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Inflationary Constraints on Type IIA String Theory

Mark P. Hertzberg, Shamit Kachru, Washington Taylor, Max Tegmark

TL;DR

In this work, the authors prove a no-go theorem for inflation in the most understood class of type IIA Calabi–Yau flux compactifications with NS-NS and R-R fluxes, D6-branes, and O6-planes at large volume and small string coupling, establishing the bound $\u0003\epsilon \ge \frac{27}{13}$ whenever the 4D potential $V>0$. They derive this by reducing to a 4D Einstein-frame action, identifying the volume modulus $\rho$ and the dilaton modulus $\tau$, and showing that the potential’s dependence on these moduli forces a large gradient along the $\hat{\rho}$ and $\hat{\tau}$ directions. The result rules out both inflation and de Sitter vacua in this regime, though it can be evaded by introducing additional ingredients such as NS 5-branes or geometric/non-geometric NS-NS fluxes, or by moving to different corners of the landscape (e.g., IIB setups). The paper thus delineates a sharp constraint on the IIA landscape and highlights promising directions (like NS5-branes and fluxes) for achieving inflationary cosmologies within string theory.

Abstract

We prove that inflation is forbidden in the most well understood class of semi-realistic type IIA string compactifications: Calabi-Yau compactifications with only standard NS-NS 3-form flux, R-R fluxes, D6-branes and O6-planes at large volume and small string coupling. With these ingredients, the first slow-roll parameter satisfies epsilon >= 27/13 whenever V > 0, ruling out both inflation (including brane/anti-brane inflation) and de Sitter vacua in this limit. Our proof is based on the dependence of the 4-dimensional potential on the volume and dilaton moduli in the presence of fluxes and branes. We also describe broader classes of IIA models which may include cosmologies with inflation and/or de Sitter vacua. The inclusion of extra ingredients, such as NS 5-branes and geometric or non-geometric NS-NS fluxes, evades the assumptions used in deriving the no-go theorem. We focus on NS 5-branes and outline how such ingredients may prove fruitful for cosmology, but we do not provide an explicit model. We contrast the results of our IIA analysis with the rather different situation in IIB.

Inflationary Constraints on Type IIA String Theory

TL;DR

In this work, the authors prove a no-go theorem for inflation in the most understood class of type IIA Calabi–Yau flux compactifications with NS-NS and R-R fluxes, D6-branes, and O6-planes at large volume and small string coupling, establishing the bound whenever the 4D potential . They derive this by reducing to a 4D Einstein-frame action, identifying the volume modulus and the dilaton modulus , and showing that the potential’s dependence on these moduli forces a large gradient along the and directions. The result rules out both inflation and de Sitter vacua in this regime, though it can be evaded by introducing additional ingredients such as NS 5-branes or geometric/non-geometric NS-NS fluxes, or by moving to different corners of the landscape (e.g., IIB setups). The paper thus delineates a sharp constraint on the IIA landscape and highlights promising directions (like NS5-branes and fluxes) for achieving inflationary cosmologies within string theory.

Abstract

We prove that inflation is forbidden in the most well understood class of semi-realistic type IIA string compactifications: Calabi-Yau compactifications with only standard NS-NS 3-form flux, R-R fluxes, D6-branes and O6-planes at large volume and small string coupling. With these ingredients, the first slow-roll parameter satisfies epsilon >= 27/13 whenever V > 0, ruling out both inflation (including brane/anti-brane inflation) and de Sitter vacua in this limit. Our proof is based on the dependence of the 4-dimensional potential on the volume and dilaton moduli in the presence of fluxes and branes. We also describe broader classes of IIA models which may include cosmologies with inflation and/or de Sitter vacua. The inclusion of extra ingredients, such as NS 5-branes and geometric or non-geometric NS-NS fluxes, evades the assumptions used in deriving the no-go theorem. We focus on NS 5-branes and outline how such ingredients may prove fruitful for cosmology, but we do not provide an explicit model. We contrast the results of our IIA analysis with the rather different situation in IIB.

Paper Structure

This paper contains 15 sections, 34 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Type IIA Compactifications
  3. Compactification
  4. The Slow-Roll Condition
  5. No-Go Theorem
  6. Potential Energy
  7. Proof of No-Go Theorem
  8. Evading the No-Go Theorem
  9. Various Ingredients
  10. An Illustration
  11. Type IIB Compactifications
  12. Discussion
  13. 4-Dimensional ${\cal N}=1$ Supergravity
  14. Kinetic Energy from Kähler Potential
  15. Potential Energy from Superpotential

Figures (1)

  • Figure 1: The potential $V(\hat{\tau})/V_{\hbox{\tiny{flux}}}$ with ($\bar{m}_{\hbox{\tiny{P}}}=1$) $B_3=1/4,\,B_0=1/4,\,B_4=3/8,\,B_{\hbox{\tiny{O6}}}=2$, and $\rho$ satisfying $\partial V/\partial \rho=0$. From bottom to top, the curves correspond to the following choices of $c$ : 2.183 (anti-de Sitter), 2.205 (Minkowski), 2.227 (de Sitter), and 2.280 (inflection), respectively.