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Global Embedding of Fibre Inflation Models

Michele Cicoli, Francesco Muia, Pramod Shukla

TL;DR

This paper advances string cosmology by constructing the first explicit globally consistent Type IIB Calabi–Yau orientifold embeddings of fibre inflation within LVS framework, using CYs with $h^{1,1}=3$ that are K3 (or $\mathbb{T}^4$) fibred over $\mathbb{P}^1$ and include a shrinkable rigid divisor. It performs a Kreuzer–Skarke scan to identify 45 suitable weak Swiss-cheese geometries, then builds globally consistent orientifold and D3/D7-brane setups, computing string-loop and higher-derivative ($F^4$) corrections to realize the fibre inflation potential and study their impact on inflaton dynamics. The explicit global model analysis shows that the flat fibre direction can be lifted to yield a controlled plateau, enabling inflation with predictions such as $r$ around $0.006$–$0.01$ and $n_s$ in the Planck-preferred range, while also validating moduli stabilisation and EFT consistency. A key limitation is that $h^{1,1}=3$ cannot accommodate a chiral visible sector, motivating future work on $h^{1,1}=4$ Calabi–Yau manifolds to incorporate visible-sector chirality and a concrete dS uplifting mechanism.

Abstract

We present concrete embeddings of fibre inflation models in globally consistent type IIB Calabi-Yau orientifolds with closed string moduli stabilisation. After performing a systematic search through the existing list of toric Calabi-Yau manifolds, we find several examples that reproduce the minimal setup to embed fibre inflation models. This involves Calabi-Yau manifolds with $h^{1,1}= 3$ which are K3 fibrations over a $\mathbb{P}^1$ base with an additional shrinkable rigid divisor. We then provide different consistent choices of the underlying brane set-up which generate a non-perturbative superpotential suitable for moduli stabilisation and string loop corrections with the correct form to drive inflation. For each Calabi-Yau orientifold setting, we also compute the effect of higher derivative contributions and study their influence on the inflationary dynamics.

Global Embedding of Fibre Inflation Models

TL;DR

This paper advances string cosmology by constructing the first explicit globally consistent Type IIB Calabi–Yau orientifold embeddings of fibre inflation within LVS framework, using CYs with that are K3 (or ) fibred over and include a shrinkable rigid divisor. It performs a Kreuzer–Skarke scan to identify 45 suitable weak Swiss-cheese geometries, then builds globally consistent orientifold and D3/D7-brane setups, computing string-loop and higher-derivative () corrections to realize the fibre inflation potential and study their impact on inflaton dynamics. The explicit global model analysis shows that the flat fibre direction can be lifted to yield a controlled plateau, enabling inflation with predictions such as around – and in the Planck-preferred range, while also validating moduli stabilisation and EFT consistency. A key limitation is that cannot accommodate a chiral visible sector, motivating future work on Calabi–Yau manifolds to incorporate visible-sector chirality and a concrete dS uplifting mechanism.

Abstract

We present concrete embeddings of fibre inflation models in globally consistent type IIB Calabi-Yau orientifolds with closed string moduli stabilisation. After performing a systematic search through the existing list of toric Calabi-Yau manifolds, we find several examples that reproduce the minimal setup to embed fibre inflation models. This involves Calabi-Yau manifolds with which are K3 fibrations over a base with an additional shrinkable rigid divisor. We then provide different consistent choices of the underlying brane set-up which generate a non-perturbative superpotential suitable for moduli stabilisation and string loop corrections with the correct form to drive inflation. For each Calabi-Yau orientifold setting, we also compute the effect of higher derivative contributions and study their influence on the inflationary dynamics.

Paper Structure

This paper contains 39 sections, 116 equations, 2 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Global embedding of fibre inflation
  3. A brief review
  4. String loop corrections
  5. Higher derivative effects
  6. Inflationary potentials
  7. Global constructions
  8. General requirements
  9. Weak Swiss-cheese CYs
  10. Divisor topologies
  11. Scanning results
  12. Orientifold involution and brane setup
  13. Computation of string loop effects
  14. Explicit global examples
  15. Toric data
  16. ...and 24 more sections

Figures (2)

  • Figure 1: The red curve shows the point where the $F^4$ term starts spoiling the flatness of the inflationary plateau as a function of the small parameter $\mathcal{R}_2$. The green and blue horizontal lines show the values where the KK loop proportional to $\mathcal{R}_1$ becomes relevant for $\mathcal{R}_1=10^{-6}$ and $\mathcal{R}_1=10^{-5}$ respectively.
  • Figure 2: Inflationary potential for different values of $\mathcal{R}_2$ and $\mathcal{R}_1$ fixed at $\mathcal{R}_1=10^{-6}$.