GRAVITATIONAL LENSING EFFECTS IN A TIME-VARIABLE COSMOLOGICAL CONSTANT COSMOLOGY

A scalar field phi with a potential V(phi) infinity phi(-alpha)(alpha > 0) has an energy density, behaving like that of a time-variable cosmological 'constant', that redshifts less rapidly than the energy densities of radiation and matter, and so might contribute significantly to the present energy density. We compute, in this spatially flat cosmology, the gravitational lensing optical depth, and the expected lens redshift distribution for fixed source redshift. We find, for the values of alpha almost-equal-to 4 and baryonic density parameter OMEGA almost-equal-to 0.2 consistent with the classical cosmological tests, that the optical depth is significantly smaller than that in a constant-LAMBDA model with the same OMEGA. (For OMEGA = 0.2 and source redshift z(s) = 2.5, in the constant-LAMBDA model the optical depth is a factor of almost-equal-to 4.3 larger than in the Einstein-de Sitter case, while in the time-variable LAMBDA model, for alpha = 4, it is a factor of almost-equal-to 2.3 larger than in the Einstein-de Sitter model.) We also find that the redshift of the maximum of the lens distribution falls between that in the constant-LAMBDA model and that in the Einstein-de Sitter model.