  A sample of quasars has been recently assembled to investigate the non-linear
relation between their monochromatic luminosities at 2500{\AA}, and 2 keV and
to exploit quasars as a new class of standardized candles. The use of this
technique for cosmological purposes relies on the non-evolution with redshift
of the UV-optical spectral properties of quasars, as well as on the absence of
possible contaminants such as dust extinction and host-galaxy contribution. We
address these possible issues by analysing the spectral properties of our
cosmological quasar sample. We produced composite spectra in different bins of
redshift and accretion parameters (black hole mass, bolometric luminosity), to
investigate any possible evolution of the spectral properties of the continuum
of the composites with these parameters. We found a remarkable similarity
amongst the various stacked spectra. The overall shape of the continuum does
not show any statistically significant trend with the accretion parameters nor
with the redshift. The composite spectrum of our quasar sample is consistent
with negligible levels of both intrinsic reddening (with a colour excess
E(B-V)< 0.01) and host-galaxy emission (less than 10%) in the optical. We
tested whether unaccounted dust extinction could explain the discrepancy
between our cosmographic fit of the Hubble-Lemaitre diagram and the concordance
{\Lambda}CDM model. The average colour excess required to solve the tension
should increase with redshift up to unphysically high values (E(B-V)=0.1 at
z>3) that would imply that the intrinsic emission of quasars is much bluer and
more luminous than ever reported in observed spectra. The similarity of quasar
spectra across the parameter space excludes a significant evolution of the
average continuum properties with any of the explored parameters, confirming
the reliability of our sample for cosmological applications.
