Direction dependence of the power spectrum and its effect on the cosmic microwave background radiation

We study several anisotropic inflationary models and their implications for the observed violation of statistical isotropy in the CMBR data. In two of these models the anisotropy decays very quickly during the inflationary phase of expansion. We explicitly show that these models lead to violation of isotropy only for low l CMBR modes. Our primary aim is to fit the observed alignment of l = 2,3 multipoles to the theoretical models. We use two measures, based on the power tensor, which contains information about the alignment of each multipole, to quantify the anisotropy in data. One of the measures uses the dispersion in eigenvalues of the power tensor. We also define another measure which tests the overall correlation between two different multipoles. We perturbatively compute these measures of anisotropy and fix the theoretical parameters by making a best fit to l = 2,3 multipoles. We show that some of the models studied are able to consistently explain the observed violation of statistical isotropy