Abstract
In the present work we consider the existence and stability of Einstein static ES Universe in Brans–Dicke (BD) theory with non-vanishing spacetime torsion. In this theory, torsion field can be generated by the BD scalar field as well as the intrinsic angular momentum (spin) of matter. Assuming the matter content of the Universe to be a Weyssenhoff fluid, which is a generalization of perfect fluid in general relativity (GR) in order to include the spin effects, we find that there exists a stable ES state for a suitable choice of the model parameters. We analyze the stability of the solution by considering linear homogeneous perturbations and discuss the conditions under which the solution can be stable against these type of perturbations. Moreover, using dynamical system techniques and numerical analysis, the stability regions of the ES Universe are parametrized by the BD coupling parameter and first and second derivatives of the BD scalar field potential, and it is explicitly shown that a large class of stable solutions exists within the respective parameter space. This allows for non-singular emergent cosmological scenarios where the Universe oscillates indefinitely about an initial ES solution and is thus past eternal.
Highlights
The modified BD theory has been investigated on a general spacetime manifold with non-vanishing torsion field [67] and it was shown that both the scalar field and spin of fermionic particles have contribution in generating the spacetime torsion field. This theory can be viewed as a sort of unification of BD theory and Einstein– Cartan (EC) theory, i.e., the simplest Poincare gauge theory of gravity, in the framework of which, the gravitational interactions are described by means of spacetime curvature and torsion with the sources being energy-momentum and spin tensors [68]
From the standpoint of ECBD theory, the BD scalar field can play the role of a mediator field i.e., from one side, it participates within the gravitational interactions through its non-minimal coupling to curvature and from another side, it behaves as a source, alongside with the spin of fermionic matter, for spacetime torsion field
It is worth mentioning that since in addition to the spin effects, the BD scalar field could act as a source of torsion field, the ECBD theory is reduced to the EC theory after the BD scalar field comes to a rest at a constant value but the torsion field may not be totally vanished as the spin effects are still present (Fig. 2)
Summary
[19], brane-world scenario [20,21,22,23,24,25], Einstein–Gauss–Bonnet theory [26,27], f (R) theory [28,29,30,31,32], f (T) gravity [33], loop quantum cosmology [35,36,37,38,39,40] and other gravity theories [41,42,43,44,45,46,47,48,49,50,51,52]. The modified BD theory has been investigated on a general spacetime manifold with non-vanishing torsion field [67] and it was shown that both the scalar field and spin of fermionic particles have contribution in generating the spacetime torsion field This theory can be viewed as a sort of unification of BD theory and EC theory, i.e., the simplest Poincare gauge theory of gravity, in the framework of which, the gravitational interactions are described by means of spacetime curvature and torsion with the sources being energy-momentum and spin tensors [68]. From the standpoint of ECBD theory, the BD scalar field can play the role of a mediator field i.e., from one side, it participates within the gravitational interactions through its non-minimal coupling to curvature and from another side, it behaves as a source, alongside with the spin of fermionic matter, for spacetime torsion field.
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