The tomographic Alcock-Paczynski ( AP ) method can result in tight cosmological constraints by using small and intermediate clustering scales of the large scale structure ( LSS ) of the galaxy distribution .
By focusing on the redshift dependence , the AP distortion can be distinguished from the distortions produced by the redshift space distortions ( RSD ) .
In this work , we combine the tomographic AP method with other recent observational datasets of SNIa+BAO+CMB+ H _ { 0 } to reconstruct the dark energy equation-of-state w in a non-parametric form .
The result favors a dynamical DE at z \lesssim 1 , and shows a mild deviation ( \lesssim 2 \sigma ) from w = -1 at z = 0.5 - 0.7 .
We find the addition of the AP method improves the low redshift ( z \lesssim 0.7 ) constraint by \sim 50 \% .