The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights

We develop a new method, which is based on the optimal redshift weighting scheme, to extract the maximal tomographic information of baryonic acoustic oscillations (BAO) and redshift space distortions (RSD) from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 quasar (DR14Q) survey. We validate our method using the EZ mocks, and apply our pipeline to the eBOSS DR14Q sample in the redshift range of $0.8<z<2.2$. We report a joint measurement of $fsigma_8$ and two-dimensional BAO parameters $D_{rm A}$ and $H$ at four effective redshifts of $z_{rm eff}=0.98, 1.23, 1.52$ and $1.94$, and provide the full data covariance matrix. Using our measurement combined with BOSS DR12, MGS and 6dFGS BAO measurements, we find that the existence of dark energy is supported by observations at a $7.4sigma$ significance level. Combining our measurement with BOSS DR12 and Planck observations, we constrain the gravitational growth index to be $gamma=0.580pm0.082$, which is fully consistent with the prediction of general relativity. This paper is part of a set that analyses the eBOSS DR14 quasar sample.