The tomographic Alcock-Paczynski ( AP ) method utilizes the redshift evolution of the AP distortion to place constraints on cosmological parameters .
It has proved to be a robust method that can separate the AP signature from the redshift space distortion ( RSD ) effect , and deliver powerful cosmological constraints using the \lesssim 40 h ^ { -1 } Mpc clustering region .
In previous works , the tomographic AP method was performed via the anisotropic 2-point correlation function statistic .
In this work we consider the feasibility of conducting the analysis in the Fourier domain and examine the pros and cons of this approach .
We use the integrated galaxy power spectrum ( PS ) as a function of direction , \hat { P } _ { \Delta k } ( \mu ) , to quantify the magnitude of anisotropy in the large-scale structure clustering , and use its redshift variation to do the AP test .
The method is tested on the large , high resolution Big-MultiDark Planck ( BigMD ) simulation at redshifts z = 0 - 1 , using the underlying true cosmology \Omega _ { m } = 0.3071 , w = -1 .
Testing the redshift evolution of \hat { P } _ { \Delta k } ( \mu ) in the true cosmology and cosmologies deviating from the truth with \delta \Omega _ { m } = 0.1 , \delta w = 0.3 , we find that the redshift evolution of the AP distortion overwhelms the effects created by the RSD by a factor of \sim 1.7 - 3.6 .
We test the method in the range of k \in ( 0.2 , 1.8 ) h Mpc ^ { -1 } , and find that it works well throughout the entire regime .
We tune the halo mass within the range 2 \times 10 ^ { 13 } to 10 ^ { 14 } M _ { \odot } , and find that the change of halo bias results in \lesssim 5 \% change in \hat { P } _ { \Delta k } ( \mu ) , which is less significant compared with the cosmological effect .
Our work shows that it is feasible to conduct the tomographic AP analysis in the Fourier space .