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Dual Nature of the Ricci Scalar and its Certain Consequences

S. K. Srivastava
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Abstract

Ricci scalar is the key ingredient of non-Newtonian theory of gravity, where space-time geometry has a crucial role. Normally, it is supposed to be a geometrical field, but interestingly it also behaves like a physical field. Thus it plays dual role in the arena of gravitation. This article is an overview of the work related to dual roles of the Ricci scalar. A scalar is a mathematical concept representing a spinless particle.Here, particle concept, manifesting the physical aspect of the Ricci scalar, is termed as riccion.It is a scalar particle with (mass)$^2$ inversely proportional to the gravitational constant. Many intereseting consequences of dual role of the Ricci scalar are discussed here. It causes inflationary scenario in the early universe without taking another scalar like ``inflaton''. It is found that a riccion behaves like an instanton also. This feature inspires``primordial inflation''.It is interesting to see that a riccion, obtained from higher-dimensional space-time, decouples into fermion and anti-fermion pair, if parity is violated. One-loop renormalization of riccion indicates fractal geometry at high energy.Homogeneous and inhomogeneous models of the early universe are derived using dual role of the Ricci scalar. Production of spinless and spin-1/2 particles, due to riccion coupling, is discussed here. Contribution of riccion to the cosmic dark energy is obtained here through one-loop renormalization and it is shown that dark energy decays to dark matter during expansion of the universe. It inspires a new cosmological scenario consistent with observational evidences.

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S. K. Srivastava. 2005-11-08. Dual Nature of the Ricci Scalar and its Certain Consequences. https://arxiv.org/abs/gr-qc/0510086

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