Impact of Relativistic Effects on the Primordial Non-Gaussianity Signature in the Large-Scale Clustering of Quasars

Relativistic effects in clustering observations have been shown to introduce scale-dependent corrections to the galaxy over-density field on large scales, which may hamper the detection of primordial non-Gaussianity $f_\textrm{NL}$ through the scale-dependent halo bias. The amplitude of relativistic corrections depends not only on the cosmological background expansion, but also on the redshift evolution and sensitivity to the luminosity threshold of the tracer population being examined, as parametrised by the evolution bias $b_\textrm{e}$ and magnification bias $s$. In this work, we propagate luminosity function measurements from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) to $b_\textrm{e}$ and $s$ for the quasar (QSO) sample, and thereby derive constraints on relativistic corrections to its power spectrum multipoles. Although one could mitigate the impact on the $f_\textrm{NL}$ signature by adjusting the redshift range or the luminosity threshold of the tracer sample being considered, we suggest that, for future surveys probing large cosmic volumes, relativistic corrections should be forward modelled from the tracer luminosity function including its uncertainties. This will be important to quasar clustering measurements on scales $k \sim 10^{-3} h \, \textrm{Mpc}^{-1}$ in upcoming surveys such as the Dark Energy Spectroscopic Instrument (DESI), where relativistic corrections can overwhelm the expected $f_\textrm{NL}$ signature at low redshifts $z \lesssim 1$ and become comparable to $f_\textrm{NL} \simeq 1$ in the power spectrum quadrupole at redshifts $z \gtrsim 2.5$.