A Geometrical Upper Bound on the Inflaton Range

TL;DR

This paper demonstrates that in type IIB LVS string models, the moduli space for the inflaton is inherently compact due to Calabi-Yau Kähler cone conditions, imposing an upper bound on the inflaton field range relevant for cosmology.

Contribution

The authors explicitly show that the moduli space is compact for all LVS vacua with h^{1,1}=3 from reflexive polytopes, providing a geometrical upper bound on the inflaton range.

Findings

Moduli space is compact for all LVS vacua with h^{1,1}=3.

Effective inflaton field range is bounded from above, often trans-Planckian only in K3 fibred cases.

New LVS geometries were identified from Kreuzer-Skarke list.

Abstract

We argue that in type IIB LVS string models, after including the leading order moduli stabilisation effects, the moduli space for the remaining flat directions is compact due the Calabi-Yau K\"ahler cone conditions. In cosmological applications, this gives an inflaton field range which is bounded from above, in analogy with recent results from the weak gravity and swampland conjectures. We support our claim by explicitly showing that it holds for all LVS vacua with $h^{1,1} = 3$ obtained from 4-dimensional reflexive polytopes. In particular, we first search for all Calabi-Yau threefolds from the Kreuzer-Skarke list with $h^{1,1}=2$, $3$ and $4$ which allow for LVS vacua, finding several new LVS geometries which were so far unknown. We then focus on the $h^{1,1} = 3$ cases and show that the K\"ahler cones of all toric hypersurface threefolds force the effective 1-dimensional LVS moduli space to be compact. We find that the moduli space size can generically be trans-Planckian only for K3 fibred examples.