# Expanding Universe Question

Assuming we are not at the center of the universe:

If V is the vector from the center of the universe to us, then -V would be the vector from the center of the universe in the direction away from us. Wouldn't a star (or whatever) on the -V vector be accelerating away from us at a larger rate than other objects, and especially objects on the +V vector that are further away from the center of the universe than we are? This is obviously assuming that everything in the universe is expanding from a single point.

Can we observe (through redshift or some other means) where the center of the universe is and where we are in relation to it?

cristo
Staff Emeritus
You shouldn't assume that the universe is "expanding from one point" since this is not true. There is, in fact, no such place as the centre of the universe; the cosmological principle does not allow for it.

Welcome to PF, by the way.

Thanks... can you explain why the cosmological principle doesn't allow for a center of the universe?

cristo
Staff Emeritus
The cosmological principle basically says that there exists no special place in the universe. Since a centre would be a special place, the cosmological principle tells us that such a centre does not exist.

you cant point any place and say, big bang happened here..

Why not ?

Actually, you can point to anywhere and say "the big bang happened here".

If there was a center (which there may not have been), we have no clue as to in which direction it may lie. However, we do have a good idea of its distance, and how long ago we separated from it.

Jon

Hubble bubble ...

The expansion of the spacetime manifold is the same everywhere. That is, the Hubble expansion (a local description) is the same everywhere, for a given stage of what might be referred as the Big Expansion of universe.

You must not imagine that the big bang was like the explosion of some gigantic firecracker and that, in principle at least, you could have stood to one side and watched. There was no "one side" because the big bang represents the beginning of the spacetime itself. So, from the point of view of our present universe, there is no position in space to which you can point and say, "the big bang happened here." It happened everywhere.
Moreover, there is no "before the big bang", because the time began with that creation event. In this context, the word "before" loses its meaning. We can, however, conjecture about what went on during succeeding intervals of time after the big bang.

It's intuitively hard to understand that there need not be a "center" of the universe from which virtually everything is expanding. I have seen two graphic demonstrations, one by Alex Filippenko and another by some other professor, that adequately demonstrate the lack of a need to have a "center". I'm sure you would see that a "center" is not necessary if you could see these demonstrations; I'll try to use some words to describe one of these illustrations.

Take a sheet of paper and draw many circles of various sizes on it, such that you can imagine that each of the circles is a galaxy. Now, use a copier and make a copy that is 15% larger. (If this second copy can be made on a viewgraph transparency, the effect is even more obvious). Now overlay the "expanded" universe on the other and notice what happens to where the galaxies are. No matter which two galaxies you use to match the locations (one from the first image and the other from the viewgraph slide image), all the other galaxies seem to be expanding from this hypothetical center. The meat of this is that you can't find any location on the first image from which a "center" can be defined such that the expansion isn't seen in the second image, regardless of the galaxie you chose to be the "center".

I hope I've described this clearly enough that you may try it; it's quite eye-opening. But the central piont of this demonstration is to debunk our intuitive notion that a "center" has to exist; further, it easily demonstrates how every point can be considered the "center" in an expanding universe. Obviously, if the universe had edges and we could view an edge, there might be a preferential location, but most cosmologists I know discount the notion that the univese has an "edge" that we could ever discern.

I hope this helps.

Moreover, there is no "before the big bang", because the time began with that creation event. In this context, the word "before" loses its meaning.

I've often been confused about the relationship between time and the Big Bang. Over last several years, I've discussed it with others and have arrived at the following understanding: Time, FOR OUR UNIVERSE, did not exist before the Big Bang. But Time, for the HyperVerse or the Branes or whatever, must necessarily have existed before the instantiation of the Big Bang event. But this is time that will never be "viewable" by us (at least with technology and science we currently understand).

Is my understanding consistent with yours?

Thanks.

Assuming we are not at the center of the universe:

If V is the vector from the center of the universe to us, then -V would be the vector from the center of the universe in the direction away from us. Wouldn't a star (or whatever) on the -V vector be accelerating away from us at a larger rate than other objects, and especially objects on the +V vector that are further away from the center of the universe than we are? This is obviously assuming that everything in the universe is expanding from a single point.

Can we observe (through redshift or some other means) where the center of the universe is and where we are in relation to it?

Einstein initially proposed a forth physical dimension to space. In this hypothesis if you were to travel in a straight line you would end up where you started. According to this "curved space" idea there could be no center to the universe. Some Alternative cosmologies to the BB that also ascribe to a finite universe in size, assert that the center of the universe would be the center of its mass. These theories are called flat-space theories. No theories that I know of believe that the center of the universe could be found. This is because for a finite size universe it could be countless millions of times larger than what we can observe.

Hello All,

I'm new to this forum, and compared to all of you here, I would be viewed as an elementrary student if I tried to hold a conversation in this subject, so please try to make any responses as elementary as possible.

I seem to have a problem trying to comprehend the following; Is the universe flat or round? If (hypothetically) we could travel at many billions times the speed of light, would we fall off the edge, or end up right back where we started? If there is an edge to the universe, is there anything outside (beyond) this edge? If not, what is nothing? If the universe is round, and expanding, shouldn't there be some kind of outer edge? Shouldn't there be something outside of this edge? White, Black, Conciousness, Another Universe, God?

Could it be possible that our universe is simply a photon (or similarly sized particle) in some much, much, larger universe that we have not yet or possibly never will detect?

Last question... If time and space or spacetime was created at the big bang, was this (ball of matter/energy) or whatever the big bang expanded into just floating around in "Nothing?" until it exploded and expanded into the universe we are aware of today? What was outside of this planck sized? ball of mass?

I look forward to hearing everyone's thoughts, and please try to take it easy on the technical aspects, like I said before, I'm wouldn't even say that I'm a Novice in this field yet.

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The expansion of the spacetime manifold is the same everywhere. That is, the Hubble expansion (a local description) is the same everywhere, for a given stage of what might be referred as the Big Expansion of universe.

Would such manifold still be equally expanding in a locality where there is gravitational contraction, such as for a cluster etc.? Would it help to focus herein on gravitation as curvature?

If there is more concentrated mass, then more curvature. But couldn't such curved surface still be equally expanding (i.e. stretching}?

Hello All,

I'm new to this forum, and compared to all of you here, I would be viewed as an elementrary student if I tried to hold a conversation in this subject, so please try to make any responses as elementary as possible.

I seem to have a problem trying to comprehend the following; Is the universe flat or round?

There universe is not "flat or round" but this better be stated as "curved or not curved (ie. 'flat')".
Measurements can not really tell, which means either that it is flat or almost flat, which indicate either an infinite universe, or very large (magitudes larger then the Hubble sphere, the observable universe).

If (hypothetically) we could travel at many billions times the speed of light, would we fall off the edge, or end up right back where we started? If there is an edge to the universe, is there anything outside (beyond) this edge? If not, what is nothing? If the universe is round, and expanding, shouldn't there be some kind of outer edge? Shouldn't there be something outside of this edge? White, Black, Conciousness, Another Universe, God?

The universe, wether finite or infinite, has no edges or boundaries.
If you squeeze the size of the universe in one direction, making it effectively a 2D space, it would fit around a sphere (like the surface of earth). The radius of that sphere is very large or infinite.

There is no "outside" of the universe.
There might be higher dimensions, but that is another topic (string theory suggests that at very small -atomic- scales, there might be another 7 space dimensions).

Could it be possible that our universe is simply a photon (or similarly sized particle) in some much, much, larger universe that we have not yet or possibly never will detect?

There has also been suggested that the universe is in fact a fractal, containing copies of itself.

Unless there is a way of testing this, that is hard to say.

Last question... If time and space or spacetime was created at the big bang, was this (ball of matter/energy) or whatever the big bang expanded into just floating around in "Nothing?" until it exploded and expanded into the universe we are aware of today? What was outside of this planck sized? ball of mass?

The suggestion is that none of that took place, and time and space were already there. Although the very idea that Big Bang = simultanious creation of time,space and matter has been popularized, and even some cosmologists promoted it, this turns out to be not the case.
It is understadable that this misconception arise, since it follows from the Einstein equations that there is a singularity at time = 0. (*)
Yet, General Relativity itself happens to break also near that point, and then we also have to deal with Quantum Mechanics. These theories are both fundamental but they are not compatible, which therefore makes it necessary to establish a new theoretical framework.
So this makes the situation very much more complicated, and you can not simply draw the line back untill you have a precise (dimensionless) point, because the theoretic framework can not handle that situation.
But this idea nevertheless has stuck.
What realy happened, is still theory in progress
.
Currently the idea is that spacetime itself inflated (= fast expansion) in the early phase, and after some rapid expansion the field that drove this inflation decayed, and the energy released as particles and radiation. Then normal expansion took over, decoupling, and matter formed (quarks, atoms, etc.).
When universe was sufficiently cooled and less dense photons were free to move which is what we see now as Cosmic Microwave Background Radiation.
Inflation theory was successfull because it explained why the universe was so large (because of the initial very rapid expansion) and homogeneous (the rapid expansion got rid of all the inhomogeneities).

(*)
Compare this for example with Newtonian physics. If the distance between two point masses becomes zero, there is also a singularity. In reality however that never happens, as real masses are not zero, and also because there is the electromagnetic force.

A good start for learning more about the Big bang theory is Ned Wright's cosmology page.
http://www.astro.ucla.edu/~wright/cosmolog.htm

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The universe, wether finite or infinite, has no edges or boundaries. There is no "outside" of the universe.
There might be higher dimensions, but that is another topic (string theory suggests that at very small -atomic- scales, there might be another 7 space dimensions).

In an infinite universe, the statement "no boundaries" makes perfect sense, but in a finite universe, the statement "no boundaries" makes "no sense" to me. How can something that is finite not have boundaries? Did you mean; even if we live in a finite universe, due to the laws of physics and "our perspective," that there is no possible way of ever reaching this boundary or "edge", therefore it is unreasonable to even ask such a question?

I don't know if this is what you were trying to say or not, but this subject is something that I am very intereted in, so let me know your thoughts.

Regarding the higher dimensions; this may take a second to sink in, but what would be the exact opposite of these supposed "higher dimensions" higher = smaller than we can find? or invisible to the human eye? What if there were "lower dimensions" that were so massive, that we could not begin to comprehend while "trapped?" within our known universe? (I know that this is an unreasonable question to even ask, but what the hell?)

I think that I may be looking at things from too much of a philosophical viewpoint as oposed to a scientific viewpoint. If anyone out there would like to respond to my questions posted here, or previously asked in this forum, it would be greatly appreciated.

You must not imagine that the big bang was like the explosion of some gigantic firecracker and that, in principle at least, you could have stood to one side and watched. There was no "one side" because the big bang represents the beginning of the spacetime itself. So, from the point of view of our present universe, there is no position in space to which you can point and say, "the big bang happened here." It happened everywhere.
Moreover, there is no "before the big bang", because the time began with that creation event. In this context, the word "before" loses its meaning. We can, however, conjecture about what went on during succeeding intervals of time after the big bang.

I'm not going to say that you are wrong about spacetime beginning with the big bang, but I am curious as to your sources for believing this. Have you done any research on this theory lately? I am finding nothing but speculation regarding this kind of thinking.

russ_watters
Mentor
In an infinite universe, the statement "no boundaries" makes perfect sense, but in a finite universe, the statement "no boundaries" makes "no sense" to me. How can something that is finite not have boundaries? Did you mean; even if we live in a finite universe, due to the laws of physics and "our perspective," that there is no possible way of ever reaching this boundary or "edge", therefore it is unreasonable to even ask such a question?
No. Jeez, we've got two of these going at once! We need a sticky for this.

Ask yourself this: does a plane flying around the earth ever reach an edge of the earth?

The same concept applies to space, but in 3d instead of 2d.

mysearch
Gold Member
#5: you cant point any place and say, big bang happened here..

#10:You must not imagine that the big bang was like the explosion of some gigantic firecracker

Certainly, from within a uniformly expanding homogeneous universe, any point will perceive itself to be the centre of expansion. Equally, modelling the universe as an explosion would appear to create some major problems given the measured uniformity of expansion and absence of blast waves, e.g. acoustic peaks? So my questions are not intending to challenge the collective wisdom that generally supports both statement above, but I would like to break the issues of an expanding universe into a number of questions that relate to the nature of a homogeneous expansion and the implication of there being no centre. We might initially start from the simplicity of a Newtonian approximation, where the force of gravity is defined as:

$$F = GMm/r^2$$

The implication of this equation is that [r] is typically the radius from the centre of gravity of a larger mass [M]. However, on the very large scale of the universe, where homogeneity is assumed, there appears to be an implicit assumption that the universe can have no centre of gravity. Another theorem of Newton’s explains how an infinite universe may have no centre of gravity, e.g. Newton’s shells, but it is not clear to me how a finite universe avoids this concept.

What I mean by uniform expansion is the assumption that each unit volume of space expands in time in accordance with the Hubble constant [H], although the actual rate may change with time. The other interesting thing about this expansion is that it does not work on all scales, such that atomic nuclei don’t expand, atoms don’t expand; neither do solar system or entire galaxies, only the large-scale space between galaxies. If so, is it conceptually possible to define a ‘force of expansion’, i.e. it is less that the gravitational force holding a star within a galaxy but less the gravitational force between two distant galaxies?

While modelling the big bang as an explosion is more than problematic, it is noted that a Newtonian derivation of the Friedmann equation can be based on the conservation of energy of a unit mass with respect to a centre of gravity [M]. This appears analogous to an explosion and also leads to questions concerning the violation of SR, i.e. the mass can end up travelling faster than light with respect to [M]. However, the approach appears to produce a reasonable approximation of the expansion of the universe, at least, within the matter-dominated era. Again, this is just an observation for clarification not an assertion.

If I define a spherical volume of space, which separates two galaxies (A) and (B), these galaxies can end up moving away from each other with a velocity > [c]. The issue of SR violations is said to be resolved because in a localised frame, the speed of light is always [c] and the velocity of the galaxy is < [c]. I am assuming that this frame of reference also resolves the issue of energy and momentum associated with SR?

Finally, in the absence of any centre of gravity, must I assume that any slow down of the expansion of the universe, now thought to be cause by dark energy, is due to localised gravitational effects. For example, our 2 galaxies (A) & (B) are being pushed apart by expanding space, but does the gravitational attraction between the 2 galaxies still effectively slow the observed rate of expansion perceived by an observer? While I can picture this model with just 2 objects, in reality, all mass objects in the universe are interconnected, given the caveat of gravitation propagation equal to [c], such that the net gravitational force on our 2 example galaxies might still be zero, even under expansion?

Appreciate any clarification of these issues.

mysearch
Gold Member
Post #17: I know that this is an unreasonable question to even ask, but what the hell?

I don’t think your question(s) are unreasonable. To some extent, I suspect that many who are interested in cosmology are spurred on by questions that transcend science. It is also important to know when science descends into speculation.

Science can only ascertain what is, but not what should be, and outside of its domain, value judgments of all kinds remain necessary. Albert Einstein

If possible, I would like to raise a few more questions, in addition to #20, that are sort of connected to the question of an expanding finite universe:

- As a broad summation, there is some speculation that our universe might be a quantum bubble that has a net energy of zero by virtue that all energy can be balanced into either positive kinetic energy or negative potential energy. As such, this might suggest that our finite universe exists within a larger quantum universe; however, I would be interested to learn whether this is based on any sound science?

- As a counterpoint to the rather bold speculation above, I wanted to highlight a few alternative issues for clarification. Quantum physics suggests that conservation of energy can only be violated for a short time, which allows the creation of particle-antiparticle pairs. I believe this is sometimes referred to as a quantum fluctuation arising from Heisenberg's uncertainty principle.

- However, in the context of an expanding universe, it is speculated that the quantum bubble expanded during inflation to create our spacetime universe. However, the annihilation of particle-antiparticle pairs suggests a net release of energy rather than zero energy. Is this correct and if so where did the net energy come from or what is its negative counterpart?

- At this point, the terms ‘vacuum energy’ or ‘zero point energy’ of even dark energy’ is often introduced into the conversation. Is there any consensus to the equivalence of these sources and is there any empirical verification of existence? Again, it does not appear that this energy can be resolved to a net zero?

- As a somewhat tangential issue, baryogenesis is a rather imposing name given to a process in which the balance between matter and anti-matter was resolved in the very early universe. I have seen figures that the imbalance between particles and antiparticles was a billion+1 particles to a billion antiparticles suggesting a huge release of energy. Is this energy accounted for in CMB?

- Finally, is baryogensis assumed to have happen before or after inflation?

Assuming we are not at the center of the universe:

If V is the vector from the center of the universe to us, then -V would be the vector from the center of the universe in the direction away from us. Wouldn't a star (or whatever) on the -V vector be accelerating away from us at a larger rate than other objects, and especially objects on the +V vector that are further away from the center of the universe than we are? This is obviously assuming that everything in the universe is expanding from a single point.

Can we observe (through redshift or some other means) where the center of the universe is and where we are in relation to it?
This document might be of interest to you: http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-11778.pdf

Hi MeJennifer,

The Adler, Bjorken & Overduin 06 paper you linked provides a very nice mathematical model for a theoretical kinematic dustball universe expanding in an empty background expanse of vacuum with a cosmological constant. Thank you for providing it. It seems to be consistent with the theoretical extrapolations of kinematic GR I've been discussing in threads here the past few months. Particularly interesting is the authors' description of an early "fireball" radiation-dominated era universe, complete with an external positive pressure gradient causing a cooler dust layer to be ejected outward ahead of the hot expanding fireball. Also their idea of the outer surface of inflation having surface tension, maintaining a constant radius. They also suggest that communication is possible between the interior and exterior of the dustball, and that multiple such dustballs may coexist.

It seems to me that the theoretical analysis is excellent. It doesn't surprise me that a paper like this hasn't been cited much, since the subject is highly abstract and it lacks the sexy, exotic physics and extra dimensions which (oddly) have been so widely embraced by the speculative wing of cosmology theorists.

Jon

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mysearch
Gold Member
I also thought the article referenced in #22 was very interesting. While I have only quickly read the article and not really considered the maths in any detail, it raised a couple of immediate questions:

- How does the dust ball avoid having a centre of gravity?
- Would the dust ball have the mass-radius characteristics of a black hole?

p.15: This singularity is analogous to the singularity of Schwarzschild geometry, which in Kruskal-Szekeres coordinates forms a future spacelike barrier to light and particles inside the black-hole surface. Note that the surface of the dust ball can be crossed by light and particles moving both inward and outward; that is, the interior of the dust ball can communicate with the exterior, and vice versa.

- Does this statement imply the dust ball does not have an event horizon?

Hi mysearch,
- How does the dust ball avoid having a centre of gravity?
It's a ball of dust, so it must have a center of gravity. It's like being inside the earth's interior; gravitational force is proportional to distance from the center. But I believe this spherically symmetrical inhomogeneity of the cosmic gravitational field would not be obvious to any individual observer regardless of their position relative to the center. They would definitely notice that their observable universe has a collapse action (along with its initial expansionary momentum plus any late-times acceleration added by Lambda), but the effects of the collapse action would appear uniform and homogeneous from their limited perspective, so they wouldn't be able to detect in which direction the collapse action was pointed. Only an observer very close to the outer surface of the dustball would notice an inhomogeneity.
- Would the dust ball have the mass-radius characteristics of a black hole?
Yes it would but for its "initial conditions", that is, its initial expansionary momentum. In a spatially flat universe at critical density, the initial outward momentum is so powerful that the singularity acts like a white hole (opposite of black), starting at infinite (or very high) density and then driving the contents of the universe perpetually outward towards ever lower density.
- Does this statement imply the dust ball does not have an event horizon?
I believe that the dust ball as a whole would not have an event horizon. But any individual observer located inside or outside the dustball would have their own traditional event horizon due to the accelerating expansion rate caused by Lambda. The authors of the paper say that individual dust balls might overlap or merge eventually. This suggests to me that matter from another dustball could enter an individual's event horizon, so by definition I guess it's only a partial event horizon.

Jon

mysearch
Gold Member
Response to #25:

Hi Jon, thanks for the feedback. I realise this is quite a speculative paper and I have no idea how it has been generally received by cosmologist, but could I press you on some details:
It's a ball of dust, so it must have a center of gravity.

- This conclusion appears to be basically supported by Newton’s shell theorem, which suggests that an infinite homogeneous universe would have no centre of gravity; but in contrast, a finite dust ball within a wider universe without any gravitational matter would probably have to have a centre of gravity within the dust ball. So while your conclusion seems logical, doesn’t it conflict with the standard model of a homogeneous universe, which I understand is said not to have any centre of gravity?

- On a different, but related point, a basic Newtonian derivation of Friedman’s equation is possible based on the conservation of energy of a unit mass [m] expanding away from a central mass [M]. However, this model appears to be more analogous to an explosion, which would raise further SR issues as the recessional velocity can exceed [c]. Even so, the expansion predicted by this more classical approach seem to align to the standard model, at least, within the matter-dominant era. Again, the question of a centre of gravity appears to be raised.

- Based on recent measurements, it has been suggested that the expansion of the universe is accelerating. As such, the conclusion seems to be that there must still be some form of active expansion energy/pressure, i.e. dark energy, which is outstripping any gravitational slowdown or collapse. As such, would the existence of a centre of gravity only be detected as a slowdown effect or would you expect it to affect the homogeneous distribution of matter?
the initial outward momentum is so powerful that the singularity acts like a white hole (opposite of black), starting at infinite (or very high) density and then driving the contents of the universe perpetually outward towards ever lower density.

I have seen similar arguments that support your position, but want to raise one additional point based on the assumption of the specific model under discussion. If the dust ball exists in a wider universe and
the surface of the dust ball can be crossed by light and particles moving both inward and outward

…could the dust ball not have formed as a smaller ‘blackhole’ dust ball and then expanded as more dust from the ‘wider universe’ fell into event horizon. This is not a serious suggestion, but I was interested in understanding why this idea would be discounted.

Hi mysearch,
So while your conclusion seems logical, doesn’t it conflict with the standard model of a homogeneous universe, which I understand is said not to have any centre of gravity?
If the universe is infinite, the concept of a center is meaningless. Also, if the universe fills all of spacetime (e.g. a simply connected 3-sphere topology) then a center is also meaningless. Analogize it to surface of the earth, which has no center.

The absence of a center is an assumption of mainstream cosmology, adopted because of the philosophical appeal of the cosmological principle, and the elegant simplicity of the math.
- Even so, the expansion predicted by this more classical approach seem to align to the standard model, at least, within the matter-dominant era.
I see no reason why the dust ball model wouldn't align to the Friedmann equations in all respects to the same degree as the standard model, other than its outside edge boundary conditions. That is the logic the authors of the paper apply.
- Based on recent measurements, it has been suggested that the expansion of the universe is accelerating. As such, the conclusion seems to be that there must still be some form of active expansion energy/pressure, i.e. dark energy, which is outstripping any gravitational slowdown or collapse. As such, would the existence of a centre of gravity only be detected as a slowdown effect or would you expect it to affect the homogeneous distribution of matter?
I would expect the dust ball universe to have the same homogeneity as the standard model, except near the edge. As I said, I believe that the directionality of the gravitational collapse action would not be locally detectible.

The authors' approach to the dust ball model seems to assume that the empty vaccuum outside the dust ball is characterized by the same homogeneous dark energy or cosmological constant as inside the dustball. That's why the exterior expands at a geometrically accelerating de Sitter rate.
…could the dust ball not have formed as a smaller ‘blackhole’ dust ball and then expanded as more dust from the ‘wider universe’ fell into event horizon.
I am not aware of any particular reason why a white hole could not arise from a predecessor black hole, e.g. because of some change in physics as a singularity is approached under certain unknown extreme conditions. But that's entirely speculative. Some astoundingly powerful "antigravity-like" form of energy would be required to accelerate matter out of the black hole's deep gravity well and up to superluminal speeds. It's a fascinating question whether matter can be accelerated to superluminal speeds without violating SR. Galaxies are observed today to be receding superluminally, and theory says they would have been receding even very much faster in the early universe. It's worth noting that in the absence of a global SR inertial frame, GR suggests that the speed limit c does not apply, except locally within the bounds of an arbitrarily defined, approximately inertial, SR local frame. Presumably when our early observable universe was incredibly dense and very tiny (say, the size of a beachball), an SR inertial frame would have needed to be so tiny as to approach or fall below the Planck scale. SR constraints such as the speed limit of c may have been irrelevant for practical purposes at that time.

Inflation of course is the currently favored theoretical cause for the initial expansionary impetus. Inflation assumes that the expansion energy came first (from quantum inflatons), before there was any (or at least very much) matter or free radiation in the universe, and then when it reached maximal velocity at the so-called reheating phase, matter and free radiation "precipitated" into the universe, already possessing an expansion velocity almost perfectly equal to the escape velocity of the newly-precipitated mass-energy density. Among its other attributes, inflation theory sidesteps any need for pre-existing matter to be accelerated to superluminal velocities. One usually sees inflatons described as appearing spontaneously from "empty" space. I'm not aware of any version of inflation theory that specifically assumes inflation arose out of a pre-existing black hole, but it wouldn't surprise me if such a version exists.

Jon

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mysearch
Gold Member
The following quote is taken from the article abstract referenced in #22:
In this work we model the universe as a finite spherical ball of dust and dark energy……….also obtain and discuss the geometry exterior to the dust ball; it is Schwarzschild-de Sitter with a naked singularity, and provides an interesting picture of cosmogenesis.

My reason for pursuing this discussion is to see whether the ideas outlined in the article might allow a wider interpretation of the standard model. When starting off on cosmology A101, there is a distinct impression that the universe is a self-contained entity, i.e. it has no outside, which started off as a singularity. As far as I am aware, the standard model proceeds on the basis that the universe expanded from this singularity, presumably as closed system, with the implicit assumption that nothing could exist ‘outside the universe’. Clearly, there is an implication, within the standard model, that our universe has a finite age from which one might assume it also has a finite size, albeit much larger than normally inferred by the current array of cosmological horizons. So was unsure about the infinite extent’ statement taken from the beginning of the article:
The model (standard) posits a spatially flat (k = 0) Friedmann-Robertson-Walker (FRW) universe of infinite extent, filled with dark energy, well described by a cosmological constant, and pressureless cold dark matter or “dust.”

However, the composite interior-exterior universe model raised some further issues in my mind:

- It seems that this model sets the stage for considering the matter-universe, as defined by the dust ball, within a much larger universe. However, is it valid to assume that both the internal (dust ball+$$\Lambda$$) and external ($$\Lambda$$) universes expand from the same singularity, starting at the same point on a common timeline, i.e. are they really just regions within a larger composite universe?

- Can we contemplate the expansion of the exterior universe being essentially unconstrained; i.e. this region has no gravitational slowdown? As such, might the exterior universe be essentially infinite, while in contrast, the expansion of dust ball universe would have been constrained to a finite size by a centre of gravity acting in accordance with Friedmann’s equation?

- As such, might this help explain why the derivation of Friedmann equation aligns to the conservation of energy of a unit mass [m] expanding away from a central mass [M], i.e. the dust ball can be modelled as expanding in to pre-existing spacetime created by the much more rapid expansion of the exterior ‘universe.

- Note, the model under discussion does not explicitly rule out the possibility of more than one dust ball 'universe' existing in the exterior deSitter universe. If so, would there be any gravitational attraction between dust ball universes?

I accept this is all highly speculative, but my interested was to some extent linked to whether the hypothesis forwarded by the article could be refuted mathematically by mainstream cosmology and, if not, whether this simply reflected the degree of speculation underpinning all models, at least, on this much larger scale?

Clearly, there is an implication, within the standard model, that our universe has a finite age from which one might assume it also has a finite size, albeit much larger than normally inferred by the current array of cosmological horizons. So was unsure about the infinite extent’ statement taken from the beginning of the article:
Standard cosmology does not assume that the universe is either finite or infinite. Even if it all started at a specific time from one singularity, that singularity could have been infinite in extent from the very beginning. There's nothing to say that something of infinite extent can't expand. Standard cosmology also makes wide allowance for the possibility that something existed before the big bang.

In the early days of cosmology, the preferred view seems to have been that the universe should be topologically simply connected, like a static sphere or expanding 3-sphere. I think cosmologists were comfortable with that picture because they were firmly attached to the cosmological principle, which they interpret to rule out a privileged center or outer edge. Even now that the universe is observed to be both expanding and spatially flat or nearly flat, cosmologists prefer to assume the universe is infinite, or to explore bizarre new topologies to allow it to be simply connected. The aversion to even modestly departing from the cosmological principle remains as strong as ever, and our increasingly better observations have not uncovered anything yet which is deemed to favor inhomogeneity.
- It seems that this model sets the stage for considering the matter-universe, as defined by the dust ball, within a much larger universe. However, is it valid to assume that both the internal (dust ball+$$\Lambda$$) and external ($$\Lambda$$) universes expand from the same singularity, starting at the same point on a common timeline, i.e. are they really just regions within a larger composite universe?
I don't know; the authors seem to assume there is just one singularity, but I'm not sure. I think it makes sense to assume that if there is Lambda inside the dust ball there is also Lambda outside, because Lambda is typically viewed as an attribute of space itself, rather than an attribute of the nearby matter. But of course one could construct a different speculative model based on the assumption there is no Lambda "outside".
- Can we contemplate the expansion of the exterior universe being essentially unconstrained; i.e. this region has no gravitational slowdown? As such, might the exterior universe be essentially infinite, while in contrast, the expansion of dust ball universe would have been constrained to a finite size by a centre of gravity acting in accordance with Friedmann’s equation?
The expansion "outside" wouldn't be entirely "unconstrained." It would proceed at a geometrically increasing rate in accordance with the de Sitter model. I think one could interpret the authors' model to assume that the "outside" began at the same time as the inside, i.e. did not predate it. If so, then the "outside" might be finite, but not if the "outside" was of infinite extent from its very beginning. Or the "outside" could be assumed to predate the dust ball, in which case again the "outside" might be infinite.
- As such, might this help explain why the derivation of Friedmann equation aligns to the conservation of energy of a unit mass [m] expanding away from a central mass [M], i.e. the dust ball can be modelled as expanding in to pre-existing spacetime created by the much more rapid expansion of the exterior ‘universe`.
Yes, I think that's what the authors have in mind.
- Note, the model under discussion does not explicitly rule out the possibility of more than one dust ball 'universe' existing in the exterior deSitter universe. If so, would there be any gravitational attraction between dust ball universes?
I suppose so. Each dust ball could be thought of as sort of analagous to a galaxy in our observable universe. The dust balls could be components of an even large scale dust ball. Etc, etc. Or not.
I accept this is all highly speculative, but my interested was to some extent linked to whether the hypothesis forwarded by the article could be refuted mathematically by mainstream cosmology and, if not, whether this simply reflected the degree of speculation underpinning all models, at least, on this much larger scale?
As I said, standard cosmology admits that the centerless universe is merely an assumption, but it strongly favors that assumption over the alternative. Unless we are "lucky" enough to be close to the outer edge, we may never be able to observationally distinguish between the two models. Perhaps future advances in GR and/or quantum mechanics will tilt the balance of probability significantly in one direction or the other. My personal opinion is that as long as the dust ball model remains observationally unchallenged and does not depend on exotic new physics, it should be accorded some respect as a plausible variation on the "standard assumption". If nothing else, exploring the dust ball models helps us identify more ways to test the standard assumption for inconsistencies or interesting attributes we haven discovered yet. It also helps us visualize the expanding universe more intuitively as a fairly straightforward mechanical system, without relying on a semi-mystical, metaphysical analogy favored in the past, "the expansion of space itself" (in the absence of any Lambda).

Jon

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mysearch
Gold Member
Response to #29:

Jon, thanks for all the knowledgeable responses, they have been very helpful.
that singularity could have been infinite in extent from the very beginning. There's nothing to say that something of infinite extent can't expand.

Are you just referring to ‘infinite extent’ in terms of time only, as a singularity would appear to be fairly finite in size? Is the inference that what we call the ‘age of the universe’ is just the time taken to reach our current estimate of its size? However, given the nature of this discussion, do we really understand the size of the universe or the processes underlying its expansion?
I believe that the directionality of the gravitational collapse action would not be locally detectible.

Your statement above is from #27 for cross-reference. On reflection, there is one aspect that I wanted to clarify based on a Newtonian assumption:

$$F = m_ia = \frac {GMm_g}{r^2}$$ such that $$a = \frac {GM}{r} = g$$

If we assume the dust ball has a centre of gravity, then I would have thought the inference of the equations above is that any mass object within the dust ball, i.e. galaxy, would experience a different rate of gravitational acceleration towards the centre of gravity as a function of its radius [r]. Wouldn’t this still be the case, even if each unit volume of space were uniformly expanding under the effects of dark energy?

mysearch
Gold Member
Correction to #30

Just noticed a typo in one of the equations in #30
Should have been: $$a = \frac {GM}{r^2} = g$$

Hi mysearch,

The dust ball model has a center of gravity, and the gravitational force is proportional to distance from the center. But the initial expansion velocity of matter is also proportional to distance from the center. So the combined effect is that gravitational force causes the same deceleration of each particle of matter in proportion to its distance from the center. As a result, I believe that the varying gravity at different distances from the center would be undetectible.

When I refer to "infinite extent", I mean infinite size. There is no theoretical maximum size of the universe at the first instant after the big bang. It could well be infinite. There is no concept at all about what size a "singularity" would be, so that's not useful to think about.

Jon

mysearch
Gold Member
Response to #32:

Hi Jon,
Thanks for the feedback; however I am struggling to see how the ‘initial expansion velocity of matter’ balanced the deceleration of gravity in your following explanation:
The dust ball model has a center of gravity, and the gravitational force is proportional to distance from the center. But the initial expansion velocity of matter is also proportional to distance from the center. So the combined effect is that gravitational force causes the same deceleration of each particle of matter in proportion to its distance from the center. As a result, I believe that the varying gravity at different distances from the center would be undetectible.

When the gravitational deceleration is exactly balanced by the negative pressure acceleration of Lambda, then the universe expands at a constant, coasting rate. That is, at the same rate it would if there were NO gravity and NO pressure. The acceleration parameter = 0.

I am not sure that the following equation is appropriate, but may provide a basic reference point for the discussion:

Negative Pressure Force = ma = $$GMm/r^2$$ = Gravitational Force

Starting with the assumption that negative pressure expands each unit volume of space, it would effectively expand the distance [r] between the unit mass [m] and any centre of gravitational mass [M]. On the assumption that the centre of mass [M] exists, in this model, gravitational acceleration between [m] and [M] would counter the net expansion of [r] between [m] and [M].

However, on the assumption that space expansion, due to negative pressure, expands in all 3 spatial directions, but gravitational deceleration only applies to the radial direction, i.e. towards the centre of gravity, would this not lead to an apparent difference in the expansion rate in the 2 directions perpendicular to [r] and would this not affect the perception of a homogeneous universe?

Hi mysearch,
Thanks for the feedback; however I am struggling to see how the ‘initial expansion velocity of matter’ balanced the deceleration of gravity....
....
I am not sure that the following equation is appropriate, but may provide a basic reference point for the discussion:

Negative Pressure Force = ma = $$GMm/r^2$$ = Gravitational Force
I don't think the Newtonian formula you described for "external" objects is the applicable one. Instead, the Newtonian Shell Theorem (also called Gauss' Law) for objects inside a solid sphere should be applied, because the dust ball in its entirety (or any large spherical subset of it) is modeled as a "solid" ball of (dust) fluid. So the formula is:

Force = $$\frac{4\pi\rho Gmr}{3}$$

Therefore gravitational force increases linearly with increasing distance from the center, and becomes zero at the center of mass. See the Wikipedia article on http://en.wikipedia.org/wiki/Shell_theorem" [Broken].

As a thought experiment let's imagine 4 test galaxies which depart the "center" at the same time and move radially away at different but constant speeds. Using an arbitrary distance and time scale, the radial speed of galaxy #1 (D/t) away from the center is 1, the speed of galaxy #2 is 2, the speed of galaxy #3 is 3, and the speed of galaxy #4 is 4.

So, for example, at t=3, galaxy #1 has moved 3 units away from the center, galaxy #2 has moved 6 units, galaxy #3 has moved 9 units, and galaxy #4 has moved 12 units away. Thus the galaxies retain homogeneous distribution at any point in time, and each galaxy perceives the other galaxies to be receding directly away from it at a recession speed proportional to the current distance, consistent with Hubble's Law.

Now let's apply some gravitational deceleration. In accordance to the Shell Theorem, gravitational deceleration is applied in linear proportion to current distance from the center. Since speed is also linearly proportional to distance from the center, by t=2 every galaxy has slowed down by the identical percentage of the speed it had at t=1. Thus homogeneous spacing and Hubble's Law are preserved.

In a spatially flat model, each galaxy's speed away from the center is equal to the Newtonian escape velocity of the total matter within the spherical ball defined by that galaxy's radius from the center. If Lambda=0, over time the speed of each galaxy away from the center will asymptotically approach, but never reach, zero. This model is baked into the Friedmann equations (along with complexities such as Lambda and spatial curvature). Lemaitre, who rediscovered the Friedmann equations about 10 years after Friedmann died, postulated in the mid-1930's that the expansion of the universe in fact eminated from an explosion of a central "primordial atom," giving rise to the original Big Bang model. (The theoretical ability of matter to collapse completely, past the Chandrasekhar Limit, into a black hole singularity had not yet been confirmed; Oppenheimer published the analysis in 1939.) Other contemporary physicists such as Einstein and Eddington did not like the religious overtones associated with such a "creation event."

In any event, this model is quite straightforward, and works exactly the same when a stationary galaxy is added at the center and additional galaxies are added moving away from the center in the opposite direction from the first bunch. Once the galaxies begin moving, observers no longer can detect the location of the center (unless they can observe enough of the edge to triangulate back), and the center doesn't retain any practical significance for such observers. The universe looks and acts exactly the same at the center as in other interior locations.
However, on the assumption that space expansion, due to negative pressure, expands in all 3 spatial directions, but gravitational deceleration only applies to the radial direction, i.e. towards the centre of gravity, would this not lead to an apparent difference in the expansion rate in the 2 directions perpendicular to [r] and would this not affect the perception of a homogeneous universe?
No, for a spherical ball of dust, the gravitational contraction action and the cosmological constant expansion action both work proportionally across all 3 spatial dimensions. E.g., for 2 galaxies initially at equal radius from the center, if gravity pulls them radially closer to the center, the tangential distance between them will decrease in the same proportion, as the azimuthal angle remains constant. This is a fundamental principle of triangles.

Jon

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No. Jeez, we've got two of these going at once! We need a sticky for this.

Ask yourself this: does a plane flying around the earth ever reach an edge of the earth?

The same concept applies to space, but in 3d instead of 2d.

I'm not quite sure i'm understanding this question. Anyways, if a spaceshuttle is traveling in a given direction, and doesn't change this direction, it would soon "pass through" earths atmosphere (edge, or boundary) and continue on into space. Now if that spaceshuttle continues on and could travel at a speed greater than that of expansion (if the universe is expanding) and given an infinite amount of fuel and time, would this spaceshuttle not eventually pass through the edge, or boundary of our universe?

Imagine that the shuttle had an unbreakable and infinitely long rope that was tied down to the earth, this way, we could be sure that we are traveling "away" from earth at all times. And, this rope and space shuttle are immuned to the effects of gravity and have the ability to pass straight through any and all matter. Now we don't have to worry about black holes or anything else being in our way that would make us change our direction.

This is the image that is running through my head that bothers me so much. If the universe is finite, wouldn't the shuttle "pass through" the universe into something/somewhere else?

**Please do not get too hung up on the scenario, it's simply to help paint the picture.