The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: a multi-tracer analysis in Fourier space for measuring the cosmic structure growth and expansion rate

Abstract

We perform a joint BAO and RSD analysis using the eBOSS DR16 LRG and ELG samples in the redshift range of $z\in [0.6,1.1]$, and detect a RSD signal from the cross power spectrum at a $\sim 4\ddot{I}ƒ$ confidence level, i.e., $f\ddot{I}{ƒ}_8=0.317\pm 0.080$ at $z_{\mathrm{eff}}=0.77$. Based on the chained power spectrum, which is a new development in this work to mitigate the angular systematics, we measurement the BAO distances and growth rate simultaneously at two effective redshifts, namely, $D_{\mathrm{M}}/r_{\mathrm{d}}(z=0.70)=17.96\pm 0.51,D_{\mathrm{H}}/r_{\mathrm{d}}(z=0.70)=21.22\pm 1.20,f\ddot{I}{ƒ}_8(z=0.70)=0.43\pm 0.05$, and $D_{\mathrm{M}}/r_{\mathrm{d}}(z=0.845)=18.90\pm 0.78,D_{\mathrm{H}}/r_{\mathrm{d}}(z=0.845)=20.91\pm 2.86,f\ddot{I}{ƒ}_8(z=0.845)=0.30\pm 0.08$. Combined with BAO measurements including those from the eBOSS DR16 QSO and Lyman-$\hat{I}\pm$ sample, our measurement has raised the significance level of a nonzero $\hat{I}{\text{c◯}}_{\hat{\mathrm{I}}›}$ to $\sim 11\ddot{I}ƒ$.

21 pages, 13 figures; version accepted to MNRAS. The data product of this work is publicly available at https://github.com/icosmology/eBOSS_DR16_LRGxELG and at https://www.sdss.org/science/final-bao-and-rsd-measurements/