The Proceedings of the Eighth International Conference on Creationism (2018)

billions of years ago everywhere to a putative initial singularity, we consider extrapolating only thousands of years near the earth and billions of years at remote locations. When we do this, we arrive at the conceptual diagram in Figure 8. This concept produces a surface that bends into the “remote past” (with reference to the usual “cosmic time” of the Big Bang cosmology). Note that if we have the surface approach the past null cone asymptotically, we produce a cosmology in which the light rays will progress toward the earth rapidly as the hyperbolic surface advances in time. We further note that specifying such a surface also produces a spacelike surface with intrinsic curvature differing from the usual FLRW curvature, and a non-uniform matter density (since the density is higher at the remote regions). In order to select a hypersurface that is asymptotically null, we transform the metric to the conformal form based on the cycloidal variable η via equation (12) above: ( ) dt a d η η = Performing the change of time coordinate to the cycloidal parameter yields. ( ) ( ) 2 2 2 2 2 K ds a d d f d η η χ χ   = − + + Ω   We take the origin, 0 χ = , to be in the general vicinity of the earth. Performing the change of time coordinate to the cycloidal parameter yields. ( ) ( ) 2 2 2 2 2 K ds a d d f d η η χ χ   = − + + Ω   We note that the past radial ( 0 θ ϕ = =   ) null geodesics are given by the equation: 2 2 0 d d η χ − + = The solution for an incoming null ray is then: ( ) χ η τ = − − In which τ is the (conformal) time at which the incoming past null ray arrives at 0. χ = We next consider a spacelike hypersurface that is asymptotic to the past null cone. It is given by the equation: 2 2 b η τ χ = − + (17) We consider this to be the creation surface for some value of τ to be specified. With this choice we are necessarily taking a subset of the usual FLRW, since we are discarding regions of the FLRW manifold for which 2 2 b η τ χ ≤ − + (cf. Figure 9). Viewed as a cross section of the FLRW cosmology the portion of the FLRW below the surface labeled “Day 1” did not exist. The constant b is a free parameter of the model. As b approaches zero the spacelike hypersurface approaches the limiting null cone, given by: η τ χ = − . Thus, a value of zero would mean the distant light would reach earth instantaneously. For non-zero values b is the time it takes light from objects at infinity to reach the earth. We now define a new time coordinate by way of the scalar function: 2 2 ( , ) b τ η χ η χ = + + Note that this specification of the function τ already utilizes a “time to creation” that is a function of χ . To simplify the analysis, we next introduce a new coordinate ρ via: sinh b χ ρ = . Then cosh b τ η ρ = + Taking the differentials gives: sinh d d b d η τ ρ ρ = − , and substituting into the metric we then obtain the following for the metric: ( ) ( ) 2 2 2 2 2 2 cosh 2 sinh sinh K ds a b d b d d b d f b d τ ρ τ ρ τ ρ ρ ρ   = − − + + + Ω   (18) We rewrite the above equation in the following form, for use later, in the 3+1 formalism: ( ) ( ) 2 2 2 2 2 2 2 2 sinh cosh sinh sinh K ds a b d b d d d f b d b ρ τ ρ τ ρ τ ρ τ ρ     = − − + + − + Ω           (19) ( ) 2 2 2 2 2 2 2 sinh cosh sinh K ds a d b d d f b d b ρ ρ τ ρ τ ρ     = − + + + Ω           (20) Note that the actual elapsed proper time registered by the comoving clock at ρ is computed from the conformal time τ by the integral: ( , ) t a d τ ρ τ = ∫ The only difference in the manifold of our cosmology and that of the standard FLRW cosmology is that the initial surface, taken to be the initial creation surface, is a “non-simultaneous” Big Bang relative to the usual FLRW “cosmological time” but viewed as simultaneous within the hyperbolic surface. If from that moment time advances uniformly then the asymptotically null spacelike surfaces maintain their hyperbolic property. However, there is nothing to preclude God from advancing the remote regions more rapidly thereby yielding a non-null hyper-surface. That concept is consistent with the biblical account. Figure 9 illustrates this concept. Relativistic principles do not distinguish any preferred initial geometry or any preferred cosmological simultaneity surface. Hence, the hyperbolic surface though not “simultaneous” with the 0 τ = surface of the FLRW cosmology is no less physically plausible. The illusion is only due to viewing the YEC as embedded in the maximally extended FLRW manifold. We can plot the paths of radial light rays using the conformal metric in above. Light rays are determined by setting 2 0 ds = . This gives: Or, sinh cosh d b d d b ρ ρ τ ρ τ   = ± +     Solving this differential equation yields, the following for incoming and outgoing null rays: ( ) ( ) 0 0 0 e e for outgoing light rays e e for incoming light rays b b ρ ρ ρ ρ τ τ − −  −  − =  −  (21) Figure 10 shows the light rays for our YEC cosmology. We note that in Figure 10 the space-time is displayed with the 0 τ = creation Dennis ◀ Young earth relativistic cosmology ▶ 2018 ICC 25