The distant Type Ia supernovae data compiled by Perlmutter et al. are used to analyze the Cardassian expansion scenario, which was recently proposed by Freese & Lewis as an alternative to a cosmological constant (or more generally a dark energy component) in explaining the currently accelerating universe. We show that the allowed intervals for n and zeq, the two parameters of the Cardassian model, will give rise to a universe with a very low matter density, which can hardly be reconciled with the current value derived from the measurements of the cosmic microwave background anisotropy and galaxy clusters (cluster baryon fraction). As a result, this Cardassian expansion proposal does not seem to survive the magnitude-redshift test for the present Type Ia supernovae data, unless the universe contains primarily baryonic matter.

The "Cardassian Expansion Scenario" was recently proposed by Freese & Lewis as an alternative to a cosmological constant in explaining the current accelerating universe. In this paper we investigate observational constraints on this scenario from recent measurements of the angular size of high-z compact radio sources compiled by Gurvits and coworkers. We show that the allowed intervals for n and zeq, the two parameters of the Cardassian model, are heavily dependent on the value of the mean projected linear size l. However, the best fit to the current angular size data prefers the conventional flat cold dark matter model to this Cardassian expansion proposal, though the latter is cosmologically credible and compatible with the-z diagramfor some values of l.

The expected chirp mass distribution of observed events for future gravitational wave detectors is extensively investigated in the presence of an exotic fluid component with an arbitrary equation of state, −1 !xpx=x<0, i. e., the so-called dark energy component. The results for a flat model dominated by dark energy are compared to those for the standard flat model dominated by cold dark matter. It is found that for a flat universe the chirp mass distribution shows a sensitive dependence on !x, which may provide an independent and robust constraint on the cosmic equation of state.

a wide variety of cosmological models characterized by the cosmic mass density M and the normalized cosmological constant, we derive an analytic expression for the estimate of magnification cross-sections by an ensemble of isothermal spheres as models of galactic mass distributions. This provides a simple approach to demonstrate how the lensing probability by galaxies depends on the cosmological parameters. An immediate consequence is that, while a non-zero cosmological constant indeed leads to a significant increase of the lensing probability as it has been shown in the literature, only a small fraction of sky to 23 can be moderately (1:3) lensed by galaxies even in a-dominated flat universe. Therefore, whether or not there is a nonzero cosmological constant, it is unlikely that the overall quasar counts have been seriously contaminated by the presence of galactic lenses.

The theoretically expected amplitude of the associations of background quasars with foreground galaxies as a result of gravitational lensing has been updated in this paper. Since the galactic matter alone yields an amplitude of quasar overdensity smaller than that observed, special attention has been paid to the examination or reexamination of the uncertainties in the estimate of the quasar enhancement factor arising from the cosmic evolution of galaxies, the core radius and velocity bias of galactic matter distributions, the clusters of galaxies, the obstruction etect by galactic disks, the nonzero cosmological constant, etc. Unfortunately, none of these factors has been shown to be able to improve the situation signi