Abstract
This paper invokes a new mechanism for reducing a coupled system of fields (including Einstein’s equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current observational astronomy.Our approach is formulated as a classical Einstein-vector-scalar-Maxwell-fluid field theory on a spacetime with three-sphere spatial sections. Analytic cosmological solutions are found using local charts familiar from standard LFRW cosmological models. These solutions can be used to describe different types of evolution for the metric scale factor, the Hubble, jerk and de-acceleration functions, the scalar spacetime curvature and the Kretschmann invariant constructed from the Riemann–Christoffel spacetime curvature tensor. The cosmological sector of the theory accommodates a particular single big-bang scenario followed by an eternal exponential acceleration of the scale factor. Such a solution does not require an externally prescribed fluid equation of state and leads to a number of new predictions including a current value of the ‘jerk’ parameter, ‘Hopfian-like’ source-free Maxwell field configurations with magnetic helicity and distributional ‘bi-polar’ solutions exhibiting a new charge conjugation symmetry.An approximate scheme for field perturbations about this particular cosmology is explored and its consequences for a thermalisation process and a thermal history are derived, leading to a prediction of the time interval between the big-bang and the decoupling era. Finally it is shown that field couplings exist where both vector and scalar localised linearised perturbations exhibit dispersive wave-packet behaviours. The scalar perturbation may also give rise to Yukawa solutions associated with a massive Klein–Gordon particle. It is argued that the vector and scalar fields may offer candidates for ‘dark-energy’ and ‘dark-matter’ respectively.
Highlights
The advent of modern satellite technology in observational astronomy has ushered in a new era for astrophysics and research into the fundamental role of gravitation on a large scale
In this article we have discussed a new paradigm for exploring a number of puzzling aspects in modern cosmology and their implications for astrophysics and observable astronomy
In this paradigm we argue that an evolutionary description of the Universe is best formulated in terms of a series of successive approximations based on a viable cosmography derived from current observations with a minimum number of phenomenological constraints on the dynamics of the unobservable early Universe
Summary
The advent of modern satellite technology in observational astronomy has ushered in a new era for astrophysics and research into the fundamental role of gravitation on a large scale. We invoke a new mechanism for reducing Einstein’s field equations (without a cosmological constant term) coupled to fluid matter, vector and scalar fields, to a dynamical system that possesses a class of simple analytic solutions for the metric scale factor exhibiting characteristics of immediate relevance to current observational astronomy. Bekenstein’s model offers a relativistic post-MOND theory designed to account for a broad range of astrophysical phenomena, including galactic rotation rates, without explicitly introducing cosmological dark-matter fields It is constructed in terms of a constrained dynamic vector field (Π), a dynamic tensor field (g), a dynamic scalar field (φ), a non-dynamic field (σ), a Lagrange multiplier field (λ), a phenomenological real-valued function (F) and four coupling parameters K, k, l, G. The concluding section summarises the essential features discussed in the paper
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