K. P. Sinha

“Cosmological” Constant and Scalar Gravitons

If a cosmological term is included in the equations of general relativity, the linearized equations can be interpreted as a tensor-scalar theory of finite-range gravitation. The scalar field cannot be transformed away be a gauge transformation (general co-ordinate transformation) and so must be interpreted as a physically significant degree of freedom. The hypothesis that a massive spin-two meson (mass m 2 ) satisfied equations identical in form to the equations of general relativity leads to the prediction of a massive spin-zero meson (mass m 0 ), the ratio of masses being m 0 / m 2 = √3.

Dual nature of Ricci scalar and creation of spinless particles

Manifestation of Ricci scalar like a matter field as well as a geometrical field, at high energy, has been noted earlier [9]. Here, its interaction with another scalar field is considered in four-dimensional curved space-time. This interaction leads to the production of a large number of pairs of spinless particle-antiparticle due to expansion of the early universe in the vacuum state (provided by temperature dependent Coleman-Weinberg like potential for Ricci field), where spontaneous symmetry breaking takes place.

f-gravity and the proton-electron mass ratio

A major puzzle of elementary-particle physics is the existence of two stable particles (i.e., those having infinite lifetime), the proton and the electron, with such a large mass ratio. An attempt is made to explain this mass anomaly as arising from the different mechanisms of the gravitational interactions for hadrons and leptons (i.e., the ability of the proton to take part in strong gravitational interactions also) just as the anomalous electromagnetic properties of the nucleons can be traced to the different nature of their electromagnetic interactions.

On the Field Equations of the Tensor-Scalar Theory of Finite Range Strong Gravity

The :field equations of a scalar-tensor theory of :finite-range strong gravity given in our previous work are solved. The possible physical significance of these solutions is discussed in terms of quantum numbers of elementary particles, along with relevant group theoretical concepts.

A singularity-free cosmological model in ECSK theory

In the framework of the ECSK [Einstein-Cartan-Sciama-Kibble] theory of cosmology, a scalar field nonminimally coupled to the gravitational field is considered. For a Robertson-Walker open universe (k=0) in the radiation era, the field equations admit a singularity-free solution for the scale factor. In theory, the torsion is generated through nonminimal coupling of a scalar field to the gravitation field. The nonsingular nature of the cosmological model automatically solves the flatness problem. Further absence of event horizon and particle horizon explains the high degree of isotropy, especially of 2.7-K background radiation.

The Brans-Dicke scalar field in Einstein-Cartan theory

In the framework of Einstein-Cartan (EC) theory, the Brans-Dicke (BD) theory is considered and it is found that a scalar field nonminimally coupled to the gravitational field gives rise to torsion, even though the scalar field has zero spin. The metric equations stay the same if the coupling constant is rescaled, but the equations of motion of a test particle, derived from the conservation equations, differ from those of the usual BD theory without torsion. The gravitational red-shift value differs considerably from the usual prediction of general theory of relativity (GTR), and rules out the possibility of a torsion version of BD theory forω<6.

Nonsingular cosmological models: the massive scalar field case

The nonminimal coupling of a massive self-interacting scalar field with a gravitational field is studied. Spontaneous symmetry breaking occurs in the open universe even when the sign on the mass term is positive. In contrast to grand unified theories, symmetry breakdown is more important for the early universe and it is restored only in the limit of an infinite expansion. Symmetry breakdown is shown to occur in flat and closed universes when the mass term carries a wrong sign. The model has a naturally defined effective gravitational coupling coefficient which is rendered time-dependent due to the novel symmetry breakdown. It changes sign below a critical value of the cosmic scale factor indicating the onset of a repulsive field. The presence of the mass term severely alters the behaviour of ordinary matter and radiation in the early universe. The total energy density becomes negative in a certain domain. These features make possible a nonsingular cosmological model for an open universe. The model is also free from the horizon and the flatness problems.

A possible model for fifth force

Recent reanalysis of the data of the Eötvös experiment suggested the existence of a new force. We show that a negative energy massive scalar field minimally coupled to gravity in a background Schwarzschild metric naturally leads to a potential which can explain the small anomalous effect in the Eötvös experiment.