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Gravitational Expansion & Flat Universe

  1. Nov 23, 2007 #1
    I would appreciate help in objectively disproving the following "alternative physics" proposition: "The large-scale geometry of the universe is compelled to be eternally flat because gravity causes the universe to expand at exactly the escape velocity of its mass/energy contents." This proposition could be disproved, among other means, by proving that the universe must be capable of non-zero curvature at large scales. Or by proving that gravity cannot be the source of spatial expansion.

    Of course I recognize that even if a proposition isn't readily disproved, doesn't mean that it's actually true. By the way,anyone who has read my posts on the cosmology forum is aware that my math skills don't go much beyond basic calculus, but I have spent some time studying cosmology. You don't need to remind me that in standard general relativity, gravity is supposed to slow down expansion, not propel it. And that once initiated (presumably by inflation), expansion is supposed to possess a sort of momentum that would keep it expanding eternally but for the retarding effect of gravity. I also understand that cosmologists prefer to work with mass/energy densities rather than with absolute values of total mass/energy used in the escape value formula. The "escape velocity" formula:

    [tex]\dot{r} = \sqrt{\frac{2GM}{r}}[/tex]

    is a trivial variation of the Friedmann expansion formula, substituting M/V for rho (density). In this approach, the cosmological constant is automatically included by incorporating its mass/energy component, without any need to separately account for its negative pressure component.

    To make a long story short, inflation theories are designed to deliver a flat initial universe expanding at exactly the escape velocity of its mass/energy contents. At its peak expansion rate, inflation "dumps" precisely the initial amount of radiation and matter plasma into the universe, the escape velocity of which matches the inflationary expansion rate.

    It is implicit in the Friedmann expansion equation that spatial expansion (at escape velocity) depends on, and derives from, the mass/energy of the contents. In effect, mass/energy must be the "repository" of the ongoing expansionary "momentum." (There are good reasons to reject any concept that the "momentum" of expansion resides in vacuum space itself.) The expansion of space involves no peculiar motion of mass/energy through vacuum space. This suggests that each particle of mass/energy is causally connected directly to the expansion of the vacuum space around it, at the escape velocity of that particle. (If many particles are gravitational bound together, the gravitational binding energy constituting their collective "mass defect" do not contribute to the expansion rate.)

    My proposition is that post-inflation, pre-dark energy-dominated expansion is NOT a "momentum" leftover from inflation. This proposition has the following key elements:

    1. So-called "negative pressure" components such as inflation and the cosmological constant DO NOT impart any expansionary momentum to the universe.

    2. Gravity DOES NOT act to restrain the expansion of space.

    3. Instead, the gravity of mass/energy actively causes real-time expansion of the space within its gravitational field, at exactly the escape velocity of that mass/energy.

    4. If an object with mass/energy departs an otherwise empty region of space, expansion of that region ceases immediately. When the object enters a new region of space, that region immediately expands at escape velocity. Thus there is no concept of retained momentum or inertia of expansion. Acceleration and deceleration of local expansion occur instantaneously.

    5. The cosmological constant accelerates the expansion rate merely by virtue of possessing simple mass/energy. There is no need for a negative pressure component.

    6. Because gravity actively maintains the instantaneous local expansion rate exactly equal to escape velocity, it is impossible for the large-scale geometry of space to ever be anything other than perfectly flat.

    I'll offer a couple of related points.

    The observable universe currently is deemed to be flat or nearly flat, and theory requires that it was no less flat at any time in the past (since inflation). Although a firm mathematical relationship between spatial expansion and curvature of space has been a central element of general relativity since its inception, isn't it still is an entirely theoretical construct which has not been proven empirically or by observation? Assuming that local curvature is a valid construct of GR to explain gravity, it seems to me that one is not compelled to also accept that holistic curvature of the universe is a necessary corollary. Specifically, with respect to two objects in the observable universe which are not gravitationally bound to each other in the context of rapidly expanding space, why isn't it reasonable to say that their individual gravitational fields are NOT in causal contact with each other (particularly across event horizons), and therefore cannot additively reinforce each other's contribution to the shape of the overall manifold of the universe?

    If my proposition were correct, then I think the 'equation of state' in GR and the Friedmann equations would need to be partially recast to reflect a different (real-time rather than static) expansion mechanism, but not different physical results. In particular, I don't see any need for the pressure terms, because the Friedmann deceleration equation can be modeled as a simple change in total mass/energy over time (for example, due to redshift of free radiation). I need to understand whether a change of that kind would cause conflicts in other aspects of physics -- such as the physics of perfect fluids.

    I would really appreciate some constructive comments. If your response is going to be to tell me I don't understand the first thing about physics, one sentence will be sufficient, no piling on is allowed.

    Last edited: Nov 23, 2007
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  3. Nov 23, 2007 #2


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    Normally ideas like this are proposed in Astronomy/Cosmology forum, and dealt with there. Rather than in Beyond standard model forum.

    To comment, Jon, I would say that, to me, your idea does not have meaning because the terms are not well-defined.
    Maybe someone in Astro/Cosmo forum can GIVE meaning to "the speed with which the universe is expanding" and "escape velocity". But for me, as a practical matter, I cannot define what they are in concrete km/second terms.

    The speed with which a particular piece of the universe (say the milky way vicinity) is receding is not well-defined because there is no reference point. And at what moment in time do you mean, since relative recession speeds change?

    the escape velocity vector at any given point is not well-defined either. In what direction does it point? (in an isotropic universe all directions are more or less the same.)
    What is the magnitude---the speed---of the escape velocity vector? (in a homgeneous universe there is roughly equal distribution of mass to the North as there is to the South, the pull forwards is the same as the pull to the rear).

    Perhaps I am missing something. Suffice to say I am baffled by your idea that you state in the quote because, since the terms are ill-defined, it seems the statement can be neither right nor wrong.


    as a footnote, if you were to PICK a reference point and make a catalog of the recession speeds of various objects you would find that at the present moment the vast majority are receding at speeds which are several times the speed of light. I don't know how that would fit in with your idea of escape velocity, and the formula for calculating it. so even if you were somehow to attribute meaning to the terms in your statement it might be difficult to establish it.

    I believe there is a nonstandard cosmology in which these things make sense, called the Milne model, but it long ago lost the attention most professionals. I imagine because it does not fit the data very well, or because it has been sitting around since 1935 and never caught on. It has a kind of alternative flavor. We occasionally get a Milne thread in Cosmology forum
    Last edited: Nov 24, 2007
  4. Nov 23, 2007 #3


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    To expand on marcus's explanation, all objects with a redshift greater than ~1.46 are receeding at superluminal velocities [in the LCDM model]. See http://arxiv.org/abs/astro-ph/0310808
  5. Nov 24, 2007 #4


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    Hi Jon,
    I had another look, now that your post is in Astrophysics forum. It looks like your r-dot term is the the TIME-DERIVATIVE OF THE SCALE FACTOR in the usual Friedmann model metric, the FRW metric.

    Time in this case would be the Friedmann model coordinate time.

    One reason, I guess, that your post looked strange to me is that I am not used to thinking of the scalefactor as a DISTANCE. I have never seen it written with a lowercase r. Usually it is written "a" or "R", and understood to depend on t, so it is really a(t) or R(t).
    I don't think of it as a physical distance in lightyears, because it's value is conventional. It is set by convention to some convenient arbitrary value, typically
    a(present) = 1
    or if the author is using cap-R he will write R(present) = 1

    the symbol for the present time is typically t0

    My understanding is that a-dot(t0) or if you prefer R-dot(t0)
    doesnt have any invariant physical meaning. You couldnt ask someone to measure it. The value is purely conventional, set to whatever is mathematically convenient.

    Sort of like when an economist decides to measure GNP in 1950 dollars, when they could just as well decide to measure in 1975 dollars.

    So it doesnt make any physical sense to say that nature forces it to be equal to some escape velocity speed.

    What DOES have a physical meaning is the RATIO

    that is the Hubble parameter

    when you make a ratio, the arbitrariness of scale cancels out, so you have a meaningful quantity.

    I hope this is helpful and that you understand what I am driving at.

    For example if a cosmologist arbitrarily decided that on Tuesday to have
    R(t0) = 2 instead of 1, then it wouldn't make any difference to his results.
    R would be twice as big, but then that would make R-dot, the time derivative, also twice as big. So when he forms the ratio, R-dot/R, he gets the same as he did on Monday.

    I looked over your post again and still do not understand. Feel free to explain some more. Maybe someone else will see what your idea is----perhaps even connect it up with some alternative cosmology model like the Milne picture (which I think was devised in the 1935, there may be a Wikipedia article about it).
    Last edited: Nov 24, 2007
  6. Nov 24, 2007 #5
    Lets ignore dark energy for the moment and think of a universe with the critical density (so that space is flat). Then I can see how this can be thought of expanding at the 'escape velocity'. However, I can't see why you should say that gravity is causing the expansion, any more than saying that gravity was responsible for the motion of a projectile which has been shot upwards.

    Furthermore, if you are trying to say that mass/energy has repulsive effects as well as attractive effects, and that these are responsible for the acceleration (rather than deceleration) of the expansion of the universe, then the same effects should apply to the earth, and so we should be accelerating away from its surface
  7. Nov 24, 2007 #6


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    We've already talked this to death in the cosmology forum, but I'll make some comments.

    1) We generally don't "disprove" alternate physics theories here at PF. There are reasons for this, which this thread illustrates - people who propose fringe theories tend to get strongly emotionally attached to them. This shows up as, for instance, people not accepting criticism, and going around reposting a personal theory until they find someone (anyone) who will agree with them, at which point they consider themselves vindicated and the theory "proven".

    2) GR does not compel the universe to be eternally flat. The curvature constant, K, in the Friedmann equations can be positive, negative, or zero. All GR says is that if the universe starts out as perfectly spatially flat, it remains perfectly spatially flat. It does *not* and never has said that the universe has to be eternally flat.

    3) Observation does not compel the universe to be perfectly flat either. It only says that K must be very small, but it doesn't guarantee that K=0.

    4) You're really "hung up" on this escape velocity idea. The only reason I understand what you mean by "escape velocity" is our previous discussions. It does turn out that your idea of "escape velocity", taken from the popular literature, is tautologically equivalent to K=0. Of course, the classic FRW universe, which obeys the cosmological principle, does not have anything for it to escape into.

    According to GR, the universe is capable of non-zero curvature at large scales, i.e. the universe is capable of K not being zero. This should be obvious, and it disproves your proposition, unless you intend that GR not be part of your "alternate physics".
    Last edited: Nov 24, 2007
  8. Nov 24, 2007 #7
    Hi Marcus,

    Thank you for considering this proposition and making constructive suggestions.

    The proposition itself is intended to be very, very simple, so your reaction tells me I haven't explained it clearly enough. Let me try again:

    This proposition is attempting to define an alternative mechanism which results in exactly the expanding observable universe we perceive. If the mechanism doesn't produce essentially an exact duplicate, then I will consider it disproved. The intent is to provide a simple mechanism to explain the expansion of the universe, both as currently observed, and as historically modeled by the Friedmann equations.

    The expansion of the universe "is what it is", as described by the Hubble flow. Galaxies are increasing their distance from us at the Hubble rate which increases in proportion to distance. Galaxies at high redshifts are increasing their distance from us at a rate faster than the speed of light. That's ok, because they aren't actually moving through space, rather the intervening space is expanding. The expansion of space occurs equally in all directions at once; thus there is no concept of expansion moving in or from any particular direction.

    The Friedmann expansion formula defines the rate of increase in the scale factor a(t) as a function of elapsed time. The scaled expansion rate (dot a / a) is defined as the Hubble factor. As I said, converting the Friedmann expansion equation to its "escape velocity" form is a trivial (but apparently unconventional) mathematical substitution. People keep asking why I do the conversion. I do it because it allows me to examine the Hubble flow BOTH as (1) the summation of many discrete local expansions, with discrete "clumpy" local masses, and (2) simultaneously as a single Hubble flow for the entire observable universe of homogeneous density (rho). For the limited purposes I am examining, I see no problem in summing up total mass/energy for the "known" volume of the observable universe (currently about 3.15E+54kg over 3.45E+80 cubic meters, representing a rho of 9.16E-27). Using the simple escape value version of the Friedmann equation generates an expansion rate for the current radius of the observable universe, at 9.85E+08 meters per second. Not coincidentally, this is exactly the same expansion rate calculated by multiplying the Hubble constant, (converted to meters per second per meter of distance, at 2.26E-18) by the current radius of the observable universe (4.35E+26 meters).

    I understand why the non-dimensional scaled metric of dot a / a is preferred in the literature, because it is independent of current estimates of radius, rho, etc., which may require adjustment over time as observations improve. Nevertheless, as long as we keep that in mind, I see no conceptual problem of speaking in terms of an actual radius and mass/energy. The math works the same both ways.

    So my proposition starts from the observation that, according to the Friedmann expansion equation, a flat universe in total will expand at exactly the escape velocity of its mass/energy contents, throughout its entire history. Neither the decline in mass/energy caused by the redshift of free radiation, nor the increase in mass/energy caused by the cosmological constant, will change that simple expansion formula. It must expand at exactly its instantaneous escape velocity at all times in order to remain flat. Flatness depends on the ratio between only two variables, total mass/energy and radius.

    The next step is to divide the observable universe into any arbitrary number of spherical subregions. At a small enough scale, individual subregions can have quite diverse values of rho because of gravitational matter clumping. If the subregions are defined in a way such that they are not gravitationally bound to other subregions, then it is logical to take the next step, which is to regard each subregion as having a discrete expansion rate equal to the escape velocity of its own contents; that is, based on its own ratio of total mass/energy to radius. Thus, expansion rates will vary locally. This doesn't seem surprising. After all, how can the expansion rate in one subregion stay in synch with the expansion rate of another subregion which is beyond its event horizon? And since the current radius of our observable universe is a rather arbitrary subset of the total (or infinite) universe, the Friedmann formulas should work in reasonably defined spherical subsets or supersets of our observable universe.

    Given that the local expansion rate appears to be derived from, and entirely dependent on, the local mass/energy, the logical next question is to ask whether there is a direct causal connection between the two. On this question, the 'standard model' seems to assume that expansion was given one big "push" by inflation, and thereafter the Einstein-de Sitter expansion "coasted" along based on some unarticulated concept of expansionary momentum or inertia. (More recently the expansion is being given additional pushes by the cosmological constant).

    The only difference in my proposition is that this expansion is deemed to have no momentum or inertia. Thus when "the foot came off of the inflaton accelerator", the expansion would have immediately stopped dead in its tracks. So what kept the expansion going? It was the subsequent, real-time, continuous pushing (or stretching, if you prefer) force which I propose is driven by gravity. Gravity seems to me to be the most logical attribute of mass/energy which could generate a dynamic pushing force without requiring the expenditure of any detectible kinetic energy. My proposition is that this gravitational expansion force is entirely local in nature; the expansion of one subregion is not influenced by the expansion rate of another subregion, unless the two are gravitationally bound together. The intended end result is that galaxies, etc., throughout the universe will observe the distance between themselves expanding, in exactly the Hubble flow we currently observe. Again, expansion is NOT caused by peculiar motion of mass/energy moving through space; it is caused by the expansion of space itself.

    Please let me know if this helps clarify things. We need to get this our heads together on this much before we can delve further.

    Thanks again,

  9. Nov 24, 2007 #8
    Hi Pervect, I didn't see your post before I responded to Marcus.

    I understand your point, but as you know from experience, I always accept critisism when it is aimed at the substance (rather than at my personal qualifications) and when the point being made actually sinks into my thick skull.

    The reason I moved over from the Cosmology category is because I had understood that the forum rules prohibit personal theories in the regular categories, and limits them to "Beyond the Standard Model." So I was quite surprised when someone moved it here. I really don't care where you put it, as long as I can get someone (like Marcus) to respond to what is admittedly a personal theory.

    I agree with you entirely. That's one of the key differences in my proposition; it requires perfect flatness at all times. So if subsequent observations prove that the universe is not perfectly flat, my proposition should be discarded.

    Yes, in my response to Marcus I explained why I choose to work with escape velocity. But I could just as well turn the question around and ask, why doesn't everyone work with escape velocity? It is a simpler formula that generates exactly the same results as the more complex Friedman expansion equation. Some people seem to relish the most difficult possible math, but I prefer the simplest path, as long as it is properly qualified.

    Pervect, if you had been carefully reading my posts all along, you would recall that this is one aspect of GR that I absolutely intend to NOT be part of my "alternative physics." After all, I couldn't honestly call it "alternative" if there wasn't something different about it! To reiterate as briefly as possible, my proposition requires four key adjustments to GR:

    1. The universe must always be perfectly flat at non-local scales.
    2. Local curvature of space (due to local gravitation) is not additive to curvature of space in other regions which are not gravitational bound to the first region.
    3. Any concept of expansionary "momentum" must be discarded.
    4. Gravitation is the cause of the local expansion of space. The important corollary of this is that gravitation does not cause the overall expansion of the universe to decelerate.

    Other than that, I think my proposition allows all other aspects of GR and SR to remain entirely intact. Other aspects of physics should also remain entirely intact, except of course for the obvious adjustments required to the Friedmann equations and the equation of state.

    Last edited: Nov 24, 2007
  10. Nov 24, 2007 #9


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    Hi Jon, I see this is addressed to Pervect but I hope you and he do not mind if I respond
    I think you may be confused about PF policy about personal theories. Beyond forum is not the place for them. Only professionally researched theories get discussed at Beyond.
    That's just how it is. In practice, Cosmology forum (even though it is not supposed to) tends to be more hospitable to personal theories. There is a special place for personal theories at PF called Individual Research, or so I understand.

    I don't speak for the management obviously. I'm just a poster like yourself. But that's my perception of how it is. I think it actually works out pretty well.

    I'm glad that you have gotten some response, and glad to be included in that, but my feeling is that it is time for you to move on and learn some more cosmology.

    Cosmological models are not guesses about how the universe works so much as parametrized solutions of General Relativity that compete to see which can best fit the data

    Largescale curvature is something that is measured, and there is an errorbar for it. You are treating it as an AXIOM (that curvature is zero) so your model is somewhat stiff and inflexible. It can't possibly fit the data as well as LCDM, for example.

    You seem smart, why not learn some more? You know what Omega is, I guess.
    Some recent published errorbars for Omega have been around 1.01 and entirely on the upside of 1. One still cannot be sure but in January 2007 there was that Ned Wright paper with a 'best fit' figure of 1.011 for Omega.

    that corresponds to a spatial finite universe with a radius of curvature of 130 billion LY.
    Nobody can say how space is really shaped and if it is finite or infinite, but it is not a good time to be postulating an axiom (as you do) that the true Omega is exactly 1.

    If it were exactly equal to 1 (i.e. zero curvature) then one might expect that when they measure it they get an errorbar that is distributed around 1----like [0.005, 1.005]---or at least that includes 1. But recently I'm seeing bars that dont even include 1, they are entirely on the upside, like [1.003, 1.019]. Roughly like that, cant remember exactly.

    Why not try your hand at devising a cosmology model which doesn't have to be exactly flat?
    Last edited: Nov 24, 2007
  11. Nov 24, 2007 #10
    Hi Marcus,

    Of course you can feel free to respond to any of my posts, regardless of who I address.

    I understand and accept your point that we may soon become convinced that the universe is not exactly flat, and in that case my proposition should be discarded.

    I would be happy to propose some exciting new theory for a non-flat universe, but none have occurred to me. Each of us is limited to that which happens to appear in our own mental "in-basket".

    I imagine that people participate in the Physics Forum because they enjoy stretching their minds. I am asking for a simple favor -- that perhaps a few individuals will stretch their minds to consider the specific proposition I have set forth. Even if it turns out not to be valid, can't it be an interesting puzzle to parse it and really think seriously about whether it works or not? There is a little happiness to be gained by explaining to someone why their great new idea doesn't work.

    But if at the end of the day this favor is to much to ask, then so be it. I will continue to be tortured by this puzzle, alone, late at night when everyone else in the house is asleep. Sigh...

    I'm a bit dismayed by your suggestion that the effort to develop "best fit" theories must never question any aspect of GR, as originally defined. GR is no doubt a rightfully entrenched theory, but surely the "scientific method" requires us to continue testing and questioning every aspect of such a theory until each and every aspect is proven empirically or by definitive observations.

    Last edited: Nov 24, 2007
  12. Nov 25, 2007 #11
    It occurs to me that if the Hubble expansion rate varies locally, observations attempting to determine the curvature of the universe (by examining the CMB radiation, etc.) might be skewed in various directions. As photons pass through a region expanding faster or slower than the average expansion rate, their progress towards an observer should be advanced or retarded compared to our expectations. Do WMAP or the other projects give any consideration to this possibility?

    Here's another thought experiment about my proposition. It would say that local space in the immediate vicinity of a black hole is expanding at or faster than the speed of light. Does that mean that eventually the black hole would be cut off from any infalling matter or radiation? Perhaps infalling matter and radiation would reach a spherical equilibrium point around a black hole, at which point they couldn't fall inward any further and they couldn't escape the black hole's gravitation in an outward direction. Infalling stuff would collide and pile up, forming a large spherical "junkyard". It seems to me that this sphere would be gravitationally fairly stable, because if an object strayed inward the ever more rapid expansion of space as it approaches the black hole would eventually carry it back out, and if it strayed outward the black hole's gravitation would eventually pull it back in. Just a thought.

  13. Nov 25, 2007 #12
    gravity could in theory be repulsive
  14. Nov 25, 2007 #13
    Hi Andrewj,

    Please feel free to expand on your statement that "gravity could in theory be repulsive." In what particular sense do you mean that?

    In my opinion, my proposition doesn't consider gravity to be "repulsive" per se. I don't think that space is literally capable of being "pushed" by gravitational expansion, just as I don't think space is capable of being "pulled" or "restrained" by gravity. Rather, I think that the presence of a gravitational field would simply induce local space to expand spontaneously. If geometry is truly incapable of departing from perfect flatness, then the presence of even the tiniest particle of mass/energy (including the cosmological constant) must inevitably cause local space to expand.

    But how it's physically accomplished, I can't really surmise. Perhaps it could be fuzzily described as matter "falling into" space (without actually moving), and dragging space with it. Sort of like frame-dragging in GR. Or maybe it could be more simply described as another aspect of the curvature of local space by gravity; in this case the curvature creating a local enlargement to the overall manifold, which remains permanently even if the massive object moves away. I don't know.

    Last edited: Nov 25, 2007
  15. Nov 25, 2007 #14


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    If there is a cosmological constant, then gravity is indeed repulsive. It's a little tricky though, since a cosmological constant on the 'geometry' side of the Einstein field equations and a non-zero vacuum energy on the 'energy' side are indistinguishable as far as cosmology is concerned. Particle physics may be able to distinguish them, though the field is murky at present.

    Mass with an equation of state greater than w=-1/3 causes the expansion of the Universe to slow, and in sufficient quantities, to reverse the expansion into a contraction. It is not true to say that 'the presence of even the tiniest particle of mass/energy must inevitable cause local space to expand'. It is not false as such, but there is not enough information in the proposition to reach the conclusion.
  16. Nov 25, 2007 #15
    Hi Wallace,

    I agree with what you say, when applied to 'standard model' physics. My post was referring to my proposition for an alternative physics. As I said in an earlier post, as far as I can tell, negative pressure (and therefore the antigravity effect it produces) are not relevant to expansion in my alternative physics.

  17. Nov 25, 2007 #16


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    Since this thread has drivted to the topic of "alternate physics", and the non-alternate physics has been exhaustively discussed in other threads, I'm going to lock it.
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