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General Cosmology: universal expansion as an illusion of changing spatial curvature
The text below is copied from my website http://quasars.org. Just as
Special Relativity was generalized into General Relativity, so I've tried to generalize the Standard Cosmological Model into a General Cosmological Model which uses the full range of mathematically valid spatial curvatures. The below model seems viable. Eric Flesch -------------------------------------- Is our Standard Cosmological Model "fit for purpose"? An engineer wouldn't think so, because there are three pieces of non-scientific magic built into it, being inflation. dark matter, and dark energy. These 3 are placeholders, quantifications of what we don't know, the gaps between the standard model and what is actually observed. That "dark matter" is so often elaborated as a form of matter, just shows the social power of a word. If instead the term was e.g., "gravitational scalar", then a more eclectic set of explanations would be presented. Same story with "dark energy", so the terms "dark matter" and "dark energy" are unfortunate. As for "inflation", it's a magic wand for transitioning the universe from its initial singularity to a larger universe that can be calculated and modelled. Well, magic will hold up neither bridges nor universes. Is today's cosmology run by a "new generation of flat Earthers"? People have grown so used to the Big Bang interpretation of the Universe, that they have grown inured to a sense of absurdity at the scenario of things flying apart at high speed. My own view is that a more general theory will remove the need for physical expansion. The current Standard model is underpinned by the "flat universe", a spatial manifold of zero curvature with local perturbations. Guth's "inflation" theory provides a mechanism whereby a flat universe was attained as the result of an unknown causal process in the Universe's earliest moments. Today's cosmologists use this flat manifold in all their cosmological calculations including matter ratios, missing (dark) matter, and so-called accelerating expansion due to "dark energy". Thus, *the flat universe is a crucial and indispensible platform for the Standard Cosmological Model*. So, to generalize the Standard Cosmological Model in a similar way as relativity was generalized, we start by designating it as the "Special Cosmological Model" -- special in that it requires a flat universal manifold. We now generalize this into a "General Cosmological Model" by incorporating non-flat geometries which is found to be a surprisingly simple change, as follows. First, a quick simple description of the geometries. In a flat (i.e., curvature=0) 3D manifold, a sphere has a surface area of 4pR˛. A 3D manifold with curvature0 is called spherical and in it a sphere has a lesser surface area, similarly curvature0 is called hyperbolic in which a sphere has a greater surface area. These "non-Euclidean" geometries are known to be mathematically complete and internally consistent just as flat space is. Note that these geometries seamlessly transition from one to the other as curvature changes. Flat space of curvature=0 is but a single point on the curvature range, just as, with time, the present is only a single point on the past-present-future time range. These two paradigms look the same and may indeed be the same paradigm -- given that "spacetime" unifies 3D space with time. As we perceive time as a forward flow akin to migration across past/future, so it is indicated that spatial curvature may also be migrating from (say) hyperbolic to spherical, with "flat" space simply being the current state -- not because of any huge coincidence, but because we natively see the current curvature as flat regardless of wherever on the curvature scale it happens to be -- just as we see the current time moment as the "present" even though it is always migrating. This notion that our space is flat simply because we see the current curvature as flat opens up interesting consequences: (1) The value of lightspeed (c) varies with spatial curvature. Hyperbolic space would look to us as the same as "flat", but if you travel in it you will find that your destination is closer -- this is because the "shells of space" contain larger volumes. As distances are less, lightspeed would cover more distance, thus is faster in terms of distance. Thus lightspeed is a simple scalar measure of the background spatial curvature. Lightspeed would be invariate by some other as-yet-unmodelled measure. (2) As we look into deep space we are unknowingly looking into a universe of greater spatial curvature, thus our luminosity functions lose accuracy. It is like the whole universe is lensed darkly, moreso the farther you observe. This accounts for what is currently interpreted as "dark energy". (3) This extrapolates to the first moment of the universe which then would have been almost infinitely hyperbolic with every place contiguous to all others, allowing instantaneous action over the whole, a.k.a. "inflation". Since then, spatial curvature would decay with time via the standard exponential decay function C(t) = C(0)*e^(-kt) where k~Hubble time. This model thus appears to replicate inflation & dark energy, and provides a mechanism for the redshift by virtue of the slowing lightspeed over the ćons. What we know as "universal expansion" is just a naďve interpretation of the migrating spatial curvature. CMB reverberations are thus far not accounted for, but its absence doesn't make this TOE wrong, just incomplete. :-) The possibility that lightspeed is decreasing with universal time puts a crimp into the modern technique of defining the length of the metre (meter) in terms of light cycles. Inflation will be seen to happen as our metre grows smaller causing old objects to measure as bigger (and heavier in metric terms), whether old standard kilograms or dinosaur bones. Issues remain but the simplicity of this General Cosmological Model appeals. |
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