Does Anisotropic "Inflation" Produce a Small Statistical Anisotropy?

TL;DR

This paper investigates anisotropic inflation models with gauge fields, revealing that stochastic effects prevent the classical attractor solution and strongly constrain the model's viability based on CMB data.

Contribution

The authors develop a stochastic formalism for vector fields in anisotropic inflation and demonstrate that the model is highly unlikely to satisfy observational constraints.

Findings

Stochastic effects disrupt the classical attractor solution.

The model is excluded by CMB constraints with 99.999% probability.

The formalism provides new insights into vector field dynamics in inflation.

Abstract

Anisotropic inflation is an interesting model with an U(1) gauge field and it predicts the statistical anisotropy of the curvature perturbation characterized by a parameter $g_*$. However, we find that the background gauge field does not follow the classical attractor solution due to the stochastic effect. We develop the stochastic formalism of a vector field and solve Langevin and Fokker-Planck equations. It is shown that this model is excluded by the CMB constraint $g_*\le 10^{-2}$ with a high probability about $99.999\%$.