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We perform a tomographic structure growth and expansion rate analysis usingthe monopole, quadrupole and hexadecapole of the redshift-space galaxy powerspectrum derived from the Sloan Digital Sky Survey (SDSS-III) BaryonOscillation Spectroscopic Survey (BOSS) Data Release 12 combined sample, whichcovers the redshift range of $0.20<z<0.75$. By allowing for overlap betweenneighbouring 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 aredshift resolution of $\Delta z\sim0.04$. Our measurement is consistent withthat presented in arXiv:1709.05173, where the analysis is performed inconfiguration space. We apply our measurement to constrain the $f(R)$ gravitymodel, and find that the 95\% CL upper limit of ${\rm log_{10}}B_0$ can bereduced by 11\% by our tomographic BAO and RSD measurement.

monthly notices of the royal astronomical society

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