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 $z \gtrsim 2.5$.
