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#1




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 nonscientific 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 socalled 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 nonflat 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 "nonEuclidean" 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 pastpresentfuture 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 asyetunmodelled 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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#2




General Cosmology: universal expansion as an illusion of changingspatial curvature
Eric Flesch said:
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 asyetunmodelled 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 over the Ä‡ons. What we know as "universal expansion" is just a naÄŹve 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 I wonder if there arenâ€™t some other aspects of a variable light speed that might show themselves. For instance, what about Matter structures? If light speed is greater, then stars can be larger, no? Presumably greater light speed means greater energies and higher pressures. Unless, the different geometry means different type reference frames for measuring energy. Greater radiation pressures make gases more difficult to collapse, but those that do will form larger stars. . And those larger stars may not be the same color as â€śtodayâ€™sâ€ť. Not only larger but longer lived. If radiation pressures are greater, large stars would remain stable. Spacetime geometry should have little effect on geometry inside a star, but variable light speed should induce differences in chemistry inside stars, relative to our era, no? Acceptance of an expanding Universe lies at the heart of this next point. Arenâ€™t galaxies inside Voids structurally different and dimmer than others â€ślivingâ€ť within the filaments and part of large scale structures? If so, that is a modern example of chemistry within stars being unaffected by the spacetime geometry they â€śliveâ€ť in. The dimming effect being a consequence of the expanding geometry of the Void. Just thoughts. Thanks. Brad 
#3




General Cosmology: universal expansion as an illusion of changing spatial curvature

#4




General Cosmology: universal expansion as an illusion of changing spatial curvature
In article ,
(Eric Flesch) writes: The current Standard model is underpinned by the "flat universe", a spatial manifold of zero curvature with local perturbations. Why do you think that? Ned Wright's cosmology calculator http://www.astro.ucla.edu/~wright/CosmoCalc.html works fine for curved space. Existing observations show that space is flat to extremely small tolerance. What I found quickly was Fig 26 at https://www.aanda.org/articles/aa/fu...a2583015.html but I'm sure I've seen better plot and more extensive discussion. The topic has been studied in great detail, and a wide variety of observations are relevant. (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 Which distance did you have in mind? All of them change with spatial curvature, but changing speed of light would be new physics. The possibility that lightspeed is decreasing with universal time... Isn't this ruled out by observations? Changing speed of light changes the ratio of frequency to wavelength. That would mean grating spectrographs, which measure wavelength, would get different results than radio observations, which measure frequency. In other words, redshifts would differ between radio and optical measurements.  Help keep our newsgroup healthy; please don't feed the trolls. Steve Willner Phone 6174957123 Cambridge, MA 02138 USA 
#6




General Cosmology: universal expansion as an illusion of changing spatial curvature
Steve Willner wrote:
changing speed of light would be new physics. Just to clarify that c is still invariant in this model, but that local places would see a different value of c as part of the illusion of flat curvature. When you said, Steve, Which distance did you have in mind? I think perhaps you meant, in a space with twice the curvature as ours, if you want to walk 20 meters, do you only have to walk 10 meters to get there? The answer is yes, but only if you are seeing the curvature  and if you are seeing the curvature, then c is the same invariant value everywhere across all curvatures. But native life doesn't see the curvature, it is mapped to flat  perhaps for reasons of sanity. And as part of the mapping, the one truly invariant thing, c, is seen to be different. Mapping is common, eyesight is mapped to upisup in the long term, so if someone hangs upside down long enough (and still lives), the brain reprocesses vision to turn things rightside up. So c is still invariant in this model, but to what value? We are just seeing the lightspeed resulted by mapping our own local curvature into flatness  our own necessary illusion. 
#7




General Cosmology: universal expansion as an illusion of changing spatial curvature

#8




General Cosmology: universal expansion as an illusion of changing spatial curvature
(Eric Flesch) wrote in :
On Mon, 4 Feb 2019, (Steve Willner) wrote: (Eric Flesch) writes: The current Standard model is underpinned by the "flat universe", a spatial manifold of zero curvature with local perturbations. Why do you think that? I've never yet seen calculations done onto evolving spatial curvature. Nowadays only static flat is used, particularly since the measurements (including that impressive Planck paper which you referenced) show a flat universe. But if we see a flat universe, there can really only be two possibilities: (1) it is flat, or (2) it isn't flat but looks like it is. (2) is the generalization of (1). (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 Which distance did you have in mind? For example, at z=1, c would be twice the value. This is as seen natively, that is a local observer at z=1 sees a flat universe just like ours but with c twice as fast. But that universe (at z=1) has twice the spatial curvature (on some absolute scale) as ours, so c is still invariant by some curvaturecompensated measure. All of them change with spatial curvature, but changing speed of light would be new physics. I'm trying to *get rid of* new physics, specifically dark matter, dark energy, and inflation, just by using spatial curvature. We know c to be invariant, but that assumes no dependence of c on spatial curvature  as seen locally. I haven't found any work done on that topic  would be interesting if there were some. The possibility that lightspeed is decreasing with universal time... Isn't this ruled out by observations? No because we've observed only here in this local place. If physicists looked for a migrating value  a very tiny change over decades  maybe they could find it. Consider the standard kilogram. It seems the oldest physical ones are annoyingly heavier by some infinitesimal amount. They blame contaminants for that  mercury contamination in particular, but I think they're just guessing? If c is migrating to slower  some imperceptible amount except to oscilloscopes  physical things would be measured to grow correspondingly  especially if you tie the meter to c, as is done now. That they have done so, makes it that much harder to measure a change in c, like tools have been disabled. Does it actually make it harder to *even just think about*?!? Maybe it wasn't such a great idea to define a unit of length in terms of c. Changing speed of light changes the ratio of frequency to wavelength. That would mean grating spectrographs, which measure wavelength, would get different results than radio observations, which measure frequency. In other words, redshifts would differ between radio and optical measurements. No, the frequency is invariant but the wavelengths compress with the slowing light  so it looks the same as if both here & there were flat. My model may be wrong but not for that reason. Eric It is a very interesting discussion. I was thinking, often I read that space is not empty, but has 'virtual particles popping in and out of existence'. The Michelson & Morley experiment has shown that an aether cannot exist as it (as with waves in water) would affect lightspeed if you moved through it, but they measured lightspeed a constant in all directions. However if these 'aether' particles were created on the spot (those that pop in and out of existence) and those would pass on the light wave energy then the aether would always move with you. That could explain the M&M experiment, and would still allow objects to travel FTL relative to other objects... I am no physicist, but always looked for a physical mechanism, other than some geometric solution. 
#9




General Cosmology: universal expansion as an illusion of changing spatial curvature
On Wed, 06 Feb 2019, Jan Panteltje wrote:
I am no physicist, but always looked for a physical mechanism, other than some geometric solution. Physical mechanisms won't do it. The solution, if decipherable, is going to be strange. "...the universe is not only queerer than we suppose, but queerer than we *can* suppose." J.B.S. Haldane (1927) 
#10




General Cosmology: universal expansion as an illusion of changing spatial curvature
In article ,
(Eric Flesch) writes: I've never yet seen calculations done onto evolving spatial curvature. Doesn't the Friedman equation say how curvature evolves? Nowadays only static flat is used, particularly since the measurements . show a flat universe. As you say, the observations seem clear, and nobody today thinks our Universe has much curvature. There were, however, plenty of papers on that subject in the past, and modern observers still look for whatever residual curvature there might be. But if we see a flat universe, there can really only be two possibilities: (1) it is flat, or (2) it isn't flat but looks like it is. You need to relate "looks like" to specific observations. It's not as though no one has thought of curvature before. SW Which distance did you have in mind? For example, at z=1, c would be twice the value. Redshift z represents the scale factor, not a distance. You need a cosmological model to translate scale factor to distance and lookback time, and there are at least three different distances relevant to cosmology. Are you suggesting that a local measurement of c at z=1 would return a value twice as large as measured at z=0? I'm pretty sure that's ruled out by observations. SW Isn't [changing c] ruled out by observations? No because we've observed only here in this local place. ??? There are plenty of redshifts for highz objects, and optical and radio redshifts agree with each other. Moreover, CO redshifts agree with H I redshifts, both measured with radio techniques. That wouldn't be the case if c were varying because the 21 cm line is a hyperfine splitting that has a different dependence on c than ordinary lines. No, the frequency is invariant but the wavelengths compress with the slowing light  so it looks the same as if both here & there were flat. My model may be wrong but not for that reason. Optical (grating) spectrographs measure wavelength. If there were a change, why wouldn't that be measured?  Help keep our newsgroup healthy; please don't feed the trolls. Steve Willner Phone 6174957123 Cambridge, MA 02138 USA 

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