The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: measuring the evolution of the growth rate using redshift space distortions between redshift 0.8 and 2.2

We measure the growth rate and its evolution using the anisotropic clustering of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 (DR14) quasar sample, which includes $148\,659$ quasars covering the wide redshift range of $0.8 < z < 2.2$ and a sky area of $2112.90$ $\rm deg^2$. To optimise measurements we deploy a redshift-dependent weighting scheme, which allows us to avoid binning, and perform the data analysis consistently including the redshift evolution across the sample. We perform the analysis in Fourier space, and use the redshift evolving power spectrum multipoles to measure the redshift space distortion parameter $f\sigma_8$ and parameters controlling the anisotropic projection of the cosmological perturbations. We measure $f \sigma_8(z=1.52)=0.43 \pm 0.05 $ and $df\sigma_8/dz (z=1.52)= - 0.16 \pm 0.08$, consistent with the expectation for a $\Lambda$CDM cosmology as constrained by the Planck experiment.