[AndroidNeox (OP)]

I really don't understand the confusion. The instantaneous appearance (the only physically meaningful factor) of the universe satisfies the Friedman eq. for flat space. However, this means that the instantaneous appearance also satisfies the Schwarzschild metric which describes the radius to mass ratio for a black hole with no spin or charge. Okay?

The average velocity of the most distant matter for us, the Hubble distance, is away from us at the speed of light. This means that no new matter would be coming into view. Okay?

If the quantity of matter within our observable space has not been increasing over time then it's just a coincidence that the Friedman eq. match observation. Also, it would mean that in the past our observable universe possessed more matter than an equivalently-sized black hole, which is not allowed.

I don't see any reason to think Friedman just happens to appear to be right by accident, so new mass must be coming into view over time. But, since it doesn't seem to be coming in at the edge of observable space, where is it coming from?

[yor_on]

Could you link "The instantaneous appearance (the only physically meaningful factor) of the universe ", so I can follow how you get to this definition, please  

"The average velocity of the most distant matter for us, the Hubble distance, is away from us at the speed of light."

If you by that mean what limit a astronomical observation, we now are observing (in time) pretty close to the big bang. Anything beyond that 'radius in time' should be empty of mass, relative us observing. That has noting to do with how big a universe is, or what mass it may consist of.

If we define a universe to inflate (and expand) isotropically and homogeneous in all points, simultaneously so. Then there is no preferred point of observation, in this universe. You can stand wherever you want, look out into the universe to find the same result, as you look back in time. In fact, you must find this to be true using the stipulates from a Big Bang, inflation and expansion, otherwise you will invalidate them.

And if this is true I don't see how one can define a mass of a universe, other than a educated guess over a average, whatever 'size' (distance) relative mass we would like to define. Although, the universe must be 'infinite' from those stipulations, so any definition of a real 'mass' of a 'whole universe' must then become a infinity too, although still a average relative some distance (mass density).
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Please TNS, set the time-limit for us correcting spelling etc, a little more generously.

[yor_on]

If you by it instead mean, and wonder, how we can keep a constant mass density, relative some distance, in a accelerating expansion? Then that is a very good question, which have me confused as well. On the other hand, it doesn't change a thing for that 'infinite universe with its infinite mass' how 'large' we might define a universe as, relative that mass.

[yor_on]

If I would make a choice for explaining a accelerating expansion I would prefer Einsteins biggest blunder A 'cosmological constant' but not using it as defining a dark energy, and mass. I like it as it was, a numerical definition giving us some value for this expansion. There are ideas that explains it from 'SpaceTime ripples' though as http://www.spacedaily.com/news/cosmology-05n.html

[AndroidNeox (OP)]

Could you link "The instantaneous appearance (the only physically meaningful factor) of the universe ", so I can follow how you get to this definition, please  

"The average velocity of the most distant matter for us, the Hubble distance, is away from us at the speed of light."

If you by that mean what limit a astronomical observation, we now are observing (in time) pretty close to the big bang. Anything beyond that 'radius in time' should be empty of mass, relative us observing. That has noting to do with how big a universe is, or what mass it may consist of.

If we define a universe to inflate (and expand) isotropically and homogeneous in all points, simultaneously so. Then there is no preferred point of observation, in this universe. You can stand wherever you want, look out into the universe to find the same result, as you look back in time. In fact, you must find this to be true using the stipulates from a Big Bang, inflation and expansion, otherwise you will invalidate them.

And if this is true I don't see how one can define a mass of a universe, other than a educated guess over a average, whatever 'size' (distance) relative mass we would like to define. Although, the universe must be 'infinite' from those stipulations, so any definition of a real 'mass' of a 'whole universe' must then become a infinity too, although still a average relative some distance (mass density).
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Please TNS, set the time-limit for us correcting spelling etc, a little more generously.

Sorry if I wasn't clear. The instantaneous appearance of the universe is how it looks at any instant. Things like co-moving frames don't describe how the universe works because they ignore things like speed of light and depend on concepts that have no physical reality (simultaneity, disproved by relativity).

Regarding, "I don't see how one can define a mass of a universe", I'm more interested in the mass of an observed volume. The volume defined by our observable universe.

That volume is (apparently) increasing in mass but the mass is not entering from the observable horizon.

[yor_on]

How do you find that the mass must increase with a expansion? To me it should be the other way, the more distance between masses, the lesser the overall gravity (possibly definable as being of one set magnitude, relative the mass existing, getting 'stretched out' by a expansion). Only if you can prove that there is more mass coming into existence can you define the mass per volume as growing, and if that was true then gravity between masses should? I don't know there what would be right, stay constant possibly?

As it is the 'mass versus gravity' we can measure, inside a galaxy or solar system, should be more or less constant, as the expansion is defined to be to 'weak' to oppose the suns etc gravity, holding together that galaxy, solar system etc. It's between galaxies the (accelerating) expansion is presumed to exist as I've seen it.

There are three 'shapes' suggested depending on matter density, 'positively curved' as a ball, 'negatively curved' as a saddle, or 'flat'. The one that seems to fit best, so far, is the 'flat' model in where a universe can be defined as 'stretching out' forever in all directions, That is the shape of our universe, accelerating its expansion, as far as I get the mainstream definition.

"The CMB holds clues to the nature and distribution of structure in the Universe, and the average density of this matter plays a key role in determining the geometry of the Universe. The geometry of the Universe can take on one of three shapes: it can be curved like the surface of a ball and finite in extent (positively curved); curved like a saddle and infinite in extent (negatively curved), or it can be flat and infinite. The geometry and density of the Universe are related in such a way that, if the average density of matter in the Universe is found to be less than the so-called critical density (roughly equal to 6 hydrogen atoms per cubic metre) the Universe is open and infinite. If the density is greater than the critical density the Universe is closed and finite. If the density just equals the critical density, the Universe is flat.

Cosmologists study the relative sizes of the oscillations of the fluid of matter and radiation at the time the CMB was released to learn more about the shape of the Universe. The oscillations translate into regions of higher and lower temperature on the CMB map, and contain information about the amount of particles present. More specifically, the shape of the Universe can be determined by looking at where the first of these oscillations appears in the power spectrum.

The location of the first oscillation corresponds to a specific size in the early Universe called the sound horizon – the maximum distance that a sound wave could have crossed from the Big Bang until the time of the CMB release. To cosmologists, the sound horizon works like a standard measure of known length. By measuring its length in the temperature fluctuations of the CMB, it is possible to determine if the Universe is flat or curved. This is expressed in terms of the parameter 'Omega_K' and is equal to zero for exactly flat space." http://www.esa.int/Our_Activities/Space_Science/Planck/History_of_cosmic_structure_formation 

And.

"At large look-back times and distances the linearity of Hubble?s law breaks down and the distances depend on the energy density of the universe. The various constituents, typically matter and radiation are considered, contribute in different ways to the energy density. Radiation ceased to be gravitationally important at a redshift of about z=1000, a time from which we can only measure the cosmic microwave background radiation. Another component is the famous cosmological constant introduced by Albert Einstein to reconcile the solutions of his equations with a static universe. He later abandoned this term, when Edwin Hubble discovered the general expansion of the universe. For many decades the cosmological constant was not considered in the world models as there was no obvious reason to include it and as it was not possible to connect it to any particle theory. In modern terms, it represents the contribution of the vacuum energy (Carroll et al. 1992). " http://www.eso.org/~bleibund/papers/EPN/epn.html

Now, that last statement about a proved 'vacuum energy' is worthy of a thread of its own, but the rest seems coherent enough to me

" The WMAP spacecraft can measure the basic parameters of the Big Bang theory including the geometry of the universe. If the universe were flat, the brightest microwave background fluctuations (or "spots") would be about one degree across. If the universe were open, the spots would be less than one degree across. If the universe were closed, the brightest spots would be greater than one degree across.

Recent measurements (c. 2001) by a number of ground-based and balloon-based experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe." http://map.gsfc.nasa.gov/universe/uni_shape.html

[yor_on]

The really weird point to a universe 'stretching out' in all directions is that it already must be infinite, although constantly begetting a even larger magnitude of 'infiniteness' with a expansion. That though, must depend on the matter (mass energy)density early (Big Bang and just after), relative what we find today of course. It gives me no little headache wondering about it, as I don't see how you can define any 'shape' to a universe, if you don't have some other frame of reference to do it relative. And we don't have any other frame of reference. We're inside it, so to speak.
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To see why it must be infinite one just need to consider something that is homogeneous and isotropic, no matter where one are, it's a archetype as I see it, setting the parameters instantly. If that is true then a definition of a inflation, and later expansion, becomes something locally definable as 'growing', although meaningless from considering a size of a universe, then or now. If the universe was so at the beginning, then it already must have been infinite. What one then could argue setting limitations of a size might be the 'time horizon' one can observe astronomically, locally defined. That will set a size, locally, but same for all observers. And that one uses 'c'.
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That is actually wrong, although right depending on how you read it.
"That will set a size, locally, but same for all observers."

It's the 'same' for all observers, if we by it refer to those local (and so 'globally defined') constants you use taking your measurements.

But it's not the 'same' if I by it would mean that all will agree on a same reading, locally measured. To fit your readings, to some guy observing a astronomical 'time horizon' from a neutron star, you will need Lorentz transformations, as I expect. Still, to me they are the same as I go out from a local definition. And as that is the (only) way you do a direct measurement, and as all constants we use should come from local measurements.

[yor_on]

The point there is what defines this 'shape' is thought to be matter (mass energy density) defining a 'overall gravitational curvature' of a universe, as I understands it. Accepting this we also then must define a universe constricted by the 'metric of gravity'. You can see that several ways I guess, as something 'inside', relative something 'outside' a universe, or as something where gravity sets some sort of limit to where we can observe. The second choice does not speak about a 'outside relative a inside' to me, more than it sets a limit for what we can observe. In a 'flat universe' then gravity must stretch forever, as that is its definition.

[yor_on]

There is a explanation to the expansion not relating it to mass, instead referring to vacuum energy. "To a good approximation (see below), we believe that the vacuum is the same everywhere in the universe, so the vacuum energy density is a universal number which we call the cosmological constant. . ...

The scale factor R(t), spatial curvature, and energy density of the universe are related by the FRIEDMANN EQUATION, which says that a positive energy density contributes positively to the curvature, while expansion contributes negatively. For simplicity, consider a flat universe -- zero spatial curvature -- so that the energy density and expansion are in perfect balance. As the universe expands, the matter within it becomes increasingly rarefied, so the energy density in matter diminishes. If matter is the dominant component of the energy, the expansion rate (as measured by the HUBBLE CONSTANT) will correspondingly decrease; if on the other hand the cosmological constant dominates, the energy density will be constant, and the expansion rate will attain a constant value. In a potentially confusing but nevertheless appropriate piece of nomenclature, a universe with a constant expansion rate is said to be ``accelerating''. This is because, while the amount of expansion undergone in any one second by a typical cubic centimeter in such a universe is a constant, the number of centimeters between us and a distant galaxy will be increasing with time; such a galaxy will therefore be seen to have an apparent recession velocity that grows ever larger. " http://preposterousuniverse.com/writings/encyc/

It builds on a vacuum, having a energy, and also presume 'new energy' to come to be, as I have understood it, in those new 'space patches' appearing. That as we need to assume that the 'space' must have a equilibrium, that won't be 'diluted' by that expansion creating 'new space'. It is also so that, as far as I can see, you need to assume this process to exist everywhere, our solar systems 'gravity' hiding it from us as the planets and sun becomes 'buoys floating' in that space, connected by mutual gravitational attraction.