String Loop Moduli Stabilisation and Cosmology in IIB Flux Compactifications

TL;DR

This work develops a robust framework for stabilising all Kähler moduli in type IIB Calabi–Yau flux compactifications via the LARGE Volume Scenario (LVS), identifying topological conditions and showing that an exponentially large volume emerges from the interplay of non-perturbative effects and $oldsymbol{
}$ corrections. It systematically analyzes string-loop corrections, uncovering an extended no-scale structure that cancels leading contributions to the scalar potential and preserves LVS robustness, while lifting otherwise flat directions in more complex Calabi–Yau geometries. The cosmological applications are then explored, with Fibre Inflation presenting a natural LVS-based model yielding observable gravity waves in K3-fibered setups; finite-temperature analyses constrain the internal volume and SUSY-breaking scales, linking the microphysics to the early- and late-time evolution of the Universe. Overall, the thesis demonstrates that LVS, augmented by controlled loop and $oldsymbol{
}$ corrections, provides a coherent link between string theory’s moduli stabilisation and testable cosmological predictions, while outlining the challenges and directions for future phenomenology and observational tests.

Abstract

This article represents the author's PhD thesis which is focused on moduli stabilisation in type IIB Calabi-Yau flux compactifications and its applications to cosmology. I derive the topological conditions on an arbitrary Calabi-Yau to give rise to the very promising LARGE Volume Scenario. After a systematic study of the behaviour of string loop corrections for general type IIB compactifications, I show how they play a crucial role to achieve full moduli stabilisation. I then apply these results to cosmology showing how, in the case of K3-fibrations, string loop corrections give rise naturally to an inflationary model which predicts observable gravity waves. Finally I compute the decompactification temperature for the LARGE Volume Scenario due to thermal effects and work out a cosmological constraint on the value of the internal volume.

Figures (28)

• Figure 1: 'Sofa' potential with the presence of a flat direction.
• Figure 2: Coupling of the Kähler modulus with the gauge fields on the brane.
• Figure 3: Coupling of the big modulus KK modes to a generic field $\Phi_s$ living on the brane wrapping the small 4-cycle.
• Figure 4: Coupling of the small modulus KK modes to a generic field $\Phi_s$ living on the brane wrapping the small 4-cycle.
• Figure 5: $\tau_{SM}$ fixed by string loop corrections. The numerical values used are $\lambda_{1}=\lambda_{2}=1$, $\lambda_{3}=50$, $\lambda_{4}=\lambda_{5}=5$ and then we have fixed $\tau_{E3}=10$ and $\mathcal{V}=\sqrt{10}e^{20\pi}$.