Abstract. The hemispherical power asymmetry, observed in the CMBR data, has generally been interpreted in terms of the dipole modulation model for the temperature fluctuations. Here we point out that this model leads to several predictions, which can be directly tested in the current data. We suggest tests of the hemispherical power asymmetry both in real and multipole space. We find a significant signal of the dipole modulation model in WMAP and PLANCK data with our tests. The dipole amplitude and direction also agrees, within errors, with earlier results based on hemispherical analysis in multipole space. We also find evidence that the effective dipole modulation amplitude increases with the multipole l in the range l = 2 − 64.

We propose a dipole modulation model for the Cosmic Microwave Background Radiation (CMBR) polarization field. We show that the model leads to correlations between l and l + 1 multipoles, exactly as in the case of temperature. We obtain results for the case of T E, EE and BB correlations. An anisotropic or inhomogeneous model of primordial power spectrum which leads to such correlations in temperature field also predicts similar correlations in CMBR polarization. We analyze the CMBR temperature and polarization data in order to extract the signal of these correlation between l and l + 1 multipoles. Our results for the case of temperature using the latest PLANCK data agree with those obtained by an earlier analysis. A detailed study of the correlation in the polarization data is not possible at present. Hence we restrict ourselves to a preliminary investigation in this case.

We relate the observed hemispherical anisotropy in the cosmic microwave radiation data to an inhomogeneous power spectrum model. The hemispherical anisotropy can be parameterized in terms of the dipole modulation model. This model leads to correlations between spherical harmonic coefficients corresponding to multipoles, l and l + 1. We extract the l dependence of the dipole modulation amplitude, A, by making a fit to the WMAP and PLANCK CMBR data. We propose an inhomogeneous power spectrum model and show that it also leads to correlations between multipoles, l and l + 1. The model parameters are determined by making a fit to the data. The spectral index of the inhomogeneous power spectrum is found to be consistent with zero.

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.

We consider an inhomogeneous model and independently an anisotropic model of primordial power spectrum in order to describe the observed hemispherical anisotropy in Cosmic Microwave Background Radiation. This anisotropy can be parametrized in terms of the dipole modulation model of the temperature field. Both the models lead to correlations between spherical harmonic coefficients corresponding to multipoles, l and l ± 1. We obtain the model parameters by making a fit to TT correlations in CMBR data. Using these parameters we predict the signature of our models for correlations among different multipoles for the case of the TE and EE modes. These predictions can be used to test whether the observed hemispherical anisotropy can be correctly described in terms of a primordial power spectrum. Furthermore these may also allow us to distinguish between an inhomogeneous and an anisotropic model.