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$α'$ Inflation: Moduli Stabilisation and Observable Tensors from Higher Derivatives

Michele Cicoli, David Ciupke, Senarath de Alwis, Francesco Muia

TL;DR

This work extends the LVS framework by incorporating higher-derivative α'^3 corrections, specifically F^4 terms, to lift all residual flat Kähler moduli directions in Calabi–Yau manifolds with at least one blow-up divisor. It shows that, together with leading F^2 effects fixing the volume and small cycles, the remaining flat directions can be stabilized in a controlled EFT, enabling a new inflationary scenario (α'-Inflation) where a single flat direction acts as the inflaton. The inflaton potential arises from a combination of F^4 corrections and winding-loop effects, yielding a plateau-like region and a steeper tail that can produce observable tensors with r around 0.01 while preserving a consistent EFT with m_V ≪ M_KK and M_inf below the KK scale. The model predicts ns ≈ 0.97 and r ≈ 0.01 for natural parameter choices and argues for the testability of r with upcoming CMB experiments, while maintaining a protection against dangerous higher-dimensional operators via an approximate shift symmetry.

Abstract

The leading order dynamics of the type IIB Large Volume Scenario is characterised by the interplay between $α'$ and non-perturbative effects which fix the overall volume and all local blow-up modes leaving (in general) several flat directions. In this paper we show that, in an arbitrary Calabi-Yau with at least one blow-up mode resolving a point-like singularity, any remaining flat directions can be lifted at subleading order by the inclusions of higher derivative $α'$ corrections. We then focus on simple fibred cases with one remaining flat direction which can behave as an inflaton if its potential is generated by both higher derivative $α'$ and winding loop corrections. Natural values of the underlying parameters give a spectral index in agreement with observational data and a tensor-to-scalar ratio of order $r=0.01$ which could be observed by forthcoming CMB experiments. Dangerous corrections from higher dimensional operators are suppressed due to the presence of an approximate non-compact shift symmetry.

$α'$ Inflation: Moduli Stabilisation and Observable Tensors from Higher Derivatives

TL;DR

This work extends the LVS framework by incorporating higher-derivative α'^3 corrections, specifically F^4 terms, to lift all residual flat Kähler moduli directions in Calabi–Yau manifolds with at least one blow-up divisor. It shows that, together with leading F^2 effects fixing the volume and small cycles, the remaining flat directions can be stabilized in a controlled EFT, enabling a new inflationary scenario (α'-Inflation) where a single flat direction acts as the inflaton. The inflaton potential arises from a combination of F^4 corrections and winding-loop effects, yielding a plateau-like region and a steeper tail that can produce observable tensors with r around 0.01 while preserving a consistent EFT with m_V ≪ M_KK and M_inf below the KK scale. The model predicts ns ≈ 0.97 and r ≈ 0.01 for natural parameter choices and argues for the testability of r with upcoming CMB experiments, while maintaining a protection against dangerous higher-dimensional operators via an approximate shift symmetry.

Abstract

The leading order dynamics of the type IIB Large Volume Scenario is characterised by the interplay between and non-perturbative effects which fix the overall volume and all local blow-up modes leaving (in general) several flat directions. In this paper we show that, in an arbitrary Calabi-Yau with at least one blow-up mode resolving a point-like singularity, any remaining flat directions can be lifted at subleading order by the inclusions of higher derivative corrections. We then focus on simple fibred cases with one remaining flat direction which can behave as an inflaton if its potential is generated by both higher derivative and winding loop corrections. Natural values of the underlying parameters give a spectral index in agreement with observational data and a tensor-to-scalar ratio of order which could be observed by forthcoming CMB experiments. Dangerous corrections from higher dimensional operators are suppressed due to the presence of an approximate non-compact shift symmetry.

Paper Structure

This paper contains 12 sections, 89 equations, 3 figures.

Table of Contents

  1. Introduction
  2. LVS with higher derivative terms
  3. Standard LVS vacua
  4. Higher derivative corrections
  5. Lifting flat directions via $F^4$ terms
  6. String loops
  7. $\alpha'$ Inflation
  8. Inflationary potential
  9. Cosmological observables
  10. Comparison with Fibre Inflation
  11. Conclusions
  12. Corrections to $F^4$ terms

Figures (3)

  • Figure 1: Plot of the inflationary potential for $R=2.74\cdot 10^{-4}$ (red line), $R=2.74\cdot 10^{-5}$ (green line) and $R=0$ (blue line).
  • Figure 2: Comparison between Fibre Inflation (blue line) and $\alpha'$ Inflation (red line) for $R=2.74\cdot 10^{-4}$. The vertical line indicates the point of horizon exit for $\alpha'$ Inflation. The potential for Fibre Inflation is too steep to support enough efoldings of inflation.
  • Figure 3: Comparison between Fibre Inflation (blue line) and $\alpha'$ Inflation (red line) for $R=2.74\cdot 10^{-5}$. The vertical line indicates the point of horizon exit for both Fibre and $\alpha'$ Inflation.