Incompatibility of a comoving Lyalpha forest with supernova-Ia luminosity distances

Recently, Perlmutter et al. (\cite{Per99}) 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 (\cite{Hoe91a}) and Liebscher et al. (\cite{Lie92a}a,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. 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 is there a clear tendency to a dark-energy Lambda fluid and the ``canonical'' value Omega_M ~ 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 cannot 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.