Mysteries of the Geometrization of Gravitation

As we now know, there are indeed at least two major difficulties with General Relativity (GR). The first one is related with its incompatibility with quantum mechanics, in the absence of a widely accepted consistent theory that combines the two theories. The second problem is related with the requirement of the dark sectors - inflaton, dark matter and dark energy by the energy-stress tensor, which are needed to explain a variety of astronomical and cosmological observations. While, these dark sectors themselves do not have any non-gravitational or laboratory evidence, the dark energy poses, in addition, a serious confrontation between fundamental physics and cosmology. Guided by the theoretical and the observational evidences, we are led to a slight modification in the notion of the existence of the source of gravitation and its manifestation in GR, which is in striking agreement with not only the theory, but also the observations without requiring the dark sectors of the standard approach. Additionally, it provides natural explanations to some unexplained puzzles.Comment: Expanded version (added with new findings) of the essay (arXiv:1206.2795) awarded `Honorable Mention' of the year 2012 by the Gravity Research Foundation; v3: Published Versio

Einstein and Beyond: A Critical Perspective on General Relativity

An alternative approach to Einstein's theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor $T^{ik}$ and unphysical solutions. The new approach emanates from a critical analysis of these problems, providing a novel insight that the matter fields, together with the ensuing gravitational field, are already present inherently in the spacetime without taking recourse to $T^{ik}$. Supported by numerous evidences, the new insight revolutionizes our views on the representation of the source of gravitation and establishes the spacetime itself as the source, which becomes crucial for understanding the unresolved issues in a unified manner. This leads to a new paradigm in GR by establishing equation $R^{ik}=0$ as the field equation of gravitation plus inertia in the very presence of matter.Comment: An invited review accepted for publication by `Universe' in its Special Issue "100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year

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