A Hubble diagram ( HD ) has recently been constructed in the redshift range 0 \lesssim z \lesssim 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 \lesssim 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/ w CDM , 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/ w CDM and R _ { h } = ct also pass the Alcock-Paczyński ( AP ) test .
The optimized parameters in \Lambda CDM/ w CDM are \Omega _ { m } = 0.20 ^ { +0.24 } _ { -0.20 } and w _ { de } = -1.2 ^ { +1.6 } _ { - \infty } ( 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/ w CDM creates some tension with their concordance values , the R _ { h } = ct Universe has the advantage of fitting the QSO and AP data without any free parameters .