  A Hubble diagram (HD) has recently been constructed in the redshift range
0<z<6.5 using a non-linear relation between the ultraviolet and X-ray
luminosities of QSOs. The Type Ia SN HD has already provided a high-precision
test of cosmological models, but the fact that the QSO distribution extends
well beyond the supernova range (z<1.8), in principle provides us with an
important complementary diagnostic whose significantly greater leverage in z
can impose tighter constraints on the distance versus redshift relationship. In
this paper, we therefore perform an independent test of nine different
cosmological models, among which six are expanding, while three are static.
Many of these are disfavoured by other kinds of observations (including the
aforementioned Type Ia SNe). We wish to examine whether the QSO HD confirms or
rejects these earlier conclusions. We find that four of these models
(Einstein-de Sitter, the Milne universe, the Static Universe with simple tired
light and the Static universe with plasma tired light) are excluded at the >99%
C.L. The Quasi-Steady State Model is excluded at >95% C.L. The remaining four
models (Lambda-CDM/wCDM, the R_h=ct Universe, the Friedmann open universe and a
Static universe with a linear Hubble law) all pass the test. However, only
Lambda-CDM/wCDM and $R_{\rm h}=ct$ also pass the Alcock-Paczynski (AP) test.
The optimized parameters in Lambda-CDM/wCDM are Omega_m=0.20^{+0.24}_{-0.20}
and w_{de}=-1.2^{+1.6}_{-infinity} (the dark-energy equation-of-state).
Combined with the AP test, these values become Omega_m=0.38^{+0.20}_{-0.19} and
w_{de}=-0.28^{+0.52}_{-0.40}. But whereas this optimization of parameters in
Lambda-CDM/wCDM creates some tension with their concordance values, the $R_{\rm
h}=ct$ Universe has the advantage of fitting the QSO and AP data without any
free parameters.
