Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe semi classical cosmology approximation for a Friedman Robertson Walker geometry coupled to a field
105
0
0.0
(
0
)
Added by
Jose Martinez-Morales L.
Publication date
2011
fields
Physics
and research's language is
English
Authors
Jose L. Martinez-Morales
Ask ChatGPT about the research
No Arabic abstract
The semi classical cosmology approximation for a Friedman Robertson Walker geometry coupled to a field is considered. A power series of the field with coefficients that depend on the radius of the geometry is proposed, and the equations for the coefficients are solved.
rate research
Read More
This paper presents a compelling argument for the physical light speed in the homogeneous and isotropic Friedman-Lemaitre-Robertson-Walker (FLRW) universe to vary with the cosmic time coordinate t of FLRW. It will be variable when the radial co-moving differential coordinate of FLRW is interpreted as physical and therefor transformable by a Lorentz transform locally to differentials of stationary physical coordinates. Because the FLRW differential radial distance has a time varying coefficient a(t), in the limit of a zero radial distance the light speed c(t) becomes time varying, proportional to the square root of the derivative of a(t) Since we assume homogeneity of space, this derived c(t) is the physical light speed for all events in the FLRW universe. This impacts the interpretation of astronomical observations of distant phenomena that are sensitive to light speed. A transform from FLRW is shown to have a physical radius out to all radial events in the visible universe. This shows a finite horizon beyond which there are no galaxies and no space. The general relativity (GR) field equation to determine a(t) and c(t) is maintained by using a variable gravitational constant and rest mass that keeps constant the gravitational and particle rest energies. This keeps constant the proportionality constant between the GR tensors of the field equation and conserves the stress-energy tensor of the ideal fluid used in the FLRW GR field equation. In the same way all of special and general relativity can be extended to include a variable light speed.
We show that the Laplace-Beltrami equation $square_6 a =j$ in $(setR^6,eta)$, $eta := mathrm{diag}(+----+)$, leads under very moderate assumptions to both the Maxwell equations and the conformal Eastwood-Singer gauge condition on conformally flat spaces including the spaces with a Robertson-Walker metric. This result is obtained through a geometric formalism which gives, as byproduct, simplified calculations. In particular, we build an atlas for all the conformally flat spaces considered which allows us to fully exploit the Weyl rescalling to Minkowski space.
It is shown that only the maximally-symmetric spacetimes can be expressed in both the Robertson-Walker form and in static form - there are no other static forms of the Robertson-Walker spacetimes. All possible static forms of the metric of the maximally-symmetric spacetimes are presented as a table. The findings are generalized to apply to functionally more general spacetimes: it is shown that the maximally symmetric spacetimes are also the only spacetimes that can be written in both orthogonal-time isotropic form and in static form.
A regularization procedure has been recently suggested for regularizing Big Bang singularities in Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes. We argue that this procedure is only appliable to one case of Big Bang singularities and does not affect other types of singularities.
All possible transformations from the Robertson-Walker metric to those conformal to the Lorentz-Minkowski form are derived. It is demonstrated that the commonly known family of transformations and associated conformal factors are not exhaustive and that there exists another relatively less well known family of transformations with a different conformal factor in the particular case that K = -1. Simplified conformal factors are derived for the special case of maximally-symmetric spacetimes. The full set of all possible cosmologically-compatible conformal forms is presented as a comprehensive table. A product of the analysis is the determination of the set-theoretical relationships between the maximally symmetric spacetimes, the Robertson-Walker spacetimes, and functionally more general spacetimes. The analysis is preceded by a short historical review of the application of conformal metrics to Cosmology.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
