The Model

The Friedmann-Lemaître-Robertson-Walker (FLRW) metric

The Friedmann-Lemaître-Robertson-Walker (FLRW) metric ds2FLRW=-dt2+a2(t)[(dr2/1-kr2)+r2(dΘ2+sin2Θdφ2)] describes a homogeneous and isotropic universe. Here τ is cosmological time, (r, θ, ϕ) are comoving coordinates, a is the scale factor and k = 0, ±1 the curvature index. The proper radial distance is defined as ar. FLRW branes with k = 0 and brane cosmological constant Λ, embedded symmetrically. The bulk is the Vaidya-anti de Sitter space-time with cosmological constant , and it contains bulk black holes with masses m on both sides of the brane. The black hole masses can change if the brane radiates into the bulk. An ansatz comparable with structure formation has been advanced in for the Weyl fluid m/a4 for the case when the brane radiates, m = m0aα, where m0 is a constant and α = 2, 3. For α = 0 the Weyl fluid is known as dark radiation and then the bulk space-time becomes Schwarzschild-anti de Sitter. The brane tension and the two cosmological constants are inter-related as 2Λ=K2λ+k2Λ’ The Friedmann equation gives the Hubble parameter to Λ, m, the scale factor a and the matter energy density ρ on the brane: H2=Λ/3+(K2 ρ/3)[1+(p/2λ)]+(2mo/a4-α) It is normally assumed that in the matter dominated era the brane is dominated by dust, obeying the continuity equation ρ+3Hρ file:///C|/Documents%20and%20Settings/paul/My%20Documents/The%20Model.htm (1 of 2) [1/9/2009 2:31:12 PM]

The Friedmann-Lemaître-Robertson-Walker (FLRW) metric

which gives ρ ~ a3. But given the modification a variable Planck scale would add to such a model the brane may be dominated by dust and vacuum pressure differences at the same time. α =<> 0 the Weyl fluid is itself a variable and then the bulk space-time becomes a variable from any of the Schwarzschild de Sitter types. In this case the universe is no longer a homogeneous and isotropic universe. It in fact would be a composite whose general global pattern tends to fit the homogeneous and isotropic universe type with Schwarzschild-anti de Sitter the global normal on the bulk space-time. If you add in the similar aspect from out of Loop Quantum Gravity of no singularity point and a recycle from this model then some matter may be present from other cycles which would tend over several cycle histories to push the cosmos eventually towards a dust dominated model which is either flat or collapsing due to a rise in matter/energy density over that history. At that future point given all the variables no one can predict with accuracy which it will end up in even though I would tend to wager towards the latter. Given all the above I would see our cosmos is somewhere in the early cycle succession stage based upon aspects from observable cosmology at present. Being a composite type the door does remain open for avenues of research into possible superluminal travel methods along several lines.

file:///C|/Documents%20and%20Settings/paul/My%20Documents/The%20Model.htm (2 of 2) [1/9/2009 2:31:12 PM]