Dark Energy Puzzle: Solved ?
    By Tommaso Dorigo | April 15th 2010 11:13 AM | 55 comments | Print | E-mail | Track Comments
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    I am an experimental particle physicist working with the CMS experiment at CERN. In my spare time I play chess, abuse the piano, and aim my dobson...

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    I read with interest and excitement a very lightweight preprint on the Cornell preprint arxiv this afternoon. Although I usually skip reading papers on subjects I know little about (Cosmology), the title startled me enough to plunge into it:

    "Solution to the Dark Energy Problem".

    Single author, Paul Howard Frampton. Hmmm. A thought crossed my mind at the very start. Was this the work of a crackpot, sneaked into the arxiv while nobody was looking ?

    The tentative answer, before reading the text, was "No". Professor Frampton is a distinguished scientist with an excellent record, and although I know at least one distinguished scientist who has apparently lost his mind, this did not appear to be the case.

    But wait. What was the date of publication ? April first ? No, April 11th. Okay, it looked like I would need to read the article to find out!

    Fortunately, the paper is just 9 pages long, and it contains a mere seven (7) formulas -not even quite hard to decypher! For a paper allegedly solving a long-standing puzzle in contemporary physics and cosmology, this must be a record. But let me discuss the contents, with the explicit caveat that I am not an expert and my judgement is as good as yours.

    The paper

    The paper is extremely colloquial and simple to read. The author start with a brief section containing a description of the problem of the accelerated expansion of the universe. This effect is with us since 1998, when it was recognized by the scientific community that the distant stars producing type-1A supernova explosions were increasingly receding from us as a function of their distance.

    Type-1A supernovae are like "standard candles", because the mechanism that ignites them guarantees that they have all the same intrinsic luminosity: thus their systematic study in distant galaxies provided the necessary input.

    The evidence for an accelerated expansion of the universe was later confirmed by independent observations. One may be thus led to speculate that a sort of "negative pressure" pervades the universe, causing it to expand at an increasing rate. This works out easily like an addendum to the equations governing the universe expansion. Frampton explains clearly how a solution of the problem can be worked out adding a "dark energy" to the energy density in the Friedmann equation.

    Section two is titled "Solution to the Dark Energy Problem". And since the statement of the problem took five formulas in section one, we are left with two formulas... Enough of a task to make a theorist's nerves stretch beyond the breaking point. But let us follow Frampton -section two is only two pages long!, so we can afford to be analytical.

    He starts with the holographic principle: all the information about the universe is encoded in its two-dimensional surface. If this is so, it allows us to consider the universe in a different light.

    A dimensionful parameter of importance in cosmology is the Schwarzschild radius of a body: it is the radius which constitutes the event horizon for the mass possessed by the body. Most heavenly bodies have a Schwarzschild radius much smaller than their real dimensions: for instance, the sun has a radius of 800,000 kilometers, but its Schwarzschild radius is of just 3 km. When the physical radius is much larger, objects are quite different from black holes.

    If one considers the whole visible universe, on the other hand, one gets a visible mass equal to about 10^23 solar masses. Its Schwarzschild radius is thus of 30 billions of light years, while its physical size is of 48 billions of light years. The universe does not seem much different from a black hole!

    The above observation provides the hint to Frampton's solution of the problem of dark energy. Quite simply, a relation can be written between the temperature at the event horizon (the second-to-last equation) and the acceleration  (last equation!), and this agrees with experimental measurements of the expansion rate of the universe. Thus the apparent dark-energy effect may be just interpreted as a thermodynamical effect for this giant black hole.

    Frampton discusses the results in a separate section. I can only quote a most meaningful statement:

    My result calls into question almost all of the work done on quantum gravity, since the discovery of quantum mechanics. For gravity, there is no longer necessity for a graviton.
    In the case of string theory, the principal motivation for the profound and historical suggestion by Scherk and Schwarz that string theory be reinterpreted, not as a theory of the strong interaction, but instead as a theory of the gravitational interaction, came from the natural appearance of a massless graviton in the closed string sector.

    I am not saying that string theory is dead. What I am saying is, that string theory cannot be a theory of the fundamental gravitational interaction, since there is no fundamental gravitational interaction.

    I confess that my understanding of the whole picture is too sketchy to allow me anything but the above summary -no insight, no extrapolations, no comment. For the little I know about the matter, I found no flaws in the reasoning described in the paper. So, before I leave the debate to the experts, all I can say is that the very concept of an accelerated expansion driven by a negative energy density has always looked a real stretch to me, and I never believed in the "official" explanation of the cosmological evidences that have piled up in the last dozen years.

    I am now eager to read more about this article elsewhere. I will add links here if I find anything worth reading!


    Sojme points:
    The numbers work out because the dark energy parameter is at the same scale as the observable universe. It is the same conincidence that has been used in anthropic arguments and would probably work in many other arguments. It is not convincing unless the theory is good. In this case I can see any real explanation of why the temerature or entropy should produce an acceleration on the same scale.

    It also works only if you assume that the observed homogeniety of the universe stops at the current scale of the observable universe, otherwise the "black hole" would be bigger. Or he could be saying that the cosmological constant varies with the scale of the universe, but the required relationship is probably not consistent with observation.

    I agree with PhilG.

    Daniel de França MTd2
    There is a nobel prize winner acknowledged. Check his 2 papers, in citation [20] e [21].

    We observe the arrow of time, the second law of thermodynamics works and so on, so our universe began in a low entropy state rather than being a fluctuation from a high-entropy state. It is still in a relatively low entropy state. I believe black holes are somehow the maximum entropy that you can stuff behind a surface with a given area; and therefore our universe is not a black hole. (If we were Boltzmann Brains then Frampton's idea might be workable.)

    All the above is my very humble opinion. I think if you want an informed answer, you should ask Bee.

    Larry Arnold
    This is beyond me I am afraid, is the suggestion somehow that we are living in a black hole, one which of course contains even more black holes?

    It's obvious enough that there is an event horizon to what we call the Universe, because if there were not we would have or will see beyond it.

    I think the problem ultimately will not be one of science, but of cognition, we will simply run out of metaphors for the concepts we cannot express directly.
    "I confess that my understanding of the whole picture is too sketchy ". Don't worry, you're not alone: the author is in the same boat.

    This sounds very similar to a recent paper asserting that Newton's laws of gravitation can be derived from first principles using a similar holographic principle assumption. This leads to the conclusion that gravity is an emergent property caused by entropy effects. Maybe these guys are onto something!

    Yes, in fact there was an article written about it here in ScientificBlogging but for the life of me I can't remember who wrote it. So it rings a bell with me as well.

    The thing is I understand the Friedman-Lemaitre stuff, and Stephen Hawking's idea that the universe started out as a black hole, an Alan Guth's inflationary theory, the Type Ia supernova cosmology survey which incidentally may be flawed because there's been a new revelation about Type Ia supernovae which I wrote about in this article: Type Ia Supernovae: A New Revelation, but which really doesn't matter since we have the WMAP data, but what I've never been clear about is this darn holographic principle. I just don't get it!
    Peter Woit had an entry on his blog concerning this. He was not convinced:

    The link to the paper should be this one:

    Now, I remember a paper on the Universe being described as the interior of a 5-d blackhole (as opposed to a 4-d one like we have here), is there a link to that? No idea whether any of that makes sense though.

    I'm impressed (hey, a thermodynamical interpretation of universal expansion, what more would one wish for?), but I missed how this advocates the elimination of gravity.

    Johannes Koelman's blog (also on ScientificBlogging) covered this very topic in January:

    with some more elucidation in this post:

    I had read the first of these but looked a bit like arithmology... I hope I'm wrong of course:) But may I point out that while it's also thermodynamical treatment of cosmology, it's not "this very topic". Verlinde rather uses the informational aspects of entropy, which are not as "tangible" (but with the bonus of applying them to microscopic level), and the novelty with Frampton is that he makes the explicit assumption of a black hole system.

    I thought it might be Johannes who wrote about it, but I wasn't sure. Thank you, Matt! But, I still don't get it! LOL ;-)
    Thanks! I had missed both. Will now read Johannes' take at this.
    tulpoeid, I asked myself the same question. The author's answer is in the first paragraph of section 3, just above the paragraph quoted by Tommaso,

    "This solution of the dark energy problem not only solves a cosmological problem, it casts
    a completely new light on the nature of the gravitational force. Since the expansion of the
    universe, including the acceleration thereof, can only be a gravitational phenomenon, I
    arrive at the viewpoint that gravity is a classical result of the second law of thermodynam-
    ics. This means that gravity cannot be regarded as, on a footing with, the electroweak
    and strong interactions."

    If I understand correctly, it's not gravity that is eliminated, it is "only" quantum gravity.

    But this paragraph says: "A might be a result of B. I prove that A is the result of C. Therefore, B is redundant", and what about the myriad of other phenomena attributed to B? I might be missing some background at this point.

    Sounds like a sensible arxiv paper for a change ... let me take a look ...

    LOL, this is a spectacularly funny piece of writing !! Just the thing the arXiv likes to ban!

    But seriously ... Anon, the idea is not that QG is eliminated, since it appears here in the BH temperature, but that all popular approaches to QG are wrong. A thermodynamic approach understands that QG is not about 'quantizing' solutions for small physical systems, and Padmanabhan's excellent work has already shown how Einstein's equations arise from thermodynamic principles.

    Anyway, if we wanted to make eqn. (7) look more like an acceleration, using the Schwarzschild radius R = 2GM/cc we obtain a horizon acceleration satisfying 2a = R / TT where T must be defined as 1/2H. That is, R = cT, the principle of Louise Riofrio's cosmology.

    Just because the holographic, principle gives approximately the right have for dark energy, does not be me, mean
    its solves dark energy. One still needs a physical field for these degrees to freedom, and these degrees of freedom must have the correct behaviour especially, not clumping over long time scales. You can note the universe is less dense that a black hole, even if close, and so no event horizon exists, to have a temperature.

    Wow! That has got to be the shortest abstract that I have ever seen! LOL I think I'm going to download the paper to hard drive and read it when I am better rested. I let you know what I think after I've read it.
    Amateur Astronomer
    The holographic principle as Frampton used it, says that any closed surface that might be constructed in space contains on it's surface in quantum Planck units a complete description of everything inside the closed surface.

    His explanation of the expanding universe is that it must expand because the information it contains is increasing.

    Now I can show that the assumption is not true that the surface contains a complete description of what's inside. Sound waves on Earth do not propagate into space so a complete record of them cannot be found on any surface in the vacuum. Some consequences of sound might propagate, but that is not a complete set of information, only the essential part that modifies the physical processes in space.

    Strictly speaking a surface of zero thickness does not exist in the physical world, only in abstract mathematics.

    Any closed surface that might be constructed in space defines a shell that is one Planck unit thick. Within the volume of the shell the quantum Planck units contain a large set of information that is sufficient to describe the local properties of space in the shell, but not a complete description of everything inside the surface. Nonessential information might propagate if there is surplus data handling capacity, but in large scale systems the non essential information does not propagate.

    Together with the information of entropic states, the shell contains energy that propagates physical processes from one place to another. Bits of data do not attract or repel each other. Entropy is more than just a databank, it is an energy function similar to a heat capacity, but modified by the information in the databank. It is the information that makes entropy different from a heat capacity.

    Everything moves at light speed unless it has rest mass. The hologram usually does not have mass, so it moves at light speed in directions that are perpendicular to the shell surface. That is why the universe expands. The energy in the vacuum expands the shell surface at light speed.
    Thank you for the explanation, Jerry. It's starting to make a little bit more sense now. : )
    Larry Arnold
    It is I think (or do I, that is another question), that it is a mistake to argue too much from what is possible in Maths, because that is to mistake the equations for the real, whereas all they are is a model or representation of the real, as much as a diagram or drawing is. The mathematics are constrained as much by our perceptual and cognitive processes as indeed is any drawing in the sand, it is a part of the way we have evolved in relationship to the phenomena we can directly experience and abstraction is merely drawn from it.

    Were we beings who can see and move in higher dimensions, we would doubtless have evolved a cognition to represent that, and it may well look nothing like the construct we call mathematics.

    Mathematics allows me to do all sorts of things, including impossibilities and absurdities. The question is whether those absurdities exist solely because mathematics is not a very complete system, or because it is a flawed system coming out of that fuzzy logic that allows us to live in this limited space we do. I am no Platonist.

    Getting to the point, it's all very well building a world out of mathematics, but it still needs to be proven in some empirical or experimental way and the fact is, we cannot ever see to the edge of the universe as it is currently, it moves on and away.

    Some answers we will never have, because we cannot contain them in those 10^15 synapses we possess. (if we are lucky, mine are boggling away at an increasing extent on this topic)
    Thanks to all for your contributions. But I would like somebody here who explained me if there is anything flawed in the paper, or if it is just irrelevant because it does not really explain anything, or if something interesting can actually be built on this idea.

    Frampton has been publishing this type of thing for a number of years, and provides entertainement amongst grad students who have the time to actually read his papers.

    There are so many bizarre things about the paper, its hard to know where to even start. For instance, the idea that we are all living in a blackhole is wrong:

    The holographic principle in so far as we know, has only been concretely demonstrated in the case of antidesitter space (although there is hope that it goes beyond that). In either case, there is no obvious reason to think the appropriate conformal boundary and where he happens to place his holographic screen (by hand) must happen to coincide with our particle horizon. No explanation or motivation is given.

    The whole 'trick' basically is the old observation that a very small number (the cc) happens to be of the same order of magnitude as the area at the horizon of the visible universe. Dividing by it, 'explains' it away to within an order or two magnitude, but is what you might call pure numerology at this point absent anything concrete.


    Amateur Astronomer

    The paper is flawed in that it represents our universe as one that is gravitationally constrained. That is an old idea that has been discredited by acceleration of galaxies. Our universe is constrained by acceleration balancing a force as Johannes described.

    The paper is not totally irrelevant but rather disappointing, because it doesn’t explain anything new. It is a vote for the end of dark physics and little else. A comparison can be made with your team at Padova University where real science is done with real data and explained clearly by a diverse team that has found a common ground in the scientific topic.

    Something interesting can be built on the holographic idea. Emergent gravity is a polite way of saying that Grand Unification is a lost cause, and the people who work on it should migrate to other topics. All of the cosmic phenomena that were ascribed to dark energy and dark matter have been shown to be features of other science with rather small and reasonable extensions of popular interpretations.

    When dark energy and dark matter go to the history archives of defunct theories, they take with them super symmetry and super string theory, because those theories are all structured together and inter dependent. Whet remains is the robust asymmetric string theory of 26 dimensions that doesn’t call on the powers of darkness for support.

    These are rather strong statements that an old retired scientist can make, but would be unwise for a recently graduated PhD who is hoping to maintain a teaching position as an assistant professor. The mid level scientists find more subtle way to express the opinions, but the end result is the same. It is the end of Dark Physics.

    Holography is a step toward describing the vacuum, what structure it has, how much energy is there, how the energy is partitioned, how entropic information is stored, and how the propagation proceeds from one place to another.

    Quantum field theory is rewriting general relativity and replacing curvature from action at a distance with a localized description of the vacuum. The Dirac sea of energy was a problem that was resolved last year by partition of the vacuum energy into a balanced system that allows a small negative cosmological constant to coexist with a large total energy in space.

    The Dirac sea argument was resolved in favor of Dirac last year when the sea of energy was derived from general relativity and the properties of black holes, in agreement with Dirac’s calculations from quantum mechanics.

    Expectations are that the cosmological constant will be eliminated completely by a correct and complete representation of energy partitions in the stress energy tensor, expressed in more than 4 dimensions within the quantum field theory. Acceleration of galaxies can be accounted for by radiant power, the slight excess of microwave background energy in space that tends to bend space backward between clusters of galaxies where it is stronger than local gravity. This is not really new science. It can be traced back as far as 1918 in the main stream of physics. The microwaves have been measured, which supports the concept of real science with real data.

    The Friedmann equation has a technical problem that has misled a lot of scientists. One interpretation of the Friedmann methods assumes that radiant power intensifies a gravitational field, in disagreement with Reissner–Nordström. Vacuum partition tends to favor Reissner–Nordström, suggesting that Friedmann should be interpreted differently.

    Notice that the leaders of holographic theory are coming from the community of quantum field theory. The two dozen papers on holography are making very small but definite statements about the replacement of dark energy by radiant power in cosmology.

    Next I would expect to hear about a team of scientists comparing the rate of measured acceleration to the magnitude of the reverse curvature from microwaves, with opinions published about whether or not the two data sets agree.
    "When dark energy and dark matter go to the history archives of defunct theories, they take with them super symmetry and super string theory, because those theories are all structured together and inter dependent."

    They are? I must have missed the memo.

    As you often say, Tommaso, only the ideas count. The way they are expressed is not so important. The main point here is the matching of a cosmological parameter (say H) to a black hole thermodynamic property (say, temperature T_b) ... R = ct, as Louise would say. There is no need to picture classical spheres in some background unphysical junk space.

    Rick Ryals
    Interesting paper, but this is even more simple stupid than the author thinks and it hits a real nerve for me, so please forgive any sarcasm that you might find in my tone.

    From the paper
    The insertion of the dark energy term Eq. (3) in Eq. (1) works very well as a part of the
    CDM model. However, it is an ad hoc procedure which gives no insight into what dark
    energy is.

    I know that this is the belief, I just don't know why, since Einstein's model makes very clear that dark energy is the same mass energy that makes up ordinary matter, except that it has rho<0, so it has negative pressure.  It amazes me how arrogantly cherry-picky the cutting edge is when it comes to Dr. E.'s theory, because they love to point out how accurate it is.. only when it is convenient to their argument just like the author of this paper did.

    From the paper:
    Of course, this present discussion of cosmic acceleration, is merely one small step towards the ultimate goal, of a cyclic model, in which time never begins or ends.

    Another problem simply resolved when you take what I said above to heart, since matter generation from Einstein's vacuum energy will necessarily increase negative pressure as well as tension between the vacuum and ordinary matter, because you can't condense huge voluminous chunks of rarefied mass energy down to the point that you achieve matter density without leaving a real hole in the vacuum that increase negative pressure while offsetting the positive gravitational effect of the newly created particle.

    Increasing tension between the vacuum and ordinary matter will eventually compromise the forces and boom, the second law of thermodynamics is preserved when we have another big bang in a universe that has pre-existing volume.

    This is also what one that wasn't utterly lost in the righteousness of the cutting edge would conclude if they simply project the expansion of the universe backwards to the point that inflationary theory becomes necessary to fill in the volume that Einstein's model explains without the need for such fantasies of the mind as "cosmic singularities" and "extraordinary rapid expansion"

    How laughably simple... I wonder if the author would help me write a *truly* simple paper... ?... since this meets his criteria... yeah, right.

    And I think that the cutting edge is out to lunch for failing to recognize what is at least contextually an obviously correct point without my having to submit a damned paper to this effect!

    Which makes ME the crackpot... in some whacked out world where cutting edge fanatics live... maybe.

    Sorry for the tude'...
    Well, I read the paper. Like you Tommaso, I simply don't have the expertize to make a judgment one way or another. Sorry I couldn't be of more help.
    HI Tommaso! I can vouch that Prof. Frampton is no cracked pot He was named distinguished professor of physics at a well-known US university, has published hundreds of papers, including some with Sheldon Glashow.

    "all the information about the universe is encoded in its two-dimensional surface"

    This is not proved so conclusions don't hold water.

    "If one considers the whole visible universe, on the other hand, one gets a visible mass equal to about 10^23 solar masses. Its Schwarzschild radius is thus of 30 billions of light years, while its physical size is of 48 billions of light years. The universe does not seem much different from a black hole!

    The above observation provides the hint to Frampton's solution of the problem of dark energy. Quite simply, a relation can be written between the temperature at the event horizon (the second-to-last equation) and the acceleration  (last equation!), and this agrees with experimental measurements of the expansion rate of the universe. Thus the apparent dark-energy effect may be just interpreted as a thermodynamical effect for this giant black hole."

    Pardon my ignorance in this field but would this article in any way be related to this?
    Hi Tommaso,

    Frampton's number, 30Gly, for the Schwarzschild radius of the observable matter in the universe, looks way too big to me. Even using his number, 10^23 solar masses for the mass of the visible universe (which seems a little high), I calculate the Schwarzschild radius to be

    R = 2 G M/c^2 ~ .3 Gly

    (Can someone confirm that, in case I've flubbed it?)

    If the Schwarzschild radius is about .3 Gly, as seems more reasonable, instead of 30 Gly as Frampton wrote, then this idea is probably dead, since that's much less than the 48 Gly radius of the visible universe.


    Ah, no, I dropped two decimal places. It does come out to 30Gly.

    Hi Garrett,
    whew! :)

    Amateur Astronomer
    In evaluation of claims about dark energy, the microwave background radiation can be compared to the Hubble acceleration of galaxies.

    A Poynting energy flux Sp was estimated in all directions from sigma, the Stefan-Boltzmann constant and temperature T, which makes some assumptions about the radiation processes in vacuum space.

    Sp = 2 sigma T4

    Local gravity acceleration gem for the electromagnetic induction component is calculated from the Poynting flux, gravity G, and light speed c.

    gem = SQRT( 4*Pi*G*Sp/c)

    gem = SQRT( 8*Pi*G*sigma/c) T2

    Electromagnetic induction is applied for microwave background of 2.725 degrees K.

    gem = 4.14 E-12 meters/second2

    The full potential of gem is not realized, because a weak gravitational curvature is always existing in deep space. Calculations on observational data of nearby galaxies and clusters lead to estimates of net acceleration of galaxies from microwaves between 1.08 E-16 meters/second2 outside the local cluster and 3.03 E-13 meters/second2 beyond the local neighborhood, at a distance of 35 Mpc from the mass center. A distance of about 200 Mpc would be needed to develop the full acceleration of gem, but that doesn’t usually happen because of the limited space between clusters.

    Hubble parameter H acceleration can be calculated for the wavelength of the microwaves at 2.725 degrees K.

    Hubble data from WMAP
    g = (hc/kT) dH/dt

    A graph is shown for WMAP data with reported differences in Hubble parameter. The actual change is probably less because part of the difference is believed to be caused by improved measurement methods. So the graph shows a maximum reported difference.

    The largest reported change is calculated below.

    dH/dt = 7.9588 E-28 (m/sec2)/m

    A gradient of this size would only be possible if the expansion only began from zero in 1915 and accelerated at a nearly constant rate since then. So the real gradient is probably a lot less. A maximum local acceleration is given for the microwave length.

    g = 4.20 E-30 meters/second2

    Microwave background radiation is more than sufficient to account for the measured acceleration of galactic clusters, even when there is competition from faint mass gravity in deep space. There is no need for dark energy or dark matter. Holographic theory is a way to get rid of dark energy and replace it with radiant power. Every paper that moves science in that direction has some value.

    The university professors have been gentile and polite in delivering the message, but the message is delivered.

    Hmmm ... that IPMU looks like a nice place to work ...

    There is one leap of logic in the paper that I don't follow, given by this sentence:
    "This temperature of the horizon information screen leads to a concomitant FDU acceler- 
    ation [8, 9, 10] a_Horizon, outward, of the horizon given by the relation
    FDU stands for Fuller-Davies-Unruh, and their work, in the cited papers, showed that an accelerating observer, in flat space, is supposed to detect thermal radiation from vacuum fluctuations.  There is a close analogy between FDU radiation and Hawking radiation, due to the fact that an observer at a constant Schwarzschild radius from a black hole is, in effect, accelerating.  So it's been established that acceleration implies radiation.  Frampton seems to assume the conditional goes the other way as well, that radiation implies acceleration.  Why? 
    T- all i'll say for now on this, given that others above have said much more in detail is -- probably not. :-> -M

    Check this out ..

    Amateur Astronomer
    Reply to JR.

    In Hubble terminology of the Frampton paper it is not appropriate to set acceleration a equal to Hc, because there is no acceleration at light speed. The correct acceleration is a fraction of Hc.

    In previous decades it was popular to define H over a long distance.

    (37.9 H = v / x

    That led to exactly one conclusion about a decelerating universe and the change of H with time.

    (37.10) dH / dt = - H2

    Since 1998 the universe was thought to be accelerating causing a revision to the Hubble mathematics that has not found it's way into the Frampton paper.

    (37.11) H = dv / dx

    (37.12) H = g / v

    (37.13) v = dx / dt

    (37.14) g = dv / dt

    (37.15) g = H v

    For relativistic velocity v* acceleration g must go to zero at light speed.

    (37.16) v = v* (1 - n2) = n c

    (37.17) g = H v* (1 - n2)

    This is the correct representation that combines Hubble parameter of general relativity with Lorentz contraction of special relativity. Then the change of H can take on any value in agreement with observational data.

    (37.18) dH / dt = dg / dx - H2

    In this representation an accelerating universe is possible when the rate of acceleration is increasing with distance at a rate higher H2.

    (37.19) dg / dx = H2 + dH / dt

    When the value of n is calculated for the acceleration nHc, the acceleration is about the same as is predicted from microwave background radiation.

    The Friedman equation can accommodate radiation parameters, but it is usually left out. When radiation is added to the Friedman equation it is often given the wrong sign and added to the gravitational parameter instead of being subtracted from gravity in disagreement with the metric of Reissner–Nordström.

    The scientific community needs to reconcile the Friedman equation with the negative sign of the electromagnetic tensor and the results obtained from it in the Reissner–Nordström metric.

    "Single author, Paul Howard Frampton. Hmmm. A thought crossed my mind at the very start. Was this the work of a crackpot, sneaked into the arxiv while nobody was looking ?

    "The tentative answer, before reading the text, was "No". Professor Frampton is a distinguished scientist with an excellent record, and although I know at least one distinguished scientist who has apparently lost his mind, this did not appear to be the case." - Tommaso's blog post.

    Distinguished, with an excellent record! So what? Politics is about being distinguished and taking papers seriously because the person has an excellent record. Science doesn't rely on authority credentials. In fact, science is about disbelieving such political claims based on expert authority. Although you then go on into the details a little more, it leaves an unpleasant taste to read this introductory material, even if written in jest. I'm sure you try not to buy into dogmas started by authority figures in science, but it's the way many laymen judge science. They think science is about fame and respect!

    My reason for being especially dismayed about this is that in May 1996, two years before Perlmutter measured the cosmological acceleration, I sent a paper to Nature journal predicting it from a quantum gravity theory. They rejected it without sending it for review. Classical and Quantum Gravity (Institute of Physics) "reviewed" it and sent me a copy of the report which said it wasn't based on string theory (which I already knew) and ignored the prediction. Another physicist who was a technical article contributor, Mike Renardson, wrote to me doubting if the predicted acceleration of ~7x10^-10 ms^-2 was big enough to ever detect. Electronics World published the 8-page paper after a notice on the letters page of the October 1996 issue. After the acceleration was detected and confirmed in 1998, I again tried to get it published in more appropriate journals, without joy and without any sensible criticism (referring to the science). So much for the popular idea that making a prediction correctly ahead of a measurement lends credibility...

    Hi Nige, if you check the second link in the post you will see that I have shown to be capable of giving the right weight, and not more, to the record of a distinguished theorist, a couple of years ago. Although this cannot justify rejecting papers with no apparent reason, you must acknowledge that it is a tough job for reviewers to decide in a totally unbiased way. Cheers, T.
    "...two years before Perlmutter measured the cosmological acceleration, I sent a paper to Nature journal predicting it from a quantum gravity theory."

    A million monkeys on a million typewriters...

    Frampton just takes the bulk of the worthy ideas in his paper with Easson and Smoot and then adds a very mild (and confusing) twist about living in a black hole. If it is a "solution to the dark energy problem" it really doesn't belong only to him.

    Amateur Astronomer
    In the change of Hubble parameter with distance a simplifying assumption can be made that is one of the few available choices to describe accelerating galaxies.

    (37.20) dg / dx = c dH / dx

    (37.21) dH / dt = H2 n / (1-n)

    This approach predicts the present change of Hubble parameter in 2010 to be much less than the previous estimate from WMAP data, and in better agreement with astronomical observations.

    (37.22) dH / dt = 3.34 E-38 / sec2

    A graph was made of these results projected backward in time with general relativity and special relativity combined in a numerical integration.

    Hubble Expansion CalculatedThe radiating horizon is the one that sends red shifted background microwaves to Earth. It has to contain some mass, otherwise it would move at light speed and could not radiate toward Earth. The 2.725 °K background microwave radiation around the Earth, is 71 °K at the moving horizon, and would look like 1855 °K to a stationary observer outside the Horizon.

    Our universe is not a black hole or a white hole. From the outside it would look like a red giant expanding near light speed, something like a supernova. Beyond the horizon is the light cone of our universe which would have to pass an external observer before the red horizon would become visible. According to the graph the light cone could be tens of billions of years beyond the horizon, so an external observer might not see both of them.

    The early creation looks like a fairly slow expansion at first driven by radiation. A more complete model would have some inflections in the curve to account for creation of mass and local transition from radiant to gravitational dominance.

    Frampton's model does not describe a black hole. It describes a universe that is larger than it's event horizon, and expanding close to light speed on the horizon.
    Amateur Astronomer
    Dark energy can be replaced by radiant power induction in expansion of the universe and acceleration of galaxy clusters. The previous assumption (37.20) can be replaced by an exact function based on finite elements.

    (37.23) H2 = gj(1/v - 1/vj) /(t - tj)

    Accelerating Universe Dominated By Radiant Induction
    Numerical integration gives an improved graph of the expansion velocity of the horizon.

    This solution does not require a big bang explosion. In stead it uses radiation dominated space with reversed curvature, allowing the expansion to start slow and accelerate. This model is in reasonable agreement with published astronomical observations concerning the age of the universe.
    Sean Carroll posted some interesting words on the subject here.

    A couple of questions:

    1. Light creates pressure.. this is the principle behind the light sail. And that pressure is cumulative over time. What impact would light pressure have on the acceleration of the universe over time, given the length of the universe and the constant accelative thrust of everything being hit by light receding from everything that produces light.

    2. Why talk about "visible" mass. It is widely believe that visible mass is only a tiny fraction of the total mass when dark mass is added to the equation. What is the necessary schwatzchild radius when all matter is factored into the equations, and how does that alter the picture.

    Hi Ian,

    I have no answer for question one -maybe some cosmologist here can answer meaningfully. As for your second question, I think the author meant to question the need for dark energy in the picture of the universe. For dark matter: the fraction which is not dark is not tiny; the coincidence discussed in the paper is still there -if only as an order-of-magnitude effect- if you include dark matter. However, if you question our understanding of the mass-energy budget in the universe, you may also end up questioning the amount of dark matter. I do not see this as a contradiction.

    What impact would light pressure have on the acceleration of the universe over time

    Or... could we make the universe expand by standing in a circle and pushing? :-) Actually, you're right, pressure does have such an effect, but it is very small. The Friedmann equation governing the expansion contains pressure p and matter density ρ in the combination ρ and p/c2 (this can be seen from dimensionality arguments) Meaning the pressure required would be tremendous. Light pressure is a spatial component of the electromagnetic stress-energy tensor, so basically for the light pressure to be significant you're asking for a situation in which the electromagnetic energy density E2 + B2 was comparable to the energy density from matter.

    James Ph. Kotsybar
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                                   -- James Ph. Kotsybar


    Could inflation have done more than we know,

    shortly after the Big Bang’s first salvo,

    and created a dense matter halo

    beyond the horizon where we can go?


    Beyond the horizon that we can see,

    is there a remote possibility

    of a most massive field of gravity

    that pulls the strings of our reality?


    Perhaps it’s just dense matter that’s the source,

    accelerating expansion perforce,

    and not some new and mysterious force,

    or change of gravity’s attractive course,

    as though we are bound by a black hole’s skin,

    that stretches space to surface dimension.


    James Ph. Kotsybar


               -- James Ph. Kotsybar

    Catch the forming stars inside dark matter pockets

    you’ve conjectured cleverly.

    Watch the forming stars inside dark matter pockets.

    Save them from dark energy


    Empiricists may tap you on the shoulder

    and ask for proof.

    You’ll just have to bluster a bit bolder

    then turn away remaining aloof.


    Catch the forming stars inside dark matter pockets

    you’ve assumed math’matic’ly.

    Watch the forming stars inside dark matter pockets.

    Talk about dark synergy.


    Then when detractors start a multiplyin’,

    an’ they just might,

    it’s easy to forget them without tryin’

    with just your nose held firmly upright.


    Catch the forming stars inside dark matter pockets

    you’ve posited cleverly.

    Watch the forming stars inside dark matter pockets.

    Save them from dark energy


    Save them from dark energy.

    (Save them from dark energy)


    Apologies to Perry Como.