide a promising framework for models of hybrid inflation in which the potential energy which drives inflation originates from the F-term of the effective supergravity theory. In the class of models considered the inflaton is protected from receiving mass during inflation by a generalisation of the Heisenberg symmetry present in no-scale supergravity models. The potential during inflation takes the positive definite form $V\sim |F_S|^2 + |F_T|^2 -3$, which allows the possibility that $V\ll m_{3/2}^2 M_P^2$ through the cancellation of the positive dilaton and moduli contribution against the negative term. We discuss a toy example where this is realised, then describe the application of this result to realistic models focusing on a particular example in which the $μ$ problem and the strong CP-problem are addressed.

Figures (3)

• Figure 1: The potential $V(S,\rho)$ in units of $m_{3/2}^2 \tilde{M}_P^2$. $b=1$, $s_0=4$, $\beta=1/32$.
• Figure 2: (a) The potential $V(S,\rho_0)$, for $s_0=4$, and different values of $b$. (b) The potential $V(S_0,\rho)$, for $s_0=4$, $b=1$ and different values of $\beta$. The potential is given in units of $m_{3/2}^2 \tilde{M}_P^2$. Note that here we have used scaled variables, whereas in Fig. (1) we used unscaled ones.
• Figure 3: Computed values of $b_0$, with the condition $\epsilon \ll 1$.