The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: a tomographic measurement of structure growth and expansion rate from anisotropic galaxy clustering in Fourier space

We perform a tomographic structure growth and expansion rate analysis using the monopole, quadrupole and hexadecapole of the redshift-space galaxy power spectrum derived from the Sloan Digital Sky Survey (SDSS-III) Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 combined sample, which covers the redshift range of $0.20<z<0.75$. By allowing for overlap between neighbouring redshift slices in order to extract information on the light-cone, we successfully obtain joint BAO and RSD constraints with a precision of $2-3\%$ for $D_A$, $3-10\%$ for $H$ and $9-12\%$ for $f\sigma_8$ with a redshift resolution of $\Delta z\sim0.04$. Our measurement is consistent with that presented in arXiv:1709.05173, where the analysis is performed in configuration space. We apply our measurement to constrain the $f(R)$ gravity model, and find that the 95\% CL upper limit of ${\rm log_{10}}B_0$ can be reduced by 11\% by our tomographic BAO and RSD measurement.