$\Lambda$CDM model with a scalar perturbation vs. preferred direction of the universe

Abstract

We present a scalar perturbation for the $\Lambda$CDM model, which breaks the isotropic symmetry of the universe. Based on the Union2 data, the least-${\chi }^2$ fit of the scalar perturbed $\Lambda$CDM model shows that the universe has a preferred direction $(l,b)=(287^{\circ }\pm 25^{\circ },11^{\circ }\pm 22^{\circ })$. The magnitude of scalar perturbation is about $-2.3\times 10^{-5}$. The scalar perturbation for the $\Lambda$CDM model implies a peculiar velocity, which is perpendicular to the radial direction. We show that the maximum peculiar velocities at redshift $z=0.15$ and $z=0.015$ equal to $73\pm 28\mathrm{km}\cdot {\mathrm{s}}^{-1}$ and $1099\pm 427\mathrm{km}\cdot {\mathrm{s}}^{-1}$, respectively. They are compatible with the constraints on peculiar velocity given by Planck Collaboration.

10 pages, 2 figures

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