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Questions related to CMB

  1. Jul 8, 2008 #1


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    While I think I understand the general principle behind CMB and blackbody radiation, I am trying to understand whether it directly supports the current assumptions about age and size of the universe. Therefore, I was hoping that some members of this forum might be able to clarify what basic implications are being drawn from the Cosmologic Microwave Background (CMB) in respect to verifying the current accepted cosmological model. Apologises for the number of initial questions, but it was difficult to separate out the dependencies of the issues. For this reason I have numbered the questions so each may be addressed separately. Would appreciate any clarification of any issue.

    1) As I understand the issue, we can measure the energy of CMB across its wavelength distribution, i.e. a black body distribution. The essence of the Penzias and Wilson discovery, in 1965, being that this distribution has a peak at a wavelength corresponding to 1.869mm in the microwave spectrum?

    2) Is this peak wavelength then used to calculate the much-quoted CMB temperature of 2.7K via Wien’s Law?

    From my reading of the accepted cosmological model, the CMB is said to be associated with the decoupling of photons and normal matter. This being a point in the expansion of the universe where the temperature falls below 3000K some 379,000 years after the Big Bang. Again, as I have understood this process, this is a temperature below which photons no longer have the energy to maintain the ionisation of hydrogen as a plasma. What surprised me was the apparent accuracy of the time this is said to have taken place.

    3) Presumably, based on Planck equation E=hf, you can work out the frequency-wavelength of photons that would have enough energy to maintain the plasma state from which I am assuming you can also determine the temperature, e.g. 3000K. However, I don’t understand how this tells you anything about how long ago it took place?

    4) As a general statement, is it true that basic age and size estimates are still essentially based on the Friedmann equation, allied with the Fluid and Acceleration equations, inserting the measurement of the Hubble constant (H) and the current homogeneous density of the universe?

    5) If so, is it fair to say that CMB is useful as a verification data point, but does not directly confirm the age or size of the universe?
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  3. Jul 8, 2008 #2


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    I think you've got a reasonable summary there. The CMB doesn't directly tell you the age of the Universe. The age is something that you can derive based on, as you say, the Friedmann equation where a number of parameters in this equation are set via observations, including observations of the CMB. However, the CMB alone leaves a lot of freedom in the parameters such that the age of the Universe is not well constrained by knowledge of the CMB alone.
  4. Jul 8, 2008 #3


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    Response to #2

    Thanks very much for the feedback, but could I just push a little on the issue of the age of the universe. There appears to be no shortage of models in cosmology, e.g. Friedmann, de Sitter, Robertson-Walker etc. However, it is quite difficult for newcomers to the subject, like myself, to judge what is substantiated fact, what is assumption and what is pure speculation.

    The basic Friedmann equations, inclusive of the Fluid and Acceleration equations, model an expanding universe, which appears to be supported by redshift observations. Reversing the concept of expansion leads to the hypothesis/theory of a finite universe in both size and age. One of the key inputs to these equations appears to be the Hubble Constant [H]. It is understood that the value of [H=71km/s/Mpc] is based on redshift [z] observations, which were originally interpreted as recessional velocity [v=zc] by multiplying [z] by the speed of light [c], but now subject to relativistic corrections.

    Given that the units of [H] simplify to 1/seconds, the inverse of [H] often appears to be directly interpreted as the age of the universe, i.e. ~13.5 billion years. This figure seems to be in general use, but the solution of the Acceleration equation for dust/matter suggests that H=2/3t would be a more accurate solution, i.e. 9 billion years. If the radiation domination in the earlier universe is factored in, this becomes H=1/2t. It is assumed that the inclusion of an inflation era would only reduce the age of the present universe even further.

    So is there a generally accepted age of the universe?
    What arguments support its estimate?

    What is not clear to me about any of the estimates is that they seem to be predicated on running a rate of expansion back from what we understand about the current homogeneous matter-density of the universe, e.g. 9.82E-27. However, many sources cite this to only represent 4% of the total energy-density of the universe. Given the level of speculation about dark matter, dark energy etc, the actual energy/matter density seems open to questioning along with the exact rate of expansion at any point in time.

    Again, thanks for the help
  5. Jul 8, 2008 #4


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    Re: Response to #2

    First things first. If you are after 'substantiated fact' then there are two options, to not study science, or alternatively, stop watching CSI and study science! What I'm trying to say is that science is not the black and white, evidence never lies, infallible tome of wisdom that shows like that and bad pop sci put out there. On the contrary, science is about determining the most likely hypothesis and trying to work out the degree of certainty in this best bet model. But this certainty is never complete, the best theory is only ever one experiment away from falsification.

    So cosmology, like all science contains some amount of assumptions, speculation and evidence. But it is wrong to think that these are pejorative terms. Anyway enough of my psedo-philosophical babble...

    The Friedmann model is a model and is thought to do a very good job of describing the history of the Universe back many Billions of years. However it is a common fallacy (very very common in fact) to incorrectly wind this model back to where the a(t) factor goes to zero. This is the very region where we know in advance our model will not work, since we know that Relativity and Quantum mechanics do not play nice, and it is the region where the two overlap (where gravity becomes as strong as the other forces on small scales) that we know the Friedmann model, a solution of GR, is sure to be incorrect.

    Therefore the Friedmann model does not say that the Universe has a finite age. Once we go far enough back in time our model, as it currently stands, out model gives no meaningful results. Much work is going into improving this with a true quantum gravity theory, but at the moment there are no clear leading theories in that area.

    The age ~ 1/H thing is actually a co-incidence. As you say the exact relationship depends on the energy content of the Universe. Put another way, in the past the age ~ 1/H relationship did not hold, and it won't in the future. The current model of the Universe has an initial matter dominated phase followed by the cosmological constant or dark energy dominated phase. In this model, there is no simple relationship between age and 1/H.

    Yes, ~13-14 Billion years. This comes from the model I described above. It is supported by the fact that the model works to fit the known data, and that is the age that results from the model.

    Yes, everything is always open to questioning. The evidence suggests that dark matter and dark energy exist. Very possibly there is an alternative explanation where different laws of physics, rather than new energy components, explain the data. At present no such model does a better job than dark matter and dark energy, but that can always change.

    Remember that the figure that 'normal' matter makes up 4% of the Universe today is a derived result from the current model. In a different model, this figure could be 100% or some other fraction. It is not a direct measurement.

    Edit: Just to be clear, when cosmologist talk about the 'age of the Universe' it is understood to mean 'the amount of time elapsed since the most distance time that we can understand', which is basically the inflation period. Like a lot of confusing terminology in cosmology, there is a big fat asterix missing every time the phrase 'age of the Universe' is used. Professional cosmologist know this, but as always they, and the authors of a lot of pop sci, get sloppy on this point when it comes to the general public.
    Last edited: Jul 8, 2008
  6. Jul 8, 2008 #5


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    Response to #4

    It was not my intention to trigger a philosophical debate about the nature of science or appear to question the integrity of the cosmological model. I believe the nature of my questions were in the context of trying to `study science`, although I have been known to watch a few episodes of CSI. However, as a beginner to this subject, it does not seem unreasonable to question even accepted tenets or assumptions. Clearly, you have a broad understanding of this subject, which probably gives you an intuitive understanding of where and when the limits of inference about any given statement must be drawn. However, for anybody new to this subject, it is often quite difficult to determine the degree of speculation attached to many of the statements being made.

    I agree. In part, this was why I was questioning the accuracy being put of the point of decoupling at 379,000 years after the Big Bang.

    This seems a very honest statement about the state of play. However, I would venture that this is not generally understood by non-experts given the near certainty that seems to be expressed about events in the first second of the Big Bang in many publications. Of course, the range of opposing opinion on the Internet only compounds this situation, which is why I came to a respected forum for some answers.

    Slightly confused by this statement and your earlier statement about the model not saying the universe has a finite age. I would appreciate any pointers to publications that explain exactly how this accepted figure is derived.

    Thanks for the footnote. However, I thought the standard model positions inflation within the first 10E-35 seconds of the Big Bang? If so, wouldn’t the margin of error on the age of the universe be pretty small? Of course, it is possible that there is a distinction between what happens in the first second and how long ago this second happen?
  7. Jul 8, 2008 #6


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    Re: Response to #4

    Apologies, I do get carried away sometimes! My remarks were intended to be fairly flippant, so I hope you don't take me too seriously! Anyway, yes hopefully I can help sort out what we are reasonably sure of and what we are just guessing at at present.

    The Friedmann model still works well (we think) at this epoch, so we really do think we know this quite accurately. Before I go on though, I should make something clear. Perhaps I am guilty of sloppy terminology myself in my last post, so let me define some things more clearly.

    The term 'after the Big Bang' is inherently problematic. This is why, contrary to pop sci, cosmologists actually define t=0 to be today. Then we work backwards in time, so things happened a certain amount of time in the past, rather than working forwards, how long after the Big Bang did something happen. This is because the point where a(t) goes to zero, at the pop-sci t=0, the model has ceased to work. Therefore all statements referring to how long something occured from 'the Big Bang' use this definition of 'when' the Big Bang happened. However, as I've said before we don't know what happened in the period where a(t) is less than some small amount. Therefore this 'Big Bang' time is a prediction of a model that we know is wrong on some level. The total time elapsed since this time is taken to be 'the age of the Universe' but that doesn't actually imply that the Universe is actually finite, or even that it is really that old. I know it's very confusing, but as I say, there is a lot of sloppy terminology to get over.

    So for decoupling, we have a very good idea of how long ago from now it occurred. That is probably the safest way of saying it. The model doesn't break down until the Universe is much denser than it was at decoupling.

    Again, I'm sorry that this is confusing. We do have a great deal of certainty about what happened when the Universe was very very dense, at a time only fractions of a second less far back in time that the time when a(t) is zero. So what you have read may well be correct, as Obi Wan would say "from a certain point of view". Going backwards in time we can say with reasonable certainty what happened up until 14ish Billion years ago. At some point the Universe is very very dense and our theories (built from observations) don't know how to describe this state, so we stop there (at the moment). If we take the theory and just go back the tiniest fraction of a second further in time we find that a(t) has gone to zero. We could therefore claim our theory predicted this a(t)=0 point, however this would be wrong, since the reason we stopped before going to this point is that we know our theories cannot accurately describe any time further back than this. Many people are working on improving the theories, but this is how things stand at present.

    So when you here someone talk about 'the first second after the Big Bang', what they are really saying (most of the time) is the first second after the most distant time in the past that we understand the history of the Universe. Sorry I think I'm rambling a bit, is this making sense?

    Again, sorry for the confusion. This 'age' is, as I say, the total time the model predicts between now and when a(t)=0 in the past. It is almost identical to the length of the history of the Universe that we understand. Despite its name, the Universe may not actually be that old, again the big fat asterix that should be there is not, cosmologists know it is but it is seldom make it clear to the general public unfortunately. This is not a failing of the theory in any way, all it says is that the total age of the Universe in the most literal sense is not something modern cosmology has anything to say about (yet).

    As for references, it is a matter of integrating the Friedmann equations. Any standard cosmological textbook will have it, otherwise see http://arxiv.org/abs/astro-ph/9905116" [Broken] great primer on cosmology. See page 8 for 'look back time'. The 'age' of the Universe is defined as the look back time until a(t)=0. This is perfectly well defined in the model, so it can be calculated. Observations are used to set the values of the parameters in the equations in that section.

    Right, so inflation happens very near in time to where the model has a(t)=0. In terms of the way you put it in the last sentence there, we have a very good idea of how long ago from today inflation occurred and we have a reasonable idea of what occurred in the second following that. What we don't know is what happened in the time before inflation. The model predicts the Universe has zero volume a very short time before this, but we know that the model doesn't work any further back in time. So we don't know. Maybe the Universe did begin at some time, but it was maybe a few seconds further back in time than the model predicts. Maybe the Universe existed for a very long time in that very dense state and for some reason suddenly inflated. Any number of possible things might have happened. At this point we don't know, but that doesn't diminish the achievements of finding out what we do know about a good 14 Billion years of the Universes history.

    It comes down to 'The Big Bang' being a very bad name for the theory of modern cosmology. The Big Bang theory just says the Universe was hotter and denser in the past, not neccessarily that there really was a moment of creation where the Universe went Bang!
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  8. Jul 9, 2008 #7


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    Response to #6

    Wallace, I very much appreciated both the content and spirit of your reply. In particular the reference to the paper by David Hogg appears to be very useful, although I have only had time to briefly skim the details.

    No problem. I am fairly new to this branch of the forum and appreciate that some of my questions may seem naïve to those who have spent a great deal more time reading into the details. I also realise that it may seem that I am trying to challenge some of the foundations of the accepted model of cosmology, which is not surprising, because I guess I am. However, it is being done in a spirit of study in order to determine what is supported fact and what is speculative hypothesis. Before going any further, I accept that I need to timeout on my questions and go away and read a few more books/articles. However, I wanted to use this opportunity to, at least, table a few `expansive’ issues for future reference. These issues all centre on the science that supports the accuracy of the assumed expansion of the universe, which then allows an estimate of its age.

    OK, but presumably whether you work forwards or backwards, cosmology needs to justify its timeline of expansion or contraction, depending your direction of time, on some physical process that drives a(t). So let me outline some of my assumptions for clarification using your backward flow of time:

    1) Today, we basically determine the Hubble constant (H=71km/s/mpc) based on redshift measurements. The units of (H) correspond to 1/t, which in some quarters was, and still seems to be, interpreted as the age of the universe, e.g. 13.5 billion years?

    2) However, the expansion rate has to be qualified by the nature of the energy/mass density of the universe as a function of time. In a matter dominant universe, the correlation of (H) and (t) changes to (H=2/3t), while in a radiation dominated universe (H=1/2t). Both of these factors would suggest the universe is younger than 13.5 billion years?

    3) Not sure about this point, but currently assuming that decoupling would be associated with the phase transition from a radiation-to-matter dominated universe. If so, do cosmologist define this time, from the current epoch, using (H=2/3t) to create the density that generates the temperature (3000K) of the phase transition as an adiabatic thermodynamic process associated with CMB?

    If these assumptions are correct, does it explain why some sources may quote very accurate timeframes for this phase transition, e.g. 379,000 years after BB? However, the problem that I had with the accuracy of this figure was based on what appears to be an incomplete understanding of the real energy-matter density of the universe. There is a widely quoted breakdown of density along the lines of:

    o 4% Matter
    o 21% Cold Dark Matter
    o 75% Dark Energy

    Given that we have no direct verification of the last 2 forms of energy-matter, doesn’t this put any estimate of any rate of expansion a(t) on rather a speculative footing? In light of these questions, the seemingly opposing statements in the following quotes confused me:

    Now the Friedmann equation, along with its fluid and acceleration counterparts, seem to give 2 solution of H(t) based on the radiation-matter dominance within the universe. Based on my earlier assumptions, which may be wrong, (H=2/3t) gets us back to approximate 400,000 years after the BB. Presumably, in a radiation-dominated earlier universe, the assumptions would be that the expansion would be more closely associated with (H=1/2t)?

    However, to be honest, I am unclear what accepted assumptions cosmology is using beyond the matter-dominant era to determine the expansion-contraction rate back to towards even earlier times? For, without accurately knowing how the expansion rate a(t) is defined for the earlier universe, it is difficult to see how the timeline is being verified. By way of reference, here are some main milestones and associated timeframe within the earlier universe that are quoted in many cosmology papers:

    o Matter-Dominance: +100 million Years
    o Decoupling: +300,000 years
    1. Nucleosynthesis: 1-180 seconds
    2. Inflation: ~10E-35 seconds
    3. Baryogenesis: 10E-35 seconds
    4. Planck: 10E-43 seconds

    Again, it is highlighted that these papers seem to be very precise about the timeline, which must lead many to believe that expansion a(t) must be very accurately known. What I would like to understand is the value of a(t) for each of these milestones and how they were determined:

    1) So if we work back from ‘decoupling’, we get to ‘Nucleosynthesis’ at which temperatures are so high (+billion degrees) even the proton/neutron nucleus is unstable. Presumably cosmologists depend of particle/nuclear physicists for the data points underpinning a(t) in this era?

    2) As I understand it,` inflation` is a general term for models of the very early Universe, which involve a short period of extremely rapid, i.e. exponential, expansion in which the universe may have grown by ~2^100, i.e. from about 10E-35m to 10cms in something of the order 10E-32 of a second. Not sure whether anybody really understands how this could of happen, i.e. what is the physics of inflation?

    3) `Baryogenesis` is the name given to a process in which the balance between matter and anti-matter was resolved in the very early universe. Baryogenesis suggest that for every billion antiparticles created, 1 billion and 1 normal particles are created, which are then all effectively converted back into energy through the process of particle-antiparticle annihilation leaving a net-gain of only 1 matter particle per billion pair particles. Would this imply that matter-density is less than 1/billionth of the energy-density? As far as it is understood, there are several hypotheses that try to explain the asymmetry of baryogenesis, but no solid theories.

    4) Finally, the universe disappears behind the Planck horizon

    So, not surprisingly, I don’t understand how the much used figure of 13.7 billion years has been derived, especially its quoted accuracy of plus/minus 120 million years, e.g. http://en.wikipedia.org/wiki/Age_of_the_universe. Equally, as one final philosophical question, I might query by what frame of reference could time even be measured in the earlier universe?

    P.S. Apologises for excessive length of this posting, but as stated, just wanted to table my thoughts. However, would still be interested in any knowledge insights on any points raised. Thanks.
  9. Jul 9, 2008 #8
    Re: Response to #6

    Hi Mysearch,

    You have touched on a very interesting observation here! If 1 matter particle survived for every billion of the particle-antiparticle pairs that annihilated then for every particle that we observe there should be two billion photons. That means the energy density of the universe is two billion times what the visible mass density suggests. As you know, the scale factor for a radiation dominated universe scales as a(t) = (t/to)^(1/2) compared to a(t) = (t/to)^(2/3) for a mass dominated universe. In other words the gravitational curvature is stronger for energy in the form of radiation compared to that of the equivalent amount of energy in the form of mass. If there is so much excess annihilation energy in the universe then the current models are off by a factor of a few billion or the excess energy simply does not exist in serious contrast to CP violation theories. On the other hand, models that suggest dark energy is due to vacuum energy suggest the accelerating expansion of the universe should be billions of time greater than is observered. Maybe the lost excess energy of CP violation and the unaccounted excess vacuum energy (over and above the observed dark energy) cancel each other out?
  10. Jul 10, 2008 #9


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    Re: Response to #6

    Yes it is a great little paper with a very low mass to light ratio!

    There are no quarters I know of that use 1/H as the age of the Universe. As I've said, for our Universe this happens to hold at the present epoch, but that is a co-incidence, not a general rule. It is not calculated in this way at all.

    Again, the 2/3 and 1/2 factors you are quoting are this kind of thing you see in textbooks as example solutions to the Friedmann equations. That are not actually used anywhere when considering the real Universe. In the case where there are multiple energy components their is no simple formula in general and the equations and usually solved numerically for the parameters that best fit the data.

    As above, it is not as simple as that, you need to consider a Universe with matter and radiation, not one or the other.

    Those figures are what the data tells us. There are basically two options, the 'speculative' energy components really exist, or GR is wrong. In the case of the first then the timeline we have is accurate. In the case of the second then we have no idea what the real theory of gravity is.

    Why are these statements opposing? They seem to be in agreement to me?

    Again, it simply isn't that simple. There is just one solution, for a universe containing matter, radiation and dark energy, not multiple solutions.

    The timeline depends on the physics that dominates at various densities. We know the laws of physics for a wide range of densities, hence we can plug this into the GR equations and get the above results (in practice this is harder than my one sentence explanation suggests, but that is the principle). What we know reasonably well is that however long ago from today inflation occurred, the 400,000 years after that follow the timeline you spelled out above. Then the +/- 120 million years accuracy comes in precisely how far into the past this all started, and that uncertainty comes basically from uncertainty in the Hubble parameter today, matter density today etc.

    We can only 'see' as far back as decoupling, so we don't need to worry about timing references in the early universe. We just model the physical processes that must have taken place.
  11. Jul 10, 2008 #10


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    Regarding the age coincidence of t = 1/H, I have made numerical calculations that show what parameters lead to such a coincidence, being the standard model of cosmology one among others. Some details here.
  12. Jul 10, 2008 #11


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    Response to #8

    Hi Kev,

    While I am not really in a position comment much further on your question, it might be worth highlighting that quantum theory appears to suggest that the singularity may have been formed as a quantum bubble that had no net-energy. In this context, the conservation of energy would appear as an accounting ledger in which positive and negative energy have to be balanced. While not a part of any accepted standard theory, which I know of, some have speculated on a process leading to a net-zero energy universe.

    Could I point you to comments in #9 from Wallace, who has been patiently trying to answer some of my questions on such issues. I will be responding directly to these comments in my next posting.

    On what basis do you draw this conclusion? The implication of H=1/2t (radiation) as opposed to H=2/3t (matter) seems to suggest that the universe would have expanded faster in a radiation-dominated universe than a matter-dominated universe. While radiation, e.g. photons, may have an equivalent kinetic mass by virtue of E=hf=mc^2, hence small gravitational field, I am not sure of your 1-to-1 comparison. I understand that there might be 1-2 billion photons per hydrogen atom, but unsure how this leads to a stronger overall gravitational curvature? Is it a function of time?
  13. Jul 10, 2008 #12


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    Response to #9

    Wallace, again many thanks for taking the trouble to answer some of my questions. Overall, I get the general impression that you are trying to tell me that I working on a too simplistic view of the current cosmological model. I take no offence at this implication, as it is more than likely to be true. The difficulty I am having is trying to ascertain some key snippets of information that would help me formulate an overview of a more up-to-date model. Anybody trying to come up to speed on this subject presumably either ends up reading what you have termed ‘pop-sci` articles, which while summarising the state-of-play don’t usually justify the evidence of their conclusions. On the other hand, more serious cosmology articles tend to focus on explicit details, in great depth, which is often difficult to piece together as a composite overview justifying the current model. Therefore, if anybody could recommend an article/book, which is generally accepted to explain (and justify) the key assumptions of the current model I would really appreciate it. Thanks

    I fully accept your statement, but was simply implying that some references still give the suggestion that 1/H is an estimate of the age of universe. What I have yet to understand is the exact method being used that gives rise to the accepted figure, which by coincidence, is comparable to 1/H. I note the Hellfire (#10) has provided some references to data that may answer my question, but I have not, as yet, had a chance to examine this information in detail. Are there any overview papers that would act as an introduction to this specific aspect of cosmology?

    Again, while I accept your statement, is there any estimate of the margin of error when using the Friedmann equations as an approximation? Is the implication of this model totally incorrect?

    Accepted, but again would say that most models attempt to simplify the real complexity. Therefore, would again be interested to know the margin of error associated with this phase transition approach.

    While I am not in a position to argue, at this stage, given the current level of debate that surrounds the existence of dark matter and energy, one might assume that the issues were not necessarily as black and white as implied.

    I assume the ‘seeing’ reference refers to the opaqueness of the universe prior to decoupling. However, wasn’t sure what you meant by ‘we don't need to worry about timing reference’?

    Anyway, thanks again for all the feedback.
  14. Jul 10, 2008 #13


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    Response to #10

    Hellfire, thanks for the reference and, in fact, the entire thread entitled ‘Cosmological Coincidences’ appears to be very useful. I will try to read the entire thread before raising any more questions, as I noticed that Wallace has also made contributions to this thread. There was also a reference to a paper about the age of the universe in `Garth #41`, which may/may not answer some of my questions

    As a general question, has anybody read the paper by a Prof Melia, which suggests that the universe might be 16.9 billions old? Just wondered if there was any consensus about the validity of this idea within the forum?

    The paper was cited in the poll about a black hole universe raised by Marcus.
    See posts #3 & #5
  15. Jul 10, 2008 #14


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    By the way, it is remarkable that the standard model of cosmology is the only flat model that fulfills this condition, and that the coincidence is better than 1%.
  16. Jul 10, 2008 #15


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    Footnote to #11

    Just by way of a quick footnote to Hellfire's link in #10. The pointer to the thread `Cosmological Coincidences’ was just what I was looking plus provides further links to many other discussions, websites and articles, which should keep me busy for a while.:rolleyes: https://www.physicsforums.com/showthread.php?p=1772161

    As a newcomer to this subject, and this forum, I was looking for information from a reliable source. However, after doing a few random searches I simply started my own thread to ask some questions about the standard model and was grateful for the help received. Now I don’t know :confused: if there is an index of key discussion threads for ‘newbies’ to reference and I just missed it, but it might be a useful feature and would probably stop a lot of repetition of questions, like mine:redface:

    I particular like the implications associated with the comment in #43 of a secondary thread entitled ‘Critique of Mainstream Cosmology’::smile:

  17. Jul 10, 2008 #16
    What does your integral predict for:

    Omega (total)
    Omega (mass)
    Omega (dark energy)
    Hubble parameter

    when the universe is twice its current age?

    I guess in 14 billion years time we will no for sure if the universe expansion is accelerating or not. The current model suggests that the universe will no longer appear to be flat and we will be heading for the big rip. My prediction is that universe will still appear flat and that flatness is an inherent property of the universe a bit like charge neutrality of the universe is an inherent property. Is it just coincidence that the number of electrons in the universe matches the number of protons? I don't think so.
  18. Jul 10, 2008 #17


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    A flat model remains always flat. With parameters [itex]\Omega_m = 0.27[/itex], [itex]\Omega_{\Lambda} = 0.73[/itex] and [itex]H = 71[/itex], the values at an age of about 27,500 billion years (twice the current age) are: [itex]\Omega_m = 0.02[/itex], [itex]\Omega_{\Lambda} = 0.98[/itex] and [itex]H = 61[/itex]. In that epoch we would not have a coincidence anymore. Moreover, this model does not lead to a big-rip (diverging scale factor) but to a phase of steady exponential expansion (de-Sitter) with dominating cosmological constant ([itex]\Omega_{\Lambda} = 1[/itex]).
    Last edited: Jul 10, 2008
  19. Jul 11, 2008 #18


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    Response to #17

    By way of a few general questions:

    1. Are the figures presented in #17 an extrapolation of a current accepted model?

    2. Is this model [itex]\lambda[/itex]-CDM or some other major contender?

    3. The reason I asked is because the value of H appears to fall from 71 to 61 and I thought there was some evidence that the rate of expansion was said to be increasing, at least, with respect to some recent observations?

    4. Do you know if anybody has posted a plot of H against Time on the net?

    5. Finally, is there any consensus of whether the ultimate fate of the universe is open, closed or flat?
  20. Jul 11, 2008 #19


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    Re: Response to #17

    These are the result of using the Friedmann equations taking as "initial" conditions the Omega and H values for today.

    Yes, this is the [itex]\Lambda[/itex]-CDM, that assumes [itex]\Omega_m = 0.27[/itex], [itex]\Omega_{\Lambda} = 0.73[/itex] and [itex]H = 71[/itex] for today.

    Increasing rate of expansion means a positive second derivative of the scale factor [itex]\ddot a > 0[/itex]. The Hubble parameter is defined as [itex]H = \dot a / a[/itex]. In a flat model without phantom energy (big-rip scenarios) the Hubble parameter will always decrease, or stay constant if the cosmological constant dominates ([itex]\Omega_{\Lambda} = 1[/itex]).

    The Hubble parameter for that model varies with the scale factor [itex]a[/itex] as:

    [tex]H = \frac{71}{a} \sqrt{\frac{0.27}{a} + 0.73 \, a^2}[/tex]

    The variation of the scale factor with time is not analytic. You can find some values with my cosmological calculator.

    Flat, open or closed are terms that refer to the geometry of space. A unique relation between geometry and fate is only given for models without dark energy or cosmological constant. With dark energy it is possible for example that a closed universe expands forever.
  21. Jul 12, 2008 #20


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    Hellfire, many thanks for the helpful and informative response to the the questions raised. Much appreciated.
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