Non-parametric dark energy reconstruction using the tomographic
  Alcock-Paczynski test
  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 $z\lesssim1$, and
shows a mild deviation ($\lesssim2\sigma$) from $w=-1$ at $z=0.5-0.7$. We find
the addition of the AP method improves the low redshift ($z\lesssim0.7$)
constraint by $\sim50\%$.
