  The non-linear relationship between the monochromatic X-ray and UV
luminosities in quasars offers the possibility of using high-z quasars as
standard candles for cosmological testing. In this paper, we use a high-quality
catalog of 1598 quasars extending to redshift 6, to compare the flat and
uniformly expanding cosmological model, $R_h$ = ct and $\Lambda$CDM
cosmological models which are the most debated. The quasar samples are mainly
from the XMM-Newton and the Sloan Digital Sky Survey (SDSS). The final result
is that the Akaike Information Criterion favors $\Lambda$CDM over $R_h$=ct with
a relative probability of 86.30% versus 13.70%.
