Towards Systematics of Calabi-Yau Landscape for String Cosmology

TL;DR

This review explores how Calabi-Yau threefold geometries influence string cosmology models, focusing on moduli stabilization, inflationary scenarios, and the importance of topology in effective potential generation.

Contribution

It provides a phenomenologist-friendly overview of the role of Calabi-Yau topologies in string model building and inflation, highlighting geometric impacts on scalar potentials and inflation dynamics.

Findings

Calabi-Yau topologies are crucial for generating effective scalar potentials.

Specific geometries impact the success of inflationary models like fibre inflation.

Multi-field approaches can overcome individual moduli limitations in inflation.

Abstract

In this review, we discuss the relevance and impact of studying Calabi-Yau threefolds in the context of global model building in string phenomenology. First, taking a phenomenologist-friendly approach, we review how the topologies of the various divisors and curves of the compactifying CY threefolds play a crucial role for generating the various ``suitable" classes of effective scalar potentials, within the framework of the popular moduli stabilization schemes such as KKLT and LVS. Subsequently, we discuss the impact of the specifics of the CY threefold geometries in the minimal LVS inflationary models such as fibre inflation, in particular, along the challenges such as the inflaton field-range bound. In this regard, we discuss a multi-field approach in which several fibre moduli assist to drive successful inflation having a sufficient number of efolds, without getting close to their individual K\"ahler cone boundaries.