### RELATIONAL SELF-SIMILAR SPACE-TIME COSMOLOGY REVISITED

#### Abstract

A 'Relational, Self-Similar' cosmological model based on a contextual relation between local and non-local space-time dimensions was reported by the author in 2000. That model was based on a radially expanding 'Minkowski-space' geometry for general space-time, superficially similar to E.A. Milne's 'toy' model of the 1930's (Milne, 1948), in that its geometry is based on Special Relativity and the Hubble expansion alone, irrespective of general gravitation. Cosmologists have recently noted a "surprising" agreement with Milne's mass-less model and evidence for expansion at or slightly above the critical universe mass density (Omega = 1). An explanation for this agreement can be found in the self-similar, dynamically expanding geometry of the relational cosmological model discussed here, which unlike Milne's model, treats space-time expansion as an intrinsic scale change resulting from relationship between local and non-local realities; rather than a 'kinematic' movement through pre-existing space as Milne imagined. The internal geometry of this cosmology is a complex, self similar relation between a non-local domain represented by dimensions in an imaginary number domain, and locally measurable space-time, as a real number domain. The effect of general mass-density (gravitation and the General Theory of Relativity) was not resolved in the earlier model, but is now interpreted as a scale change under which the basic self-similar geometry remains invariant with respect to any evenly distributed mass-density, because the general gravitational effect is itself a self-similar scale change that alters local space-time measurements. The effect is thus detectable only in mass density anomalies, the general gravitation being non-detectible by local measure. These results suggest an interpretation of space-time in which the effective roles of 'special' and 'general' relativity are exchanged, such that Special Relativity holds for the universal geometry and General Relativity holds locally, governing the dynamics of local mass density anomalies. This view eliminates the need for 'dark energy' to correct the standard models, but adds the implication of dual time reference frames - intrinsic and observational - and the idea of an intrinsic formal domain ontology existing outside of measurable space-time coordinates. This geometry is self-determining in the imaginary space-time dimensions (modeled by the imaginary numerical domain),

Applying the model with empirical confirmation of Omega ~ 1 suggests that the universe itself is geometrically similar to the inside of a black hole (with the stable outer limit of 'flat' expansion corresponding to a Schwarzschild radius). Some theories claim that the zero-point ('quantum vacuum') energy (ZPE) is indeed sufficiently great to classify protons as ZPE black holes. Given the model's geometrical treatment of gravitation, the next question centers on the origin and fate of matter, which can no longer be seen as being propelled through space as a result of a giant cosmological explosion (big bang), but rather must originate and be conserved in local space-time that already has the relativistic properties of expansion. The model thus becomes open to a suitable 'steady-state' theory of generation and annihilation of matter in local space, perhaps in terms of quantum vacuum dynamics; while, owing to the model's dual time reference, all the observational (relativistic) properties of a 'big bang' universe are also preserved. Finally, as originally intended, the model is suitable for describing space-time at any scale, thus providing a means for linking quantum and relativistic phenomena, or, with additional non-local linkages, applying it as a model for proposed "orchestrated space-time selections" in the explanation of consciousness and perception.