Dipole anisotropy of galaxy distribution: Does the CMB rest frame exist in the local universe?

The peculiar motion of the Earth causes a dipole anisotropy modulation in the distant galaxy distribution due to the aberration effect. However, the amplitude and angular direction of the effect is not necessarily the same as those of the cosmic microwave background (CMB) dipole anisotropy due to the growth of cosmic structures. In other words exploring the aberration effect may give us a clue to the horizon-scale physics perhaps related to the cosmic acceleration. In this paper we develop a method to explore the dipole angular modulation from the pixelized galaxy data on the sky, properly taking into account the covariances due to the shot noise and the intrinsic galaxy clustering contamination as well as the partial sky coverage. We applied the method to the galaxy catalogs constructed from the Sloan Digital Sky Survey Data Release 6 data. After constructing the four galaxy catalogs that are different in the ranges of magnitudes and photometric redshifts to study possible systematics, we found that the most robust sample against systematics indicates no dipole anisotropy in the galaxy distribution. This finding is consistent with the expectation from the concordance {Lambda}-dominated cold dark matter model. Finally, we argue that an almost full-sky galaxy survey such as Large Synoptic Survey Telescope may allow for a significant detection of the aberration effect of the CMB dipole having the precision of constraining the angular direction to {approx}20 deg in radius. Assuming a hypothetical Large Synoptic Survey Telescope galaxy survey, we find that this method can confirm or reject the result implied from a stacked analysis of the kinetic Sunyaev-Zel'dovich effect of X-ray luminous clusters in Kashlinsky et al. (2008, 2009) if the implied cosmic bulk flow is not extended out to the horizon.