Recently Perlmutter et al .
( 1999 ) suggested a positive value of Einstein ’ s cosmological constant \Lambda on the basis of luminosity distances from type-Ia supernovae ( the “ SN-method ” ) .
However , \Lambda world models had earlier been proposed by Hoell & Priester ( 1991 ) and Liebscher et al .
( 1992a , b ) on the basis of quasar absorption-line data ( the “ Q-method ” ) .
Employing more general repulsive fluids ( “ dark energy ” ) encompassing the \Lambda component we quantitatively compare both approaches with each other .

Fitting the SN-data by a minimum-component model consisting of dark energy + dust ( pressureless matter ) yields a closed universe with a large amount of dust exceeding the baryonic content constrained by big-bang nucleosynthesis .
The nature of the dark energy is hardly constrained .
Only when enforcing a flat universe there is a clear tendency to a dark-energy \Lambda fluid and the ‘ canonical ’ value \Omega _ { M } \approx 0.3 for dust .

Conversely , a minimum-component Q-method fit yields a sharply defined , slightly closed model with a low dust density ruling out significant pressureless dark matter .
The dark-energy component obtains an equation-of-state { \cal P } = -0.96 \epsilon close to that of a \Lambda -fluid ( { \cal P } = - \epsilon ) . \Omega _ { M } = 0.3 or a precisely flat spatial geometry are inconsistent with minimum-component models .

It is found that quasar and supernova data sets can not be reconciled with each other via ( repulsive ideal fluid+incoherent matter+radiation ) -world models .
Compatibility could be reached by drastic expansion of the parameter space with at least two exotic fluids added to dust and radiation as world constituents .
If considering such solutions as far-fetched one has to conclude that the Q-method and the SN-Ia constraints are incompatible .