Study of the Magnitude-Redshift Relation for type Ia Supernovae in a Model resulting from a Ricci-Symmetry

Models with a dynamic cosmological term \Lambda (t) are becoming popular as they solve the cosmological constant problem in a natural way. Instead of considering any ad-hoc assumption for the variation of \Lambda, we consider a particular symmetry, the contracted Ricci-collineation along the fluid flow, in Einstein's theory. We show that apart from having interesting properties, this symmetry does require \Lambda to be a function of the scale factor of the Robertson-Walker metric. In order to test the consistency of the resulting model with observations, we study the magnitude-redshift relation for the type Ia supernovae data from Perlmutter et al. The data fit the model very well and require a positive non-zero \Lambda and a negative deceleration parameter. The best-fitting flat model is obtained as \Omega_0 \approx 0.5 with q_0 \approx -0.2.Comment: 14 pages including 1 figure, accepted for publication in Gen. Relativ. Gra

Einstein-de Sitter model re-examined for the newly discovered SNe Ia

Consistency of Einstein-de Sitter model with the recently observed SNe Ia by the Hubble Space Telescope is examined. The model shows a reasonable fit to the observation, if one takes into account the extinction of SNe light by the intergalactic metallic dust ejected from the SNe explosions. Though the fit to the new data is worsened considerably compared with the earlier data, it can still be regarded acceptable. We should wait for more accurate observations at higher redshifts (as expected from the coming space missions such as SNAP and JWST) in order to rule out a model, which seems to explain all the other existing observations well (some even better than the favoured $\Lambda$CDM model), is consistent with beautiful theoretical ideas like inflation and cold dark matter, and is not as speculative as the models of dark energy.Comment: 14 pages including 2 figures, to appear in the Mon. Not. Roy. Astron. So

A Machian Model of Dark Energy

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 $\Lambda$ 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.Comment: Received an Honorable mention in the Essay Contest-2002 sponsored by the Gravity Research Foundation; A paragraph added on how the model can explain the CMB anisotropy observations; To appear in the Classical and Quantum Gravit