Inflationary Universe with Anisotropic Hair

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 counterexample to the cosmic no-hair conjecture.

Figure 1

Phase flow for $\varphi$ is depicted. Here, we took the parameters $c=2$ and $\kappa m={10}^{-5}$. We also put initial conditions ${\varphi }_i=12$ and ${\dot{\varphi }}_i=0$. There are two different slow-roll phases. The transition occurs around $\kappa \varphi =9$.

Figure 2

Evolutions of the anisotropy $\Sigma /H$ for various $c$ are shown. One can see the attractorlike behavior of the anisotropy.