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

A Curious Explanation of Some Cosmological Phenomena

While observational cosmology has shown tremendous growth over the last decade, deep mysteries continue to haunt our theoretical understanding of the ingredients of the concordance cosmological model, which are mainly `dark'. More than 95 percent of the content of the energy-stress tensor has to be in the form of inflaton, dark matter and dark energy, which do not have any non-gravitational or laboratory evidence and remain unidentified. Moreover, the dark energy poses a serious confrontation between fundamental physics and cosmology. This makes a strong case to discover alternative theories which do not require the dark sectors of the standard approach to explain the observations. In the present situation, it would be important to gain insight about the requirements of the `would be' final theory from all possible means. In this context, the present paper highlights some, hitherto unnoticed, interesting coincidences which may prove useful to develop insight about the `holy grail' of gravitation. It appears that the requirement of the speculative dark sectors by the energy-stress tensor, is indicative of a possible way out of the present crisis appearing in the standard cosmology, in terms of a theory wherein the energy-stress tensor does not play a direct role in the dynamics. It is shown that various cosmological observations can be explained satisfactorily in the framework of one such theory $-$ the Milne model, without requiring the dark sectors of the standard approach. Moreover, the model evades the horizon, flatness and the cosmological constant problems afflicting the standard cosmology. Though Milne's theory is an incomplete, phenomenological theory, and cannot be the final theory of gravitation, nevertheless, it would be worthwhile to study these coincidences, which may help us develop insight about the would-be final theory.Comment: 7 pages, including 2 figure

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