Dual Nature of the Ricci Scalar and Its Certain Consequences

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 physical aspect of the Ricci scalar, is termed as riccion. It is a scalar particle with (mass) inversely proportinal to the gravitational constant. Many interesting consequences of dual role of the Ricci scalar are discussed here. It causes inflationary scenario in the early universe without taking an another scalar like “inflaton” also. 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 1