Applying Alcock-Paczynski Test to the Large Scale Structure

The main idea of the Alcock-Paczynski (AP) test is that, if we use a wrong distance-redshift relation to infer the shape of a spherical object in the Universe, this object may look non-spherical. To probe the cosmic expansion history through the AP test, the key point is to find something which is known as spherical in the Universe. We propose two possible ways applying the AP test to the large scale structure (LSS): 1) Based on the observed galaxies or quasars, one built up the beta-skeleton tracing the LSS, and investigating the inhomogeneity of the connections; 2) One reconstructs the smoothed density-contrast gradient field based on LSS observations, and investigating the inhomogeneity of the gradient vectors. Compared with some existed methods probing AP effect through 2-point correlation function, galaxy pairs, or voids, our methods have various advantages: 1) The information of both the high and low dense regions of the LSS are taken into account. 2) The redshift space distortion as the main contamination to the AP effect can be easily removed.