  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.

High Energy Physics - Theory;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology