Relating the inhomogeneous power spectrum to the CMB hemispherical anisotropy

We relate the observed hemispherical anisotropy in the cosmic microwave radiation data to an inhomogeneous power spectrum model. The hemispherical anisotropy can be parametrized 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.

Figure 1

The extracted value of the dipole modulation parameter, $A$, as a function of the multipole $(l)$, after fixing the direction parameters, for the three chosen multipole bins, 2–22, 23–43, 44–64.

Figure 2

The statistic, $S_H^{\text{data}}$, as a function of the multipole $l$. Here the statistic in the three bins is extracted by fixing the direction parameters to be equal to the mean direction over the entire multipole range. The dotted line represents the theoretical fit corresponding to $\alpha =0$, $g_0=0.047\pm 0.008$.