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We apply the methodology developed in \cite{Li2014,Li2015} to BOSS DR12galaxies and derive cosmological constraints from the redshift dependence ofthe Alcock-Paczynski (AP) effect. The apparent anisotropy in the distributionof observed galaxies arise from two main sources, the redshift-space distortion(RSD) effect due to the galaxy peculiar velocities, and the geometricdistortion when incorrect cosmological models are assumed for transformingredshift to comoving distance, known as the AP effect. Anisotropies produced bythe RSD effect are, although large, maintaining a nearly uniform magnitude overa large range of redshift, while the degree of anisotropies from the AP effectvaries with redshift by much larger magnitude. We split the DR12 galaxies intosix redshift bins, measure the 2-point correlation function in each bin, andassess the redshift evolution of anisotropies. We obtain constraints of$\Omega_m=0.290 \pm 0.053,\ \ w = -1.07 \pm 0.15$, which are comparable withthe current constraints from other cosmological probes such as type Iasupernovae, cosmic microwave background, and baryon acoustic oscillation (BAO).Combining these cosmological probes with our method yield tight constraints of$ \Omega_m = 0.301 \pm 0.006,\ w=-1.054 \pm 0.025$. Our method is complementaryto the other large scale structure probes like BAO and topology. We expect thistechnique will play an important role in deriving cosmological constraints fromlarge scale structure surveys.

Cosmological constraints from the redshift dependence of the Alcock-Paczynski effect: application to the SDSS-III BOSS DR12 galaxies