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A Newtonian-Einstein-De Sitter Universe in Cosmological Mirror Super- Symmetry Pacificap@Hotmail.Com A Newtonian-Einstein-De Sitter Universe in Cosmological Mirror Super- symmetry [email protected] http://www.tonyb.freeyellow.com/ Abstract: The introduction of a characteristic length scale λo into the kinematics of the Poincare-Lorentz group of a descriptive flat Minkowski spacetime renders the latter a curved de Sitter space-time with a cosmological lambda parameter Λo relating this length scale as a Planck-Length 3 (L P=√[hG/2 πc ] ) and where λo becomes a transformed minimum configuration for the local description of classically geometric General Relativity and its derived dynamics. Expressed as energy density, the lambda function Λ(n=H ot) then naturally supplements the gravitational energy-stress-momentum tensor in the standard FRLW-cosmology to reformulate the Hubble Law H(t) as a function of the expansion parameter a(t) in co-moving reference frames R(t)=a(t)R o relative to a cosmological displacement scale given by the Hubble horizon Ro=R Hubble . The characteristic length scale L in Minkowski space of a local sub-realm of de Sitter space then assumes a local lambda parameter ΛL as the conformal mapping from the de Sitter curvature 2 2 space into the local Minkowski flatness in the form of L= λ /L P with ΛL~1/L for λ relating the local energy density, say in a de Broglie lambda λdB =h/mv or a Compton wavelength λC= h/mc=hc/E. The Hubble radius R o so depicts a limiting curvature scale for the Friedmann cosmology, being 2 -4 conformal to de Sitter space in the factor L=R o=λ /L P with λ=√[R oLP] ~ 1.2x10 m, that is a bacterial-microbial scale on the biological phenomenological level and characterised by a -52 2 vanishing local curvature of order 10 ~1/R o . The so called 'Dark Energy' then manifests as intrinsic part of the space-time geometry as the ratio of the trace of the energy-momentum tensor of the Friedmann cosmology to its static Schwarzschild metric in curved de Sitter space-time encompassing it. One major consequence for the intrinsic de Sitter curvature becomes the 'Dark Energy' manifesting in a differential of acceleration between inertial and non-inertial frames of references. The local solar system is a co-moving part of the Friedmann expansion into de Sitter space-time and so becomes a non-inertial co-moving reference frame relative to the inertial and static reference frame of de Sitter spacetime. This then leads to a logical explanation for the Pioneer anomaly measured for the last decade or so. As the flat Friedmann universe requires a critical density for its flatness, which is supplied in the 'Dark Energy' in the form of the de Sitter Lambda encompassing the Minkowski universe in positive curvature and closure; the 'missing mass' in the open Friedmann cosmology readjusts the critical mass in the formulations describing the 'Dark Energy'. This manifests in the 'higher dimensional' curved de Sitter space-time forming an acceleration gradient relative to the 'lower dimensional' flat Minkowski space-time. Considering the de Sitter cosmology to be 'background'-inertial then results in the Minkowski spacetime to be rendered non-inertial by the experience of a 'de Sitter' force or pressure. It shall be shown, that the present de Sitter lambda in Minkowski space-time is 2.8% its value in de Sitter space-time, resulting in the formulations: Omega+Milgrom=Lambda to become {2.807x10 -11 -1.162x10 -10 = -8.812x10 -11 } for the Friedmann cosmology and {9.989x10 -10 - 1.162x10 -10 =+8.827x10 -10 } for the de Sitter cosmology in acceleration units for the present time. The flat Friedmann universe for a zero cosmological constant so balances the Omega deceleration with the Intrinsic (Milgrom) acceleration and omits the de Sitter component, which acts in addition to the Omega for the present time to balance the Milgrom in opposite direction. Introduction: This paper shall attempt to refine the contemporary standard model of the Big Bang cosmology in examining various initial- and boundary conditions of its cosmogony. The model for this cosmogony - the universe's absolute beginnings within parameters of space and time and matter - described in this paper; shall enable the prevailing paradigm to dramatically revise and finetune its cosmological parameters and solve the 'riddles' of the 'horizon problem'; the 'lambda problem'; the 'monopole problem' and the 'flatness problem' in the determination of the responsible boundary- and initial conditions for the stated cosmogony. The great 'culprit' in the present Friedmann-Robertson-LeMaitre-Walker (FRLW) cosmological description and solution for Einstein's Field equations, is the Hubble-Law in the form of its interpretation through the cosmological expansion parameter 'a'. The expansion parameter is defined to describe the dynamical evolution of the universe in the rate of its expansion and as a dimensionless quantity scaling a curvature radius R to some co-moving reference scale R o in defining a(t)=R(t)/R o. From this the Hubble-Law develops in the ratio of the generalised Hubble- Frequency: H(t)=(dR/dt)/R. The FRLW-Equation then inserts this expression: [H(t)] 2=8 πGρ(t)/3 - kc 2 + Λc2/3 into the Einsteinian Tensor equation of General Relativity: and seeks to describe the equations of motion for the universe in terms of H(t) and so the expansion parameter a(t), and where the density ρ(t) incorporates all energy densities, including radiation pressure and neutrino distributions. The gravitational effects produced by a given mass are described in General Relativity by 16 coupled hyperbolic-elliptic non-linear partial differential equations, called the Einstein field equations. As result of the symmetry of tensorial components, the actual number of equations reduces to 10, although there are an additional four differential identities (the Bianchi identities), which must be satisfied to render the coordinate descriptions self-consistent. The non-linearity of the Einstein field equations stems from the fact that masses affect the very geometry of the space in which they dwell. Mass is said to fundamentally curve the geometry of space-time, and the geometry of space-time in turn 'forces' mass how to move. The Tensor components are the Ricci curvature tensor Rµν ; the scalar curvature R; the metric tensor gµν and the stress-momentum-energy tensor Tµν and where the Einstein-Riemann tensor Gµν = Rµν - ½ gµν , so describes a curvature inherent in space-time independent of its inertia given by Tµν . is the cosmological constant, G is the gravitational constant and c is the speed of light. 4 The Einstein-Riemann Tensor G uv = R uv - ½ g uv R for G uv + g uv Λ = 8 πGT uv /c relating the Riemann-Metric g uv with scalar tensor R to the Ricci-Tensor R uv for a stress-energy density tensor T uv . The Weyl Curvature in R uv preserves volume as a tidal shear effect, whilst the Ricci Curvature acts on the density and changes the density and so the volumes. The Weyl Curvature Nullification hypothesis of Roger Penrose (Oxford University, UK) shows, that the Weyl Curvature must become 0 at the threshold between General Relativity's metrics and the 'singularity' of quantum mechanics for the self-consistency of the physical universe to hold in its inertial parameters. A 0 Weyl curvature means that the Lorentz Contraction of a tangential displacement vector travelling around a 'wormhole singularity' or Weyl-Centre as Black Hole event horizon must dewarp itself at that wormhole perimeter in accompanying invariance of the scalar orthogonal radius vector not subject to the Lorentz contraction of Special Relativity in say a rotating system. We shall describe this Weyl-Limit as a superbrane parameter negating the mathematical singularity of General Relativity in a minimum superstring condition: λo=2 πro. It shall be shown, that the FRLW-Equation above should be applied for a de Sitter universe with a curvature k=1 and a cosmological 'constant' Λ=ΛE=ΛEinstein , where this 'constant' is however not constant at all, but describes an intrinsic parameter for the dynamical universe as Λo. In particular, Λo=ΛE describes the evolutionary dynamics of the universe as a superposed 2 2 curvature radius 1/L =1/f(n).R o and where the positive curvature k=1 remains constant in the expression H o=c/R o for all time relative to the de Sitter cosmology, but accommodates the zero curvature of the Friedmann universe, simulating an infinite asymptotic expansion in that time. The overall curvature of the universe so becomes asymptotically defined in a quasi-flat Minkowski space-time, but only attains k=0 in superposition with the k=1 de Sitter curvature in the function f(n)=[T(n)] 2=[n(n+1)] 2, that is as a summation integral of oscillatory space-times described in a reformulated expansion parameter a=n/(n+1) or equivalently n=a/(1-a). The boundary condition for the universe so becomes set at a de Broglie inflaton-instanton, which ascertains R o as the reference scale of the universe at any time of its linear evolution, but as a nodal boundary condition for the minimum Hubble-Frequency in the asymptotic dynamics and as H o=dn/dt=c/R o, so giving a temporality parameter of proper time t=n/H o. The de Sitter curvature so redefines k=1 after the completion of the first semi-cycle of the cosmic dynamics for a ∞=1 and for an electromagnetic expansion of the de Sitter space superposed onto the inertial and mass-parametric expansion of the Friedmann space, the latter carrying the expansion factor a(1)=½. In other words, whilst a c-constant non-inertial expansion has travelled a light path x=ct=R o; a c- limited inertial expansion has travelled only half that light path x=½R o in the same linear time interval n=H ot=1.
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