The Start of Dark Energy and the limits of the Universe

[BurtJordaan]

The uniform (cosmic) time coordinate is a mathematical devise used in models that sets time as a constant similar to the use of comoving coordinates. It does not operate in the natural world or in relativity where time dilations are involved. It is not real and it does not make the light year a constant anywhere except on paper.

Cosmological time is the proper time of all comoving observers, as measured on their atomic clocks. So it is firmly rooted in the everyday time (UTC) that we use on Earth. In mainstream cosmology, these are the modern uses of distances and times:



I hope the graphs come out readable. The bottom panel is for a "paper time" called conformal time and is used with comoving distance to make the spacetime diagram have a linear light cone that resembles special relativity. It is from a formal paper by Tamara M. Davis and Charles H. Lineweaver, titled "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe".

[bangstrom]

In the mainstream it comes from the metric expansion of the universe. Now this is elementary cosmology.

I have asked the question a few times before in different ways but what is the “metric of expansion?” Is it longer space, slower time, shorter space, faster time, or some other change?

The value of c is a ratio of the distance light travels divided buy time and the ratio always comes out as c. In GR both space and time are variables but their ratio remains the same in light related events.

As far as the "stretching" light years are concerned, you have your elementary cosmology wrong.

The increase in wavelength happens gradually, as the light from distant sources travels through successive small local inertial frames at speed c, en route through the void. If you could use a radar locally in such a frame to continuously measure the distance between its "ends", you will find two things: there is a small redshift in the return signal and the distance measured by the radar gets progressively larger, both rather slowly due to the smallness if the frame. This is metric expansion of space. More light years, not "longer light years".

One can actually add up all the small redshifts and end up with the redshift of a cosmologically distant source. It can be adapted for large distances through the void as well, but then it becomes more technical.

I don’t follow your radar example. It makes no sense no matter how I try to interpret it. Light does not redshift locally within one reference frame to the next but light frequency can shift from one period of time to the next with changes the global metric of expansion.

Redshifts do not add, they lengthen, and the same holds true for light years. Adding more redshifts or more light years to an EM signal would increase the number of wavelengths which would be a blueshift.

[BurtJordaan]

The simplest way to look at both your questions is via the old imperfect inflating balloon analogy. Pick any two spots on the cosmic balloon surface. Set up a hypothetical (mass-less) radar at the one and a reflector at the other. These two objects are now comoving observers (they are static on the surface, representing free space).

Since light crawls at precisely c past any spot on the cosmic balloon, the radar will detect a redshift and an increase of the radar distance. Say they were one lyr appart, the return signal will come back in a tiny, tiny bit over 2 yrs. The radar operator will interpret this as that the reflector is slowly moving away in his inertial frame and is a tiny bit farther than 1 lyr now. This is metric expansion of space. For the radar operator, the speed of light is c, the light year is still the same, there is just more distance (space,lyrs) between the two.

In this way we can can set up connecting inertial frames all the way between two distant points and add up all the tiny redshifts (converted to recession speed). Note that none of these radar points move along the balloon surface ("fabric" of space analogy), so there is no time dilation or length contraction involved, because SR gets involved only if objects move along the surface, not if they are just 'along for the ride', i.e comoving.

Another definition of comoving observers is that they all observe the CMB radiation as isotropic in terms of redshift and temperature (i.e. identical black body spectra).

[bangstrom]

This is metric expansion of space. For the radar operator, the speed of light is c, the light year is still the same, there is just more distance (space,lyrs) between the two.

That is similar to the way I see it except the metric expansion is one of both time and space. There is no adding more space or light years between the two points. The redshift is a matter of GR where time quickens and distances lengthen as the local gravitational field declines. EM emissions blueshift as the global gravitational density declines as the galaxies move farther apart. Light emissions received from the past are redshifted when compared with modern light .

The distance between the two remote points doesn’t matter because they are comoving and share the same reference frame. The redshift takes place along the timeline of any point and it takes place over time in an environment of declining gravitational field. An observer at either point sees the other redshifted because she is observing light as it was emitted long ago when the rate of time was slower, distances were shorter. Wavelengths were longer because they were emitted over a longer period of time and when when distances were shorter.

Go back to your cosmic balloon analogy and draw a wavy line on the balloon surface to indicate the waves of a light signal and the number of light waves in a light year between the two remote points. As the balloon expands, the distance of a light year grows longer but the the number of wavelengths remains the same. This is why I say the distance of a light year expands as the universe expands and a light signal redshifts in sync with the expansion. The light year is not “added to” it is stretched out.

[BurtJordaan]

That is similar to the way I see it except the metric expansion is one of both time and space. There is no adding more space or light years between the two points. The redshift is a matter of GR where time quickens and distances lengthen as the local gravitational field declines.

This is your repetitive non-mainstream position, and as such is not really tolerable in this mainstream section. Although we are much more relaxed on such issues here than in some other mainstream forums, there is a limit to permitting private views here. So I'm weighing up the relative effort of continuing pointing out the false statements versus removing all those posts to a new thread under Personal Theories.

That warning issued, for the final time here the following: Cosmological time does not expand, because it is the proper (atomic) time of inertial observers that sees the CMB as precisely isotropic. We do not talk other times here, because they are very technical and not quite digestible by most readers here.

Relative time does not depend on the 'strength' of the gravitational field, just on the gravitational potential. The comoving observers are all at the same gravitational potential. We confirm this when observing distant quasars and supernovae - we see redshift due to metric expansion, but zero redshift due to the higher densities. The whole universe started out many orders of magnitude larger than the observable part, and indications are that it was for all practical purposes infinitely large at the BB.

The observable universe did not "climb out of a gravitational well", nor did the light that we observe from distant sources. You cannot compare this to light that 'climbs out' of a normal GR gravitational well, where the local system is hugely non-homogeneous. The universe at large is highly homogeneous.

The distance between the two remote points doesn’t matter because they are comoving and share the same reference frame.

False. The definition of comoving in cosmology is observers that 'go with the Hubble flow' and hence they drift apart according to Hubble's law, which depends on the proper distance between them.

Go back to your cosmic balloon analogy and draw a wavy line on the balloon surface to indicate the waves of a light signal and the number of light waves in a light year between the two remote points. As the balloon expands, the distance of a light year grows longer but the the number of wavelengths remains the same.

Even for the very imperfect cosmic balloon analogy, this is an incorrect statement. The radial dimension is fictitious and not observable and hence the radial component cannot be added to spatial lengths.

Please accept the above as the mainstream view, very compactly stated for a non-expert audience. Or start a new thread under Personal Theories, were everyone realizes that it may be somewhere between science and speculation.

[bangstrom]

I am always interested in exploring novel cosmologies and yours is new to me. Perhaps I could see the logic to it if I knew more about it.

Cosmological time does not expand, because it is the proper (atomic) time of inertial observers that sees the CMB as precisely isotropic.

The CMB isn’t exactly isotropic but it is mighty close so what is the connection between proper time and the CMB? I understand proper time to be the local time of any given individual reference frame and time can vary from one inertial frame to another but how is it related to the CMB?

Relative time does not depend on the 'strength' of the gravitational field, just on the gravitational potential.

I thought relative time varied with the strength of the gravitational field in GR and how is gravitational potential different?

The comoving observers are all at the same gravitational potential. We confirm this when observing distant quasars and supernovae - we see redshift due to metric expansion, but zero redshift due to the higher densities.

I understand how metric expansion could overwhelm redshifts due to gravitational densities but how do you know that a bit of the redshifting is not gravitational?

The whole universe started out many orders of magnitude larger than the observable part, and indications are that it was for all practical purposes infinitely large at the BB.

The entire universe may still be much larger than the observable part but, if the BB universe was infinitely large and the only the observable part is expanding, how can the observable expansion increase the Hubble distance between galaxies?

The definition of comoving in cosmology is observers that 'go with the Hubble flow' and hence they drift apart according to Hubble's law, which depends on the proper distance between them.

The radial dimension is fictitious and not observable and hence the radial component cannot be added to spatial lengths.

How do reconcile these two statements? I thought the Hubble expansion was a radial expansion.

[BurtJordaan]

I am always interested in exploring novel cosmologies and yours is new to me. Perhaps I could see the logic to it if I knew more about it.

Novel cosmology? What I've written here describes a cosmology that will be a century old in 3 years, originally described by Alexander Friedmann in 1922 as an exact solution to Einstein's field equations (of 1915) under certain simplifying conditions. All you needed to do is to pick up any introductory textbook on cosmology, or read an online mainstream course or tutorial and it would all have been old hat for you.

My guess is that you may have read too many popular books and/or wacky websites and too little mainstream articles and/or papers. Granted, I have my own way of presenting cosmology (like most physicists have), but it does not deviate from the mainstream theory. Even my avatar, the infinite lattice, is not novel. It has been used in many mainstream texts to illustrate an infinite, possibly spatially flat universe.

The CMB isn’t exactly isotropic but it is mighty close so what is the connection between proper time and the CMB?

I have answered this in posts http://www.sciencechatforum.com/viewtopic.php?f=72&t=35309&start=90#p347774 and http://www.sciencechatforum.com/viewtopic.php?f=72&t=35309&start=90#p347782 read together.

I thought relative time varied with the strength of the gravitational field in GR and how is gravitational potential different?

This is elementary GR, do you really want me to explain it here? The strength of a gravitational field can be thought of as the steepness of a slope, while the potential is how far up or down the slope the object is, irrespective of the actual slope.

I understand how metric expansion could overwhelm redshifts due to gravitational densities but how do you know that a bit of the redshifting is not gravitational?

I have said this many times: comoving observers are all at the same gravitational potential and hence there is no overall gravitational redshift. In reality distant sources are not quite comoving observers, nor are we as observers. The light from a source has to typically climb out of its local cluster's gravitational well to reach the slightly higher potential of a void, but finally it has to descend into our local cluster's well to reach our lower potential. So it redshifts a little initially and finally blue-shifts a little. Cosmologists take these and many more small effects on the signals into account.

The entire universe may still be much larger than the observable part but, if the BB universe was infinitely large and the only the observable part is expanding, how can the observable expansion increase the Hubble distance between galaxies?

Now who said only the observable part undergoes metric expanding? Metric expansion does not refer to a radius that grows larger - it means proper distances between any two comoving observers increases over time

The definition of comoving in cosmology is observers that 'go with the Hubble flow' and hence they drift apart according to Hubble's law, which depends on the proper distance between them.

The radial dimension is fictitious and not observable and hence the radial component cannot be added to spatial lengths.

How do reconcile these two statements? I thought the Hubble expansion was a radial expansion.

The Hubble flow is along the surface of the balloon. The whole balloon analogy is misleading due to the fictitious "inside/outside space". I prefer the infinite lattice - also an analogy and hence imperfect, but it avoids that pitfall. I also have initially been led down the garden path by the balloon, but still find it useful to introduce people to the idea of metric expansion. As long as one stays away from seeing the radius of the balloon as a time coordinate!

PS: A good online introduction to cosmology is this one by Ned Wright: http://www.astro.ucla.edu/~wright/cosmo_01.htm

[Faradave]

[I still find the balloon analogy] useful to introduce people to the idea of metric expansion. As long as one stays away from seeing the radius of the balloon as a time coordinate!

If it makes more sense to you, let the radius be the scale factor (or function) a(t). That's far more tenable than characterizing the radius as "fictitious". If time doesn't have an explicit place in either model (flat lattice of balloon), we're denying Einstein's unification of spacetime.

[BurtJordaan]

[I still find the balloon analogy] useful to introduce people to the idea of metric expansion. As long as one stays away from seeing the radius of the balloon as a time coordinate!

If it makes more sense to you, let the radius be the scale factor (or function) a(t). That's far more tenable than characterizing the radius as "fictitious". If time doesn't have an explicit place in either model (flat lattice of balloon), we're denying Einstein's unification of spacetime.

Yes FD, the radial is in fact a(t), the scale factor as a function of cosmic time. But it is not t, which should be pictured orthogonal to the both the balloon surface and the a(t) axis. Mixing the two is bound to create false impressions.

[BurtJordaan]

Yes FD, the radial is in fact a(t), the scale factor as a function of cosmic time. But it is not t, which should be pictured orthogonal to the both the balloon surface and the a(t) axis. Mixing the two is bound to create false impressions.

I suppose you know that there is another way of representing the closed universe and that is to use a variable scale for time (not variable time) and plot it as "billion year rings" along the radial. Then the spacing of billion year rings are large at the beginning and get smaller until they eventually get larger again due to accelerated expansion.



This is perfectly fine as long as one realizes that the radial is r=100 a(t), not a time, with the 100 arbitrary for presentation purposse and has no physical meaning.The red and blue lines are the past lightcone in this coordinate system. It is sometimes called the "cosmic teardrop".

One can also visualize the fact that the total universe radius is much larger than the 46 Gly radius of the observable universe, into which the past lightcone fits. The 46 Gly is just the balloon surface segment indicated by the dotted lines, i.e. the 92 Gly diameter of the observable universe.

[bangstrom]

The CMB isn’t exactly isotropic but it is mighty close so what is the connection between proper time and the CMB?

I have answered this in posts http://www.sciencechatforum.com/viewtopic.php?f=72&t=35309&start=90#p347774 and http://www.sciencechatforum.com/viewtopic.php?f=72&t=35309&start=90#p347782 read together.

We are talking past each other about an important point which is why it keeps coming up and I don’t know how to explain it any differently without making it sound more complicated than it is.

Assume there are a trillion galaxies and each galaxy resides within a global gravitational field, not just its own but that of the surrounding trillion galaxies. If at one time the galaxies were ten times more crowded together than they are today would their gravitational fields from the surrounding galaxies be the same. I say they would be stronger in the past.

Would a galaxy today and a similar galaxy ten billion years in the past be considered comoving. I say no. They reside in remarkably different times and different gravitational environments.

Two different galaxies may be comoving today and observe the CMB as the same but our galaxy and another galaxy we we can see ten billion light years away are not visibly comoving because we see the other galaxy as it was ten billion years in the past.

This is why I say our galaxy and the galaxies we see are not visibly comoving and why light from the distant galaxies is moving out of a deep gravitational well which is the BB at the base.

The entire universe may still be much larger than the observable part but, if the BB universe was infinitely large and the only the observable part is expanding, how can the observable expansion increase the Hubble distance between galaxies?

Now who said only the observable part undergoes metric expanding? Metric expansion does not refer to a radius that grows larger - it means proper distances between any two comoving observers increases over time

How am I misinterpreting your quote below about an infinite universe and an expanding visible part?

Another thing that you have wrong is that the universe started out as a tiny thing - it is only the observable universe that started out tiny, simply because light could only have moved a short distance in the first nanosecond after the BB. As far as we can establish, the universe itself started out infinitely large and obviously then still is...

If both the unseen, infinite universe and the observable portion are expanding at the same rate, how could the observable part expand. By expand, I mean see more stars and internally measure the greater in radius rather than just see the same stars farther apart.

[BurtJordaan]

If both the unseen, infinite universe and the observable portion are expanding at the same rate, how could the observable part expand. By expand, I mean see more stars and internally measure the greater in radius rather than just see the same stars farther apart.

This is not what metric expansion or cosmological expansion means. It simply means that comoving observers and clusters of galaxies separate from each other, i.e. that there is a larger proper distance, more space, whatever you want call it, between them as time marches on. How many cluster there are and how large the universe is, has nothing to do with it.

Yes, expansion dynamics has something to do with the energy density of the universe, which anyway does not depend on cosmic size, just on what energy there is per cubic light year. It does not depend on the sort of gravitational well that you favor.

All we can measure about the size of the total universe is perhaps its spatial curvature, which points strongly towards flat, which can only sensibly be interpreted as spatially infinite. But, we don't know that for sure, only that the curvature indicates an extremely large universe at large. More about that later, for now I'm signing out for a long road trip...

[davidm]

How am I misinterpreting your quote below about an infinite universe and an expanding visible part?

Another thing that you have wrong is that the universe started out as a tiny thing - it is only the observable universe that started out tiny, simply because light could only have moved a short distance in the first nanosecond after the BB. As far as we can establish, the universe itself started out infinitely large and obviously then still is...

.

I think your misinterpretation of what he said lies in the fact that there is more than one observable universe. In fact, in a spatially infinite universe, there are an infinite number of observable universes, because there are an infinite number of locations — and the key point is, that all the observable universes, not just ours, are undergoing expansion. IOW, the entire universe, even if infinite, is expanding, which is another way of saying, very simply, that the distances between galaxies are growing larger over time.

Imagine that you take a flat sheet of paper, a square. Draw a bunch of dots on it. These dots represent galaxies.

Say you have one hundred or so dots on the paper, arranged in rows and columns.

Now, find a dot at the very center of the page, and designate it to be the Milky Way.
This flat paper is a 2d representation of a 3d spatial universe. Now you must imagine that this paper is actually infinite in size — that it goes on forever in all its 2d directions.

The finite square section of the paper is the observable universe, but only as seen from the center dot — the Milky Way.

However, because the paper is actually infinite, there could be observers at any dot, and they will have their own observable universe, and, as for us, it will seem that they are at the center of the whole shebang, and all the galaxies are moving away from them.

For example, if the Milky Way is the center dot, take a dot on the left edge of the paper, and suppose it has sentient observers. It should be evident that, since the paper is infinite in all its directions, these observers will see a different observable universe than we see — their observable universe, and ours, will only partly overlap. They will see parts of the universe that we cannot see, and we will see parts that they cannot see.

But both will see the same phenomenon — that their observable universes are expanding; i.e., the spaces between that galaxies that each set of observers are able to see is growing greater over time. And both will imagine themselves to be at the center of it all, even though there is no actual center.

This means you could redraw the sheet of paper (observable universe) from the vantage point of the left-edge dot, and now THAT dot would be at the center of the page.

Now take two more sheets of paper of the same size. Suppose, again, that the initial sheet of paper had one hundred dots on it, with the Milky Way dot arbitrarily assigned to the center of the page. One paper (the Milky Way observable universe) will no longer have one hundred dots on it, but instead, say, fifty dots. This a snapshot of the future, in which the distances between the galaxies have grown so large that from the Milky Way vantage point, only half as many galaxies will be in the MW’s observable universe, compared with the paper representing the earlier time.

On the next sheet of paper, you could arbitrarily draw as many dots on it as you want — a billion, and trillion — with the Milky Way again arbitrarily at the center of the paper. (The left edge dot I mentioned earlier would, then, be at the center of its own paper.) This would be a snapshot of the universe, from our vantage point, much earlier in time, compared with the initial sheet with one hundred dots. So now there are many more objects in our observable universe — just as there would also be in the left-edge dot’s observable universe.

But again, there are an infinite number of observable universes, which is the same thing as saying there are an infinite number of different locations. So ALL these locations will see the same phenomenon — their observable universe expanding over time; earlier in time, the dots will all be closer together. And each set of observers will imagine themselves to be at the center of it all. Note further that if the universe is spatially infinite, as it seems to be, the vast, vast majority of observable universes do not overlap at all — but each observer will see the same phenomenon, expansion.

The upshot, again, being that in an infinite universe, there are an infinite number of observable universes, and all of them are expanding.

I should add, as a fascinating side note, that in a spatially infinite universe, we should expect there to be an infinite number of sentient observers, including observers with their own telescopes, internets, etc.; and this is true no matter how rare life is — even if we, ourselves, are the only sentient observers in the Milky Way, or indeed in our (own) observable universe. This is because in an infinite space, any event with a non-zero chance of happening should be expected to happen infinitely many times. Clearly, life and intelligence happened at least once, and so … do the math.

The philosopher Brad Monton gave the example of a really bad dart thrower named Fred. Fred hits the bull’s eye (sentience, in the analogy) only once every one billion throws. But what if Fred throws his dart infinitely many times? He gets an infinite number of bull’s eyes.

[Faradave]

I suppose you know that there is another way of representing the closed universe and that is to use a variable scale for time (not variable time) and plot it as "billion year rings" along the radial.

Actually, I don't recall coming across that model before (I don't yet have any books on cosmology) but I like it and hope to explore it further. In particular, I'd be interested in a light path originating other than from the center. I interpret the rings as cross sections of spatial 3-spheres (i.e. simultaneities).

Granted a variable scale for time on the radii, I would expect that a particle at rest with respect to the center (and cosmic background) would have a radial timeline (subject to scale). I expect that any observer in that frame would still experience his own watch ticking normally (despite being subject to scale). If we apply that to every location on a 3-sphere, that simultaneity and it's slow-moving inhabitants will claim to experience time as linearly as we do.

[bangstrom]

This is not what metric expansion or cosmological expansion means. It simply means that comoving observers and clusters of galaxies separate from each other, i.e. that there is a larger proper distance, more space, whatever you want call it, between them as time marches on. How many cluster there are and how large the universe is, has nothing to do with it.

Yes, expansion dynamics has something to do with the energy density of the universe, which anyway does not depend on cosmic size, just on what energy there is per cubic light year. It does not depend on the sort of gravitational well that you favor.

Gravitational density is extremely important. In GR time quickens and distances appear greater as the local gravitational density declines so gravity determines our observation of distance and time.
The energy density of the universe also declines with time as evidenced by a decline in temperature but it is an effect rather than the cause of expansion.

The gravitational density for the universe is found in the Friedmann equation as the density value represented by the Greek letter rho ρ. This is the value that E. Harrison found to be a few magnitudes too low to conform to the observed universe. The gravitational density is the mass of the universe per cubic light year and it declines with time as the volume increases. A declining gravitational density is what characterizes the emergence from a gravity well of any kind.

The energy density of the universe is a different part of the Friedmann equation and is represented by the letter p. The two are not the same.

[bangstrom]

I think your misinterpretation of what he said lies in the fact that there is more than one observable universe. In fact, in a spatially infinite universe, there are an infinite number of observable universes, because there are an infinite number of locations — and the key point is, that all the observable universes, not just ours, are undergoing expansion. IOW, the entire universe, even if infinite, is expanding, which is another way of saying, very simply, that the distances between galaxies are growing larger over time.

This does not appear to be a multiverse theory but a multi observer theory where sentience creates a universe of its own. If the population of the Earth increases, does that create more universes and where do you draw the line with sentience?

If the number of observable galaxies is declining, are the universes growing smaller? Yours appears to be a metaphysical view rather than one that can be described by physics and I don’t think that is interpretation Burt Jordaan had in mind.

[davidm]

I think your misinterpretation of what he said lies in the fact that there is more than one observable universe. In fact, in a spatially infinite universe, there are an infinite number of observable universes, because there are an infinite number of locations — and the key point is, that all the observable universes, not just ours, are undergoing expansion. IOW, the entire universe, even if infinite, is expanding, which is another way of saying, very simply, that the distances between galaxies are growing larger over time.

This does not appear to be a multiverse theory but a multi observer theory where sentience creates a universe of its own. If the population of the Earth increases, does that create more universes and where do you draw the line with sentience?

If the number of observable galaxies is declining, are the universes growing smaller? Yours appears to be a metaphysical view rather than one that can be described by physics and I don’t think that is interpretation Burt Jordaan had in mind.

I have no idea where you are getting this. It comports with nothing that I wrote.

The observable universe is not getting smaller. Where did I say that? However, as the universe expands, fewer objects will be seen in it, because the distances between the objects gets larger over time. This is what expansion means.

If the universe is spatially infinite, then it has an infinite number of locations. Whether these other locations have actual observers or not, is irrelevant. In principle, they could be standpoints of observation. And if there are observers, they will see the universe expanding. I am trying to show you that that universe is expanding everywhere, not just OUR observable universe — all observable universes are expanding. I explained it as clearly as I could, and don’t know what else to add. Where in the world did you derive “If the population of the Earth increases, does that create more universes and where do you draw the line with sentience?” from anything I actually wrote or implied?

My position is NOT metaphysical, it is standard run-of-the-mill science, and I believe this will comport with Burt Jordaan’s position, but he can speak for himself.

[davidm]

Perhaps this explains better, what I tried to explain.

[BurtJordaan]

My position is NOT metaphysical, it is standard run-of-the-mill science, and I believe this will comport with Burt Jordaan’s position, but he can speak for himself.

Welcome to this thread David. I agree with the essence of what you wrote - it's perfectly standard cosmology.

You may find it hard going, because everything you write may be misinterpreted, causing circularity in the discussion.

PS: I'm at an overnight stop, fortunately with fair internet.

[BurtJordaan]

Gravitational density is extremely important. In GR time quickens and distances appear greater as the local gravitational density declines so gravity determines our observation of distance and time.

Not if the energy density is the same everywhere, like for the large scale cosmos. I think you are still confusing the large scale with the small (local) scale. Cosmic time runs the same everywhere if you ignore the small gravitational field inhomogeneity. This is what we observe from cosmologically distant sources.

I still have the feeling, that despite being entertaining, your posts distract from the scientific purpose if this sub-forum. Please supply mainstream references if you want to continue here.

[BurtJordaan]

In particular, I'd be interested in a light path originating other than from the center. I interpret the rings as cross sections of spatial 3-spheres (i.e. simultaneities).

It is not a "model", just an interesting coordinate system in which one can present a standard closed universe. Remember that the 'teardrop' is the past light cone, so the source of every photon that reaches us "now" lies on the teardrop, just at different emission times and distances.

You are right about the simultaneities and that the paths of original particles/objects are radial, most of which we can never observe. Any radial that lies inside the teardrop represents an emission event at a time and distance fixed by the crossing point of the teardrop surface.

[BurtJordaan]

The gravitational density for the universe is found in the Friedmann equation as the density value represented by the Greek letter rho ρ.
...
The energy density of the universe is a different part of the Friedmann equation and is represented by the letter p. The two are not the same.

The term is not "gravitational density", but energy density, of which matter is only one component.
The letter p represents pressure in the Einstein field equations.

Sorry, I do not have time for more detailed comments today.

[bangstrom]

Perhaps this explains better, what I tried to explain.

I agree that the citation is a correct description of the conventional model but where does it model the infinite part of the universe?

This may be the origin of an infinite Universe.
http://www.astro.ucla.edu/%7Ewright/cos ... aq.html#RB
"Is the Universe really infinite or just really big?"

"We have observations that say that the radius of curvature of the Universe is bigger than 70 billion light years. But the observations allow for either a positive or negative curvature, and this range includes the flat Universe with infinite radius of curvature. The negatively curved space is also infinite in volume even though it is curved. So we know empirically that the volume of the Universe is more than 20 times bigger than volume of the observable Universe. Since we can only look at small piece of an object that has a large radius of curvature, it looks flat. The simplest mathematical model for computing the observed properties of the Universe is then flat Euclidean space. This model is infinite, but what we know about the Universe is that it is really big.- Ned Wright"

I conclude from this discussion that the universe is “really big” but not necessarily infinite.

“Since we can only look at small piece of an object that has a large radius of curvature, it looks flat. The simplest mathematical model for computing the observed properties of the Universe is then flat Euclidean space.”- Ned Wright

This is the common practice used by cartographers to draw the surface of our curved planet on a flat map. It would be wrong to extend this simplification to consider the Earth as flat or to consider the curved Riemann geometry of the universe as Euclidian. This the kind of mathematical simplification John Bell called a FAPP. Something added “for all practical purposes” of a calculation and he warned against falling into the FAPPTRAP.

I have two questions:
Is the universe really infinite?
If the lengthening of distance is the dynamic of expansion, what is the effect, if any, on time where light has to travel a greater distance now than it did in the past if c is to equal d/t?

[bangstrom]

Perhaps this explains better, what I tried to explain.

I agree that the citation is a correct description of the conventional model but where does it model the infinite part of the universe?

This may be the origin of an infinite Universe.
http://www.astro.ucla.edu/%7Ewright/cos ... aq.html#RB
"Is the Universe really infinite or just really big?"

"We have observations that say that the radius of curvature of the Universe is bigger than 70 billion light years. But the observations allow for either a positive or negative curvature, and this range includes the flat Universe with infinite radius of curvature. The negatively curved space is also infinite in volume even though it is curved. So we know empirically that the volume of the Universe is more than 20 times bigger than volume of the observable Universe. Since we can only look at small piece of an object that has a large radius of curvature, it looks flat. The simplest mathematical model for computing the observed properties of the Universe is then flat Euclidean space. This model is infinite, but what we know about the Universe is that it is really big.- Ned Wright"

I conclude from this discussion that the universe is “really big” but not necessarily infinite. It may have the possibility of unlimited expansion, but for now, the universe has a finite size.

“Since we can only look at small piece of an object that has a large radius of curvature, it looks flat. The simplest mathematical model for computing the observed properties of the Universe is then flat Euclidean space.”- Ned Wright

This is the common practice used by cartographers to draw the surface of our curved planet on a flat map. It would be wrong to extend this simplification to consider the Earth as flat or to consider the curved Riemann geometry of the universe as Euclidian. This is the kind of mathematical simplification John Bell called a FAPP. Something added “for all practical purposes” of a calculation and he warned against falling into the FAPPTRAP.

I have two questions:
Is the universe really infinite?
If the lengthening of distance is the dynamic of expansion, what is the effect, if any, on time where light has to travel a greater distance now than it did in the past if c is to equal d/t?

[Positor]

If the lengthening of distance is the dynamic of expansion, what is the effect, if any, on time where light has to travel a greater distance now than it did in the past if c is to equal d/t?

I do not understand your question. If d increases, then t increases equally. But that just means that if the distance between two objects increases (for whatever reason), then light takes longer to travel between them. It does not mean that time 'changes speed' (whatever that means).

As I understand it, the metric expansion of space is not limited by c. In any frame, light is observed to travel at c, but metric expansion increases the apparent age of the light. It does not involve an 'acceleration of time'.

[BurtJordaan]

As I understand it, the metric expansion of space is not limited by c. In any frame, light is observed to travel at c, but metric expansion increases the apparent age of the light. It does not involve an 'acceleration of time'.

Correct, except that I would not describe it as an "increase in the apparent age of the light", because that can be confusing. The speed of light is indeed only precisely c in local inertial frames, wherever that local frame may be in the universe.

In terms of proper distance and cosmic time, the apparent speed of light can be anything - "incoming" photons from distant sources can even initially move away from us in terms of proper distance, before starting to come towards as as the expansion rate slows down. These photons were initially outside the Hubble radius, but since the Hubble radius increased rapidly in the beginning, they 'entered' the Hubble radius and then could make headway against the expansion.

This defines the observable universe to a large degree. I can expand on this and give references if someone is interested in the details.

I know that Bangstrom does not find this acceptable and as far as I can see, the only reason for that is that he does not understand mainstream cosmology and is reluctant to learn it.

[bangstrom]

The speed of light is indeed only precisely c in local inertial frames, wherever that local frame may be in the universe.

Think if the difficulty of trying to measure the distance of a light year locally in an expanded universe.

If light takes a longer time to travel the distance that was formerly a light year, that means that the distance of a light year is now shorter than it was in the past. Any measurements made in light years or fractions of a light year, such as a meter, will make local distances appear longer than they were in the past consistent with expansion.

But this raises the question of whether the universe has really expanded or did our units of measurement grow smaller?

[BurtJordaan]

Any measurements made in light years or fractions of a light year, such as a meter, will make local distances appear longer than they were in the past consistent with expansion.

No, this is nonsense. Local distances do not expand with the universe. We can measure local distances up to tens of million of light of years away precisely by means of parallax, e.g. satellites like Hipparcos (https://en.wikipedia.org/wiki/Hipparcos) and GAIA (https://sci.esa.int/web/gaia/-/53278-measuring-stellar-distances-by-parallax).

The distances between galaxies in our cluster (Virgo) does not expand with the rest of the universe, because they are proven to be gravitationally bound (bounded orbits around their common center of mass).

[davidm]

Perhaps this explains better, what I tried to explain.

I agree that the citation is a correct description of the conventional model but where does it model the infinite part of the universe?

It is completely irrelevant to what is being discussed here, whether the universe is spatially infinite or not. WMAP surveys suggest that the universe is flat (spatially infinite) to a high degree of probability, but even if it is not, it doesn’t matter. It may be that the universe is ultimately finite but unbounded. This has absolutely no bearing on what is being discussed, that the universe is expanding from all points of view, no matter where observers may be located, if there are any observers apart from us.

[bangstrom]

No, this is nonsense. Local distances do not expand with the universe. We can measure local distances up to tens of million of light of years away precisely by means of parallax, e.g. satellites like Hipparcos (https://en.wikipedia.org/wiki/Hipparcos) and GAIA (https://sci.esa.int/web/gaia/-/53278-measuring-stellar-distances-by-parallax).

The distances between galaxies in our cluster (Virgo) does not expand with the rest of the universe, because they are proven to be gravitationally bound (bounded orbits around their common center of mass).

Gravity may hold a galactic cluster together against expanding spacetime but how does gravity hold spacetime together against universal expansion? There is no barrier surrounding a galactic cluster to confine space within, like air in a bottle, to keep local space from expanding as intergalactic space expands.

The weak gravity of a galactic cluster may barely slow the universal expansion within but not bring it to a halt. Expansion is only observable at great distances where the changes are more extreme. Our units of distance and time and the value of c are all mutually defined so we can’t detect local changes. A light year will always be a light year when measured locally no matter the degree of local change.