Universality in D-brane inflation

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 7·107 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 Ne e-folds of inflation is a power law, P(Ne)∝Ne−3, and wederivethe same exponent from a simple analytical model. The success of inflation is relatively insensitive to the initial position: we find attractor behavior in the angular directions, and the D3-brane can begin far above the inflection point without overshooting. Initial radial or angular velocities, on the other hand, can have a significant effect on the duration of inflation. In favorable regions of the spaces of initial velocities and of Lagrangian parameters, models yielding 60 e-folds of expansion arise approximately once in 103 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 105 trials. The emergence of robust predictions from a six-field potential with hundreds of terms invites an analytic approach to multifield inflation.