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An Inflationary Model in String Theory

Norihiro Iizuka, Sandip P. Trivedi

TL;DR

This work demonstrates a viable slow-roll inflation mechanism within a stabilized string-theory framework by placing a D3-brane between symmetrically arranged anti-D3-branes in a warped Type IIB compactification. A key insight is that curvature-induced mass for the D3-brane moduli can be nearly canceled by brane-anti-brane interactions, creating a broad maximum that supports small-field inflation with $H$ around $10^{10}$ GeV and suppressed tensor modes. The model yields a low inflation scale set by density-perturbation data and highlights a narrow, but navigable, parameter window for $r_1$, $Z$, $L$, and $g_s$, pending explicit string constructions. The discussion also explores generalizations and implications for eternal inflation, the landscape of maxima, and future work on ending inflation and embedding the Standard Model.

Abstract

We construct a model of inflation in string theory after carefully taking into account moduli stabilization. The setting is a warped compactification of Type IIB string theory in the presence of D3 and anti-D3-branes. The inflaton is the position of a D3-brane in the internal space. By suitably adjusting fluxes and the location of symmetrically placed anti-D3-branes, we show that at a point of enhanced symmetry, the inflaton potential V can have a broad maximum, satisfying the condition V''/V << 1 in Planck units. On starting close to the top of this potential the slow-roll conditions can be met. Observational constraints impose significant restrictions. As a first pass we show that these can be satisfied and determine the important scales in the compactification to within an order of magnitude. One robust feature is that the scale of inflation is low, H = O(10^{10}) GeV. Removing the observational constraints makes it much easier to construct a slow-roll inflationary model. Generalizations and consequences including the possibility of eternal inflation are also discussed. A more careful study, including explicit constructions of the model in string theory, is left for the future.

An Inflationary Model in String Theory

TL;DR

This work demonstrates a viable slow-roll inflation mechanism within a stabilized string-theory framework by placing a D3-brane between symmetrically arranged anti-D3-branes in a warped Type IIB compactification. A key insight is that curvature-induced mass for the D3-brane moduli can be nearly canceled by brane-anti-brane interactions, creating a broad maximum that supports small-field inflation with around GeV and suppressed tensor modes. The model yields a low inflation scale set by density-perturbation data and highlights a narrow, but navigable, parameter window for , , , and , pending explicit string constructions. The discussion also explores generalizations and implications for eternal inflation, the landscape of maxima, and future work on ending inflation and embedding the Standard Model.

Abstract

We construct a model of inflation in string theory after carefully taking into account moduli stabilization. The setting is a warped compactification of Type IIB string theory in the presence of D3 and anti-D3-branes. The inflaton is the position of a D3-brane in the internal space. By suitably adjusting fluxes and the location of symmetrically placed anti-D3-branes, we show that at a point of enhanced symmetry, the inflaton potential V can have a broad maximum, satisfying the condition V''/V << 1 in Planck units. On starting close to the top of this potential the slow-roll conditions can be met. Observational constraints impose significant restrictions. As a first pass we show that these can be satisfied and determine the important scales in the compactification to within an order of magnitude. One robust feature is that the scale of inflation is low, H = O(10^{10}) GeV. Removing the observational constraints makes it much easier to construct a slow-roll inflationary model. Generalizations and consequences including the possibility of eternal inflation are also discussed. A more careful study, including explicit constructions of the model in string theory, is left for the future.

Paper Structure

This paper contains 8 sections, 48 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Model
  3. Basic Set-up
  4. The Curvature Coupling: A positive mass
  5. Symmetrically Located Throats
  6. The Resulting Inflationary Scenario
  7. Parameter Constraints
  8. Discussion

Figures (1)

  • Figure 1: Two symmetrically located Klebanov-Strassler throats in Calabi-Yau space. Anti-D3-branes are at the bottom of each throats and mobile D3-brane is in between.