Volume modulus inflation and a low scale of SUSY breaking

TL;DR

This work investigates volume-modulus-driven inflation in type IIB string compactifications, aiming to achieve a high inflationary Hubble scale $H$ while keeping the gravitino mass $m_{3/2}$ light. It shows that with a tree-level Kähler potential and standard racetrack-type superpotentials, slow-roll inflation near non-SUSY saddles is generically forbidden due to the negative $\eta$-matrix trace, a problem that can be mitigated only with targeted Kähler corrections and specific superpotential structures. The authors demonstrate that KL-type models cannot realize inflation even with ${\alpha'}$ corrections, but a triple gaugino condensation model with leading string corrections can yield slow-roll inflation with $H\gg m_{3/2}$ and $n_s\approx0.94$, predicting negligible tensor modes. However, achieving the tiny gravitino mass requires additional fine-tuning, and the authors discuss rescaling symmetries that preserve inflationary predictions, outlining a plausible, though delicate, path to reconciling inflation with low-scale SUSY breaking in this framework.

Abstract

The relation between the Hubble constant and the scale of supersymmetry breaking is investigated in models of inflation dominated by a string modulus. Usually in this kind of models the gravitino mass is of the same order of magnitude as the Hubble constant which is not desirable from the phenomenological point of view. It is shown that slow-roll saddle point inflation may be compatible with a low scale of supersymmetry breaking only if some corrections to the lowest order Kahler potential are taken into account. However, choosing an appropriate Kahler potential is not enough. There are also conditions for the superpotential, and e.g. the popular racetrack superpotential turns out to be not suitable. A model is proposed in which slow-roll inflation and a light gravitino are compatible. It is based on a superpotential with a triple gaugino condensation and the Kahler potential with the leading string corrections. The problem of fine tuning and experimental constraints are discussed for that model.

Figures (8)

• Figure 1: Typical structure of the scalar potential (\ref{['potential']}) for $\tau=0$.
• Figure 2: Plot presents disappearing of the barrier for increasing $\tau$. Different lines correspond to different values of $c\tau$: (a) $c\tau=0$, (b) $c\tau=0.2$, (c) $c\tau=0.4$, (d) $c\tau=0.5$.
• Figure 3: Plot of the expression (\ref{['vttau']}) for $dt_{\rm mink}=1$. Different lines correspond to different values of $\delta$: (a) $\delta=0.1$, (b) $\delta=0.2$, (c) $\delta=0.3$, (d) $\delta=1$.
• Figure 4: Plot of the potential without corrections (straight lines) and with maximal possible correction $\kappa_{\rm mink}=1$ (dashed lines) for different values of $c\tau$: (a) $c\tau=0$, (b) $c\tau=0.45$.
• Figure 5: Plot of the $\tau$-dependent part of $\frac{\partial V}{\partial t}$ expanded to the order of $\tau^2$ with the condition $dt_{\rm mink}=1$ imposed. The value of $\delta=0.2$ is used but the plot does not differ qualitatively for other values of $\delta$. $\kappa_{\rm mink}$ is the value of $\kappa$ (defined in (\ref{['kappa']})) at the Minkowski minimum. $\kappa_{\rm mink}=0$ corresponds to the case without corrections, while $\kappa_{\rm mink}=1$ and $\kappa_{\rm mink}=-1$ correspond to the case of the correction at the border of validity of the perturbative expansion. We recall that only corrections with positive $\kappa$ give positive contribution to the trace of the $\eta$-matrix.