Universality in D-brane Inflation

TL;DR

This study investigates the universal behavior of six-field D-brane inflation on the conifold, revealing common dynamics, probabilistic inflation durations, and insensitivity to initial conditions through extensive numerical simulations.

Contribution

It demonstrates universal inflationary behavior in a complex six-field model and derives probability distributions for inflation duration, supported by large-scale numerical analysis.

Findings

Prolonged inflation typically involves rapid angular motion and spiraling into an inflection point.

Probability of N_e e-folds follows a power law P(N_e) ∝ N_e^{-3}.

Models with 60 e-folds occur roughly once in 10^3 trials; effective single-field models with 120 e-folds occur once in 10^5 trials.

Abstract

We study the six-field dynamics of D3-brane inflation for a general scalar potential on the conifold, finding simple, universal behavior. We numerically evolve the equations of motion for an ensemble of more than 7 \times 10^7 realizations, drawing the coefficients in the scalar potential from statistical distributions whose detailed properties have demonstrably small effects on our results. When prolonged inflation occurs, it has a characteristic form: the D3-brane initially moves rapidly in the angular directions, spirals down to an inflection point in the potential, and settles into single-field inflation. The probability of N_{e} e-folds of inflation is a power law, P(N_{e}) \propto N_{e}^{-3}, and we derive the same exponent from a simple analytical model. The success of inflation is relatively insensitive to the initial conditions: we find attractor behavior in the angular directions, and the D3-brane can begin far above the inflection point without overshooting. In favorable regions of the parameter space, models yielding 60 e-folds of expansion arise approximately once in 10^3 trials. Realizations that are effectively single-field and give rise to a primordial spectrum of fluctuations consistent with WMAP, for which at least 120 e-folds are required, arise approximately once in 10^5 trials. The emergence of robust predictions from a six-field potential with hundreds of terms invites an analytic approach to multifield inflation.