Volume Modulus Inflation and the Gravitino Mass Problem

TL;DR

The paper addresses the tension between high-scale inflation and low-energy supersymmetry in string-inspired vacua, where the Hubble scale during inflation is bounded by the gravitino mass $H \lesssim m_{3/2}$ (and more strongly $H \lesssim m_{3/2}^{3/2}$ in large-volume scenarios). It proposes a mechanism in which inflation ends along a volume-runaway toward a distant large-volume minimum, allowing the present-day $m_{3/2}$ to be at the TeV scale, with an attractor solution seeded by a small amount of radiation that dissipates energy and guides the system to the final minimum. The authors illustrate the concept with a 1-modulus toy potential featuring an inflection point for inflation and a separate large-volume minimum, and extend the analysis to a full two-modulus model where the heavy modulus can be integrated out to obtain an effective single-field runaway potential; in both cases a radiation-seeded tracker prevents overshoot. While promising as a proof of principle, the scenario requires substantial fine-tuning and faces challenges such as isocurvature perturbations and moduli cosmology, pointing to potential refinements in KL/racetrack frameworks or hybrid inflation variants as future directions.

Abstract

The Hubble constant during the last stages of inflation in a broad class of models based on the KKLT mechanism should be smaller than the gravitino mass, H <~ m_{3/2}. We point out that in the models with large volume of compactification the corresponding constraint typically is even stronger, H <~ m_{3/2}^{3/2}, in Planck units. In order to address this problem, we propose a class of models with large volume of compactification where inflation may occur exponentially far away from the present vacuum state. In these models, the Hubble constant during inflation can be many orders of magnitude greater than the gravitino mass. We introduce a toy model describing this scenario, and discuss its strengths and weaknesses.

Figures (9)

• Figure 1: The lowest curve with dS minimum is the potential of the KKLT model. The second one shows what happens to the volume modulus potential when the inflaton potential $V_{\rm infl}={V(\phi)\over \sigma^3}$ added to the KKLT potential. The top curve shows that when the inflaton potential becomes too large, the barrier disappears, and the internal space decompactifies. This explains the constraint $H\lesssim m_{3/2}$.
• Figure 2: An illustration of the scenario put forward in this article. At relatively small volume, high-scale inflation occurs due to fine-tuned quantum corrections. After inflation the volume modulus evolves over a long range of many Planck scales, eventually settling in the large volume minimum with TeV gravitino mass. Although the barrier protecting from decompactification is very small compared to the initial energies, an attractor solution guides the fields to the minimum and prevents overshooting.
• Figure 3: The potential at small $\Phi$. Inflation occurs near the inflection point at $\Phi \sim 1.3$, in Planck units.
• Figure 4: The potential at large $\Phi$. Vacuum state corresponds to the minimum at $\Phi \sim 19$.
• Figure 5: The evolution of the radiation-background attractor solution as it approaches the minimum. The solid dashed horizontal line shows the location of the barrier to decompactification, and the narrow horizontal line the location of the true minimum. The attractor solution settles at the minimum and does not overshoot. The different paths correspond to different initial conditions. $N = \ln a$ is the time variable.