  We review an inflationary scenario with the anisotropic expansion rate. An
anisotropic inflationary universe can be realized by a vector field coupled
with an inflaton, which can be regarded as a counter example to the cosmic
no-hair conjecture. We show generality of anisotropic inflation and derive a
universal property. We formulate cosmological perturbation theory in
anisotropic inflation. Using the formalism, we show anisotropic inflation gives
rise to the statistical anisotropy in primordial fluctuations. We also explain
a method to test anisotropic inflation using the cosmic microwave background
radiation (CMB).
