We study the magnitude-redshift relation for the Type Ia supernovae data and the angular size-redshift relation for the updated compact radio sources data (from Gurvits et al) by considering four variable Λ-models:It is found that all the variable Λ-models, as well as the constant Λ-Friedmann model, fit the supernovae data equally well with χ 2 /dof ≈ 1 and require non-zero, positive values of Λ and an accelerating expansion of the universe. The estimates of the density parameter for the variable Λ-models are found higher than those for the constant Λ-Friedmann model.From the compact radio sources data, it is found, by assuming the noevolution hypothesis, that the Gurvits et al' model (Friedmann model with Λ = 0) is not the best-fitting model for the constant Λ case. The best-fitting Friedmann model (with constant Λ) is found to be a low density, vacuumdominated accelerating universe. The fits of this data set to the (variable, as well as, constant Λ-) models are found very good with χ 2 /dof ≈ 0.5 and require non-zero, positive values of Λ with either sign of the deceleration parameter. However, for realistic values of the matter density parameter, the only interesting solutions are (a) estimated from the supernovae data: the best-fit solutions for the flat models (including the constant Λ case); (b) estimated from the radio sources data: the global best-fit solutions for the models Λ ∼ H 2 and Λ ∼ ρ, the best-fit solution for the flat model with Λ = constant and the Gurvits et al' model.It is noted that, as in the case of recent CMB analyses, the data sets seem to favour a spherical universe (k > 0).

Abstract. By modifying the Chen and Wu ansatz, we have investigated some Friedmann models in which Λ varies as ρ. In order to test the consistency of the models with observations, we study the angular size -redshift relation for 256 ultracompact radio sources selected by Jackson and Dodgson. The angular sizes of these sources were determined by using very long-baseline interferometry in order to avoid any evolutionary effects. The models fit the data very well and require an accelerating universe with a positive cosmological constant. Open, flat and closed models are almost equally probable, though the open model provides a comparatively better fit to the data. The models are found to have intermediate density and imply the existence of dark matter, though not as much as in the canonical Einstein-de Sitter model.

We calculate the expected angular power spectrum of the temperature fluctuations in the microwave background radiation (MBR) generated in the quasi-steady state cosmology (QSSC). The paper begins with a brief description of how the background is produced and thermalized in the QSSC. We then discuss within the framework of a simple model, the likely sources of fluctuations in the background due to astrophysical and cosmological causes. Power spectrum peaks at l ≈ 6 − 10, 180 − 220 and 600 − 900 are shown to be related in this cosmology respectively to curvature effects at the last minimum of the scale factor, clusters and groups of galaxies. The effect of clusters is shown to be related to their distribution in space as indicated by a toy model of structure formation in the QSSC. We derive and parameterize the angular power spectrum using six parameters related to the sources of temperature fluctuations at three characteristic scales. We are able to obtain a satisfactory fit to the observational band power estimates of MBR temperature fluctuation spectrum. Moreover, the values of 'best fit' parameters are consistent with the range of expected values.

Einstein believed that Mach's principle should play a major role in finding a meaningful spacetime geometry, though it was discovered later that his field equations gave some solutions which were not Machian. It is shown, in this essay, that the kinematical Λ models, which are invoked to solve the cosmological constant problem, are in fact consistent with Mach's ideas. One particular model in this category is described which results from the microstructure of spacetime and seems to explain the current observations successfully and also has some benefits over the conventional models. This forces one to think whether the Mach's ideas and the cosmological constant are interrelated in some way.