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Comparison of the Mainstream and the Self Creation Freely Coasting models

  1. Jun 13, 2005 #1

    Garth

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    SpaceTiger has created a very valuable thread on Mainstream Cosmology. For good scientific practice it is important to compare standard theories with testable alternatives, however ST's thread is not the place to do it. The theory of Self Creation Cosmology (SCC) presents itself as such a testable alternative theory and there are several posts about it on these forums. However, sometimes my posts have been taken as an intrusion, therefore I have started this new thread for a specific discussion on both the SCC and the Freely Coasting models. In so doing, I am looking for critical analysis as well as general comments about that comparison and I have been grateful for all the reasoned criticism posted so far.

    Introduction

    The Freely Coasting model is an empirical model, proposed by a team at the University of Delhi, in which the universe expands strictly linearly with time R[t] ~ t. Its motivation was the realisation that such a model would not require inflation to explain the horizon, flatness or smoothness problems of GR as they would not exist in the first place. It was then realised that the model was surprisingly concordant with cosmological constraints without the further addition of concepts such as DM or DE that remain undiscovered in laboratory physics. There have been several papers published and PhD’s gained exploring this alternative cosmological paradigm, viz: A coasting cosmology
    Freely Coasting Cosmology
    A Concordant “Freely Coasting” Cosmology
    A case for nucleosynthesis in slowly evolving models
    Nucleosynthesis in a Simmering Universe and a PhD thesis available on the physics ArXiv:
    GRAVITATIONAL LENSING IN STANDARD AND ALTERNATIVE COSMOLOGIES
    However the shortfall of this concordant empirical theory is that it requires a mechanism to deliver the strict linear expansion.

    Independently from the Indian team’s work I have been developing an alternative gravitational theory, SCC, that modifies GR to include a ‘non-minimally connected scalar field’. I have published seven papers and eprints, viz:
    The original paper, Barber, G.A. : 1982, Gen Relativ Gravit. 14, 117. 'On Two Self Creation Cosmologies'.
    'A New Self Creation Cosmology, a 'semi-metric' theory of gravitation' , Astrophysics and Space Science 282: 683–730, (2002)
    but the new theory can be recovered in five electronic pr/eprints that followed;
    Self Creation Cosmology - An Alternative Gravitational Theory to be published in "Progress in General Relativity and Quantum Cosmology. " Nova Science Publishers, Inc. New York.
    The Self Creation challenge to the cosmological concordance model
    The derivation of the coupling constant in the new Self Creation Cosmology
    Experimental tests of the New Self Creation Cosmology and a heterodox prediction for Gravity Probe B
    and
    The Principles of Self Creation Cosmology and its Comparison with General Relativity
    There have also been 47 other author citations in peer-reviewed journals.

    The SCC scalar field follows that in the theory of Brans Dicke (BD) and is coupled to the distribution of matter in motion in the universe in order to fully incorporate Mach’s Principle. SCC modifies BD in that it allows the scalar field to act on particles and thus violates the equivalence principle. The presence of the scalar field in BD and SCC perturbs space-time. This is the reason BD is not concordant with solar system experiments. However in SCC the scalar field force operates on particles, but not photons, and corrects this perturbation. The geodesics of test particles and photons are the same in SCC as GR. SCC is concordant with all experiments to date, however there are several tests that easily falsify the theory. One of these is being carried out at present, the Gravity Probe B satellite experiment, and the results will be known next year.

    It has two conformal frames of measurement, the Jordan frame in which particle masses increase with gravitational potential energy and in which gravitational trajectories and cosmological evolution are calculated, and the Einstein frame in which particle masss are constant and in which other physics is most easily described.

    When the Jordan frame cosmological solution, (which turns out to be the same as Einstein's original cylindrical static model) is transformed into the SCC Einstein frame it turns out to be a strictly linearly expanding solution - that is it provides the linear expansion mechanism for the "Freely Coasting" model.

    More to come...

    Garth
     
    Last edited: Jun 13, 2005
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  3. Jun 13, 2005 #2

    Garth

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    Taking up the lead from my post #66 on ST's “Review of Mainstream Cosmology” thread I here compare time-lines between the standard model, R(t) ~ t2/3, and the SCC model R(t) ~ t.

    The look back time tl as a function of red shift z is given by:
    In GR
    tl/tH = (2/3)(1 - 1/(1 + z)3/2)
    In SCC
    tl/tH = (1 - 1/(1 + z))



    With tH = 10.2/h Gyrs.
    WMAP determines h = 0.72 so tH = 14.2 Gys.
    and the age of the universe = 2/3tH = 9.44 Gyrs. in GR
    and the age of the universe = 14.2 Gyrs. in SCC.

    Using tz=x to be the age of an object now observed at a red shift x we have:

    For "re-combination" - the surface of last scattering of the CMB, z = 1000,
    tz=1000 = 300,000 yrs. in GR
    tz=1000 = 14.2 Myrs. in SCC

    for the onset of metallicity, i.e. Pop III stars, z = 20
    tz=20 = 100 Myrs. in GR
    tz=20 = 676 Myrs. in SCC

    for quasar 'ignition' z = 8
    tz=8 = 350 Myrs. in GR
    tz=8 = 1.58 Gyrs. in SCC

    for 'modern' metallicity in Quasar SDSS J1030+0524 z = 6.28
    tz=6.28 = 480 Myrs. in GR
    tz=6.28 = 1.95 Gyrs. in SCC.

    The comparison shows that there is considerably more time for the development of Pop III stars, Quasars and early metallicity than in the mainstream model.

    The longer nucleosynthesis period results in a baryonic density of over 20% closure density and a primordial metallicity 108 times that of GR primordial metallicity.

    The problem with the SCC model is there would be no primordial deuterium and the observed D has to be produced by another process such as spallation. (See Deuterium production by high-energy particles )

    Garth
     
    Last edited: Jun 13, 2005
  4. Jun 13, 2005 #3

    pervect

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    I think there may be some problems with using the "matter dominated" formula for lookback times for standard cosmology.

    A quick web search turned up

    http://home.att.net/~numericana/answer/cosmos.htm#lookback

    which has the cautionary note

    "If the Universe was indeed dominated by ordinary matter, it would be younger than the oldest stars in it !"

    However, while this web page quotes two different simple lookback formulas, I didn't find anything like as a "standard" lookback formula. I think Ned Wright's javascript calculator could be useful here

    http://www.astro.ucla.edu/~wright/CosmoCalc.html

    However, I couldn't quite follow his posted derivation of the formulas
     
  5. Jun 13, 2005 #4

    Garth

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    [As I said] [Edit: This addition was lost in transmission!] The lookback time can be extended into the past by cosmological acceleration.

    However I was using the formula primarily to derive a time-line from the beginning t = 0. Here the problem is whether there was enough time in the standard model for evolved objects to form and produce metallicity.

    The point being, of course, is to compare that with the greater times available in SCC.

    Note as well, that while the SCC/freely coasting model does not have acceleration, it has an age for the universe that is comfortable with the ages of the oldest stars and globular clusters.

    In this respect this model is more concordant with observation than the standard model.

    Garth
     
    Last edited: Jun 14, 2005
  6. Jun 14, 2005 #5

    Chronos

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    Garth, does your model include a big bang, or is it a steady state thing? I forget [I'm old and should take notes].
     
  7. Jun 14, 2005 #6

    Garth

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    Expansion

    i) Expansion

    Hi Chronos! Thank you for your question.
    This question is answered by first asking: "How do we measure the universe 'out there' with standards of measurement defined in a laboratory 'down here'?" :-
    a. What standard do you use?
    b. How do you transport that standard measurement to the far ends of the universe in order to make the comparison, what conservation principle does it depend on?

    In GR the principle of equivalence requires atomic masses to be constant, so by they are defined to be so when that principle is applied to our understanding of physical observations. Consequently, atoms are adopted as an appropriate basis of making measurements of mass, length and time. That is, the size of the atom determines the length of the ruler, and the frequency of atomic processes determines the 'rate' of the clock. [Here I am talking about the rate of an atomic process in a distant quasar/galaxy being compared with that of the same process here on Earth.]

    The atom, in a gedanken experiment, is to be physically transported across the universe and assumed to retain its properties unchanged. However we may ask, what if the mass actually does increase, either with cosmological age, or say, with potential energy as it is raised in a gravitational field? Einstein pondered this and concluded that if the rest mass of an atom did increase with altitude (PE) then that would also apply to the standard kilogram as well. To make a comparison the two masses would have to be brought together and an increase would not be detected; therefore, he concluded, they can be safely thought of as constant.

    Constant atomic mass also applies in the SCC Einstein conformal frame. In this frame the universe expands strictly linearly from a Big Bang, it is a Freely Coasting theory.

    However we do not actually transport clocks and rulers across the universe, instead we have to rely on observation of photons that have come from those nether regions, and photons suffer cosmological red shift.

    In the Jordan conformal frame of SCC atomic masses are defined to vary with gravitational potential energy: energy is locally conserved,
    m = m0exp[Phi]
    where Phi is the dimensionless Newtonian gravitational potential.

    In this frame of SCC the principle of the Local Conservation of Energy as measured in the preferred Machian frame of the Centre of Mass (Centroid) requires photons to be of constant energy, so by they are defined to be so when that principle is applied to interpret astronomical data here on Earth. In this frame photons become the standard measure of mass (their energy) length (their wavelength) and time (the inverse of their frequency).

    In this frame, as energy is locally conserved, gravitational and cosmological red shifts are interpreted as a gain of energy (mass) by the apparatus rather than a loss of energy by the photon.

    Gravitational orbits and cosmological evolution have to be calculated in this frame and it is found that:
    a. trajectories of test particles are identical with the GR geodesics in vacuo. SCC is concordant with the GR experimental tests to date.
    b. as (CMB) photons ‘expand with the universe’ (in GR as well as SCC) the universe, as measured by those photons, is static and eternal. (The ‘frequency’ of a CMB photon tends to infinity as t tends to zero)
    c. it also works out that the universe is spatially spherical and therefore closed. The SCC Jordan frame universe is Einstein’s original static cylindrical model!

    Therefore summing up, in answer to your question. Choose the appropriate conformal frame to analyse a situation.
    1. The Einstein frame for nuclear processes, stellar formation and evolution etc. In this frame the universe is a linearly expanding big bang universe.
    2. The Jordan frame for gravitational orbits and cosmological evolution. In this frame the universe is Einstein's static cylindrical universe.
    It depends on how you look at it and how you measure it.

    We can compare this with SpaceTiger's Review of Mainstream Cosmology thread:
    Note: The Jordan frame of SCC is the opposite of a 'Tired Light' theory, photons retain their energy, it is the apparatus that gains mass with cosmological time.

    I hope this helps, do cross-examine me!

    Garth
     
    Last edited: Jun 14, 2005
  8. Jun 14, 2005 #7

    Garth

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    2. The Big Bang Theory

    From 'Review of Mainstream Cosmology".
    How does SCC compare with this excellent summary of the standard theory 'Big Bang'?

    Again the question is: “If the universe is expanding how do you measure it? For example does the 'ruler' expand with the universe?"

    In the SCC Einstein frame the atomic ruler has fixed length and the universe expands around it. Gravitational red shift is Doppler in nature and nucleosynthesis in SCC is similar to the standard theory albeit in a linear expansion with no inflation. Nucleosynthesis continues much longer than the GR ~3 minutes, for four years! To get the correct amount of helium the baryonic density has to be increased to over 20% closure, in others words equal to the Dark Matter component. So is DM baryonic after all? If so what form does it take today and why can't we see most of it? Also with that duration of nucleosynthesis all the Deuterium is destroyed. The D observed today has to be created in some other way - spallation for example?

    In the Jordan frame the ruler (the wavelength of a CMB photon) does 'expand with the universe'; the universe is static and the BB has been projected back in time to the 'infinite' past. The universe is eternal. The mass of an atom increases exponentially with cosmological time:
    m(t) = m0exp(Ht)
    where t is the time measured by the frequency of a CMB photon and
    where t = 0 is the present epoch and m0 its present mass.

    Cosmological red shift is caused by the atoms of the apparatus having gained mass since the epoch when the photon was emitted, the photon itself has not lost energy at all, indeed why should it, it has travelled across space-time 'instantaneously' along its light-like null-geodesic. No work has been done on or by the photon, so why should it loose energy? In this frame the standard model appears to be a 'tired light' model!!

    In the distant past atoms had hardly any mass and so were very large, the diameter of an atom is inversely proportional to its mass, other things being equal. The distant past in the Jordan frame was just as crowded as the Big Bang in the Einstein frame!

    More to follow...

    Garth
     
    Last edited: Jun 14, 2005
  9. Jun 14, 2005 #8

    pervect

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    I'm not 100% sure if this is right, but my picture of your cosmology is this:

    The Einstein frame in your model is the familiar and standard "big bang" model, in which the universe evolves with a(t). The difference is that the expansion is freely coasting.

    Time measured in the Einstein frame is proper time, the time measured by clocks as we know them.

    Your Jordan frame seems to be closely tied in with conformal time - which I would describe as an arbitrary rescaling of the time parameter used to make the geodesics of light 45 degree lines. (My view on this may be myopic).

    Thus "time" in the Jordan frame is not the "physical time" measured by ticking clocks. Because the conformal time is the logarithm of the proper time, the time coordinate goes to minus infinity at the big bang.

    What this means is that physically, as measured by a clock, the universe has a finite age. The causal structure of the universe is such, though, that any two points no matter how distant share a common history ( a consequence of the fact that conformal time extends back to infinity).

    This is illustrated by the last diagram at the bottom of the following webpage:

    http://www.astro.ucla.edu/~wright/cosmo_03.htm
     
  10. Jun 14, 2005 #9

    Garth

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    Thank you perfect.
    Correct
    The Jordan SCC frame is a non-invariant conformal transformation of the Einstein frame and vice versa. However it depends on what clocks you deem to be physical as to whether this time is "physical time".

    Photons are just as much part of the physical world as particles. Indeed in most of astronomy all we have of our objects of study are the photons received from them.

    Whether you deem particles or photons as more physical depends on whether you want to conserve energy-momentum or energy respectively. Lift an apparatus, where does the energy used lifting it go? In GR it 'goes into the field' non-localised and the apparatus' rest mass remains constant. However a photon transmitted from one apparatus down below and received by an identical apparatus at the top of a 'cliff' is observed to suffer from gravitational red shift. Where did the photon's energy go to? No work has been done on or by that photon.

    In GR the energy went 'into the field.' In the SCC Jordan frame the energy of lifting the apparatus goes into increasing its rest mass.

    The measurement of frequency of the photon is a comparison of the energy of the photon relative to the mass of the apparatus, and red shift is the difference between such measurements at the bottom and top of the 'cliff'. SCC interprets such red shift as the apparatus really increasing in mass by the gain of potential energy and that increase is observed/measured by comparison with a photon.
    That is a useful diagram that we have discussed in another Forum! If we deal with physical particles rather than mathematical points, in the SCC Jordan frame as t -> -∞ the particles increase in size d -> +∞ , so yes in the asymptotic limit as the universe is filled with infinite sized particles they all do overlap, yes they share a common history!

    Garth
     
    Last edited: Jun 14, 2005
  11. Jun 14, 2005 #10

    pervect

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    Alright, let's scratch "physical" clocks and replace it with "SI" clocks.

    If we stick with SI units as closely as we can, would the age of the universe be finite in SI units?

    There might be certain difficulties in maintaining a SI cesium clock all the way up to the big bang. The same issue arises with the SI meter (at some point a spacelike geodesic could not be a meter long.). Still, we can try and ask, if we had an SI meter, would a photon bounce across it a finite number of times since the big bang? (When the meter starts to become too long to fit in the universe without bending, we cut it in half, and require a photon to transverse the halved-meter twice to advance our time count once).

    At this point I'm mentally quite tied to the view that the gravitational field does do work on the photon, I'm afraid - which is the POV that the photon frequency does shift.

    Since I suspect a lot of other people are mentally tied to this same POV, it might be worthwhile to give this POV a name. I think this POV is your "Einstein" frame.
     
  12. Jun 15, 2005 #11

    Garth

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    What is your SI metre rule constructed from, steel? In which case you are in the Einstein frame and the universe expands around it. However in fact we cannot transport a steel metre rule to the ends of space and back to the BB, all we can do is observe photons from those regions. (If you could transport it all the way back to the BB, a photon would bounce back and forth across it an infinite number of times!)
    [Edit: Correction; the photon would bounce back and forth a finite number of times, but it would vibrate an infinite number of times. According to the steel rule the universe has a finite age, according to the photon its age is infinite. - Sorry about that!]
    So keep the steel rule on Earth and define a metre with it, so many vibrations of a light wave emitted by a particular spectral line of Caesium for example, and use that photon to measure the universe. Now you are in the Jordan frame. The key point of SCC is the gravitational and cosmological field equation has to be solved in this frame.
    But is the POV consistent with GR, or are you still partially stuck in a classical physics with its gravitational potential energy? Remember no forces are acting on the photon, the null-geodesic world-line of the photon simply passes through a space-time with curvature.

    Many standard authors, MTW (pg 187), Weinberg (pg 85), use a kind of classical PE argument and energy-conservation to explain GR gravitational red shift so that POV is understandable; but are they being consistent within the GR paradigm?

    However, do I expect GR to predict g. red shift? Yes!
    Because energy is conserved? No! But because energy is not generally conserved in GR!! (Remember we are deep in a gravitational field on Earth, there are no Killing vectors between the bottom and the top of the cliff. Energy is not conserved, rather energy-momentum is, but that is different.)

    Garth
     
    Last edited: Jun 15, 2005
  13. Jun 15, 2005 #12

    pervect

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    That is what I more-or-less expected, however I have to point out that the current defintion of the SI meter is

    http://physics.nist.gov/cuu/Units/current.html

    I presume that this doesn't change anything, and that the answer is still yes, we have a finite number of SI seconds since the Big Bang?


    The answer is a double yes - the POV is consistent with GR, and yes, I still am partialy stuck in classical physics with it's gravitatioanl potential energy.

    The GR approach would be to say that the photon travelling from the bottom of the earth to the top is following a geodesic as you say.

    But since the space-time of the Earth is reasonably static, we DO have time-like Killing vectors at both the bottom and top of the cliff! If you don't like the actual example of the Earth, think of being in the exterior region of an idealized Schwarzschild metric where this is exactly true.

    The product of any tangent vector of a geodesic and a Killing vector is a constant. Because k^a is a unit vector, the zeroeth component of the energy-momentum 4-vector of the photon, E_a is conserved. (This is also true for a free-falling particle). So the energy-momentum conservation law gives us gravitational redshift in the Schwarzschild metric without reference to any semi-classical concepts. If you have Wald, you can check out pg 137, or follow through with E = sqrt(-E_0 E^0) = sqrt(-E_0 g^00 E_0) = E_0 sqrt(-g^00), and remember that E_0 must be a constant for any given light ray. Since E=hv, this gives us the frequency.

    In the expanding universe case of a flat FRW metric, we don't have any time-like Killing vectors, so we don't have a conserved energy. We do have some space-like Killing vectors, though, due to isotropy. These give us a conserved "momentum" in this case (very handy for actually solving for the geodesics).
     
  14. Jun 15, 2005 #13

    Garth

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    Yes; the fundamental measurement question is: How do we measure time?" Using a caesium (cesium? American spelling?) atom in the definition places the time measurement firmly in the Einstein frame - it is equivalent to a steel rule but more accurate.
    Although I find that POV (photons fighting a gravitational potential well) persuasive I don't find it consistent with the GR paradigm.
    The killing vector exists for the photon, which is why its energy is conserved, but not for the apparatus, that has to be carried up the cliff, against the field. Its geodesic would take it straight down again and its killing vector would not survive the crash at the bottom!

    Note the correction in my last post above: "the photon would bounce back and forth a finite number of times, but it would vibrate an infinite number of times. According to the steel rule the universe has a finite age, according to the photon its age is infinite." You were correct about the photon and the ruler, sorry :blushing:.

    Garth
     
    Last edited: Jun 15, 2005
  15. Jun 15, 2005 #14

    Garth

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    Further note: Wald (pg 137) has got it right, (i.e. gravitational red shift) he follows Synge (1955) in explaining grs as a time dilation effect, but then he 'spoils it' by saying
    In GR? Exactly which force is it that is degrading the photon's energy?

    Garth
     
  16. Jun 15, 2005 #15

    pervect

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    LOL. Methinks the Killing vectors would survive the crash much better than the instrument package.

    We seem to be getting into the issue that Pete always raises, about how the mass of a system is to be calculated if the system is not isolated. This is clearly the case here, the measuring system is not following a geodesic, though the photons are. So the time-like Killing vectors exist, but since the package isnt' following a geodesic, they don't help us find it's energy.

    Currently I have no answer as to how to calculate the mass of a non-isolated system with full GR. It may even be a fundmanetally ambiguous notion, I'm not sure at this point.

    I think that your scalar field starts to enter the picture somewhere around here, resolving the difficulties in SCC for the energy of an interacting system, but not saying anything about what the solution (if any) is for GR.

    Ah - that helps a lot. Besides the warm fuzzy feeling of beign right :-), it gives me a clear mental picture of the situation.
     
  17. Jun 15, 2005 #16

    Garth

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    I would be interested in your opinion on my calculation of red shift under the "local conservation of energy paradigm" in my eprint "The derivation of the coupling constant in the new Self Creation Cosmology" page 22-24.

    Garth
     
  18. Jun 15, 2005 #17

    Chronos

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    We still have issues in that model. SW and GZK effects are problematic in the Jordan reference frame, IMO. And so far as photons are concerned, time does not exist.
     
  19. Jun 16, 2005 #18

    Garth

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    Everything is measured with reference to a set of standards, mass, length, time here in a laboratory on Earth. The frequency of a 'standard photon' has to be ideally defined in a Machian centre of Mass freely falling frame of reference, however here on the Earth's surface will do for now. From our laboratory the rest of the universe may be 'mapped out', measured, using the photons received from that universe.

    Time is defined by the number of vibrations of that photon as measured by an atomic process in the laboratory here on Earth, and from that number of vibrations, length and energy/mass too.

    Remember that atomic masses are varying in the Jordan frame, therefore in order to examine a physical process such as the SW and GZK effects it is easier to transform into the Einstein frame in which masses are constant.

    Now there is no intrinsic problem with the Sachs-Wolfe effect in the Einstein frame - it simply puts a constraint on cosmological parameters. Do you want to discuss numbers on this issue?

    As far as the GZK effect is concerned I don't think anybody can explain the high energy cosmic rays or GRB's, do you? Can Gamma Ray Bursts Produce the Observed Cosmic Rays Above 1020 eV?

    Garth
     
    Last edited: Jun 16, 2005
  20. Jun 16, 2005 #19

    Garth

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    But also note: Because of the significant energy loss by the GZK (Greisen-Zatsepin-Kuzmin 1966) mechanism, the present universe is not transparent to the highest energy cosmic rays (1020 eV), here.
    Therefore any sources contributing to the bulk of these cosmic rays should be within 500 Mpc of earth.

    What could be their source? As such high energies are involved there might be a natural accelerator out there - but that would not result in an isotropic flux.

    So, is the flux isotropic? Small-Scale Anisotropy of Cosmic Rays Above 10^19 eV Observed with the Akeno Giant Air Shower Array.
    Another possibility, which I would suggest as an educated guess, is that black holes must be involved - a lot of them roughly isotropically distributed across the sky. Is this evidence of a population of IMBH's making up the DM halo of our galaxy (1019 eV cosmic rays) and the IGM of our galactic cluster (1020 eV cosmic rays)?

    Garth
     
    Last edited: Jun 16, 2005
  21. Jun 16, 2005 #20

    wolram

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