On Calabi-Yau Threefolds For Unified LVS Inflation

Abstract

Fibre inflation, Poly-instanton inflation and (Loop) Blow-up inflation are among the most popular Kähler moduli based inflationary models realized in the standard LARGE volume scenarios (LVS). In this article, we present a unified framework in which all these three LVS inflationary models can be realized by using (different orientifolds of) a single Calabi-Yau (CY) threefold. In fact, the desired CY threefold needs to have a K3- or ${\mathbb{T}}^4$-fibration structure along with two diagonal del Pezzo divisors, and a so-called `Wilson' divisor which corresponds to a surface realized as a ${\mathbb{P}}^1$ fibration over ${\mathbb{T}}^2$s. For classification purpose, we perform a detailed scan of the CY geometries with $1\le h^{1,1}(\mathrm{CY})\le 6$ that arise from the triangulation of the four-dimensional reflexive polytopes of the Kreuzer-Skarke database. In this regard, after scanning around 100,000 CY geometries and the corresponding topologies of around a million of toric divisors, we find two CY threefolds satisfying these requirements for $1\le h^{1,1}(\mathrm{CY})\le 4$, while there are 14 and 45 candidate CY geometries for $h^{1,1}(\mathrm{CY})=5$ and $h^{1,1}(\mathrm{CY})=6$, respectively. We discuss the extended applications of such CY threefolds for cosmological model building in string theoretic frameworks.

Comments: 42 pages