Modelling the WMAP large-angle anomalies as an effect of a local density inhomogeneity

We investigate large-angle scale temperature anisotropy in the Cosmic Microwave Background (CMB) with the Wilkinson Microwave Anisotropy Probe (WMAP) data and model the large-angle anomalies as the effect of the CMB quadrupole anisotropies caused by the local density inhomogeneities. The quadrupole caused by the local density inhomogeneities is different from the special relativity kinematic quadrupole. If the observer inhabits a strong inhomogeneous region, the local quadrupole should not be neglected. We calculate such local quadrupole under the assumption that there is a huge density fluctuation field in direction $({284}^{\circ },{74}^{\circ })$, where the density fluctuation is ${10}^{-3}$, and its center is $\sim 112h^{-1}\mathrm{M}\mathrm{p}\mathrm{c}$ away from us. After removing such mock signals from WMAP data, the power in quadrupole, $C_2$, increases from the range $(200\sim 260\mu {\mathrm{K}}^2)$ to $\sim 1000\mu {\mathrm{K}}^2$. The quantity S, which is used to estimate the alignment between the quadrupole and the octopole, decreases from $(0.7\sim 0.74)$ to $(0.31\sim 0.37)$, while the model predict that $C_2=1071.5\mu {\mathrm{K}}^2$, $S=0.412$. So our local density inhomogeneity model can, in part, explain the WMAP low-$\mathrm{\ell }$ anomalies.