Inflationary Universe with Anisotropic Hair

TL;DR

The paper proposes an inflationary model in which a vector field nonminimally coupled to the inflaton generates a persistent, small anisotropy during inflation. The vector energy density tracks that of the inflaton, leading to a universal relation between the resulting anisotropy and the slow-roll parameter, and offering distinctive observational signatures. The analysis shows that for a wide class of potentials and couplings the anisotropy is of order the slow-roll parameter, providing a concrete counterexample to the cosmic no-hair conjecture. These results imply measurable statistical anisotropies in the CMB and possible correlations between scalar and tensor modes, motivating future observational and theoretical work. The phenomenon is dubbed hairy inflation, highlighting how even small vector hairs can influence early-universe dynamics.

Abstract

We study an inflationary scenario with a vector field coupled with an inflaton field and show that the inflationary universe is endowed with anisotropy for a wide range of coupling functions. This anisotropic inflation is a tracking solution where the energy density of the vector field follows that of the inflaton field irrespective of initial conditions. We find a universal relation between the anisotropy and a slow-roll parameter of inflation. Our finding has observational implications and gives a counter example to the cosmic no-hair conjecture.

Figures (2)

• Figure 1: Phase flow for $\phi$ is depicted. Here, we took the parameters $c=2$ and $\kappa m=10^{-5}$. We also put initial conditions $\phi_i=12$ and $\dot{\phi}_i=0$. There are two different slow-roll phases. The transition occurs around $\kappa\phi= 9$.
• Figure 2: Evolutions of the anisotropy $\Sigma/H$ for various $c$ are shown. One can see the attractor like behavior of the anisotropy.