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Dark Matter and Dark Energy

Sean Carroll, in a CosmicVariance blog in August 2006 entitled Dark Matter Exists,including a comment there by Karel, said ( with my comment here setoff by brackets [ ] ):

"... In the Bullet Cluster, more formally known as 1E 0657-56, we actually find two clusters of galaxies that have (relatively) recently passed right through each other. It turns out that the large majority (about 90%) of ordinary matter in a cluster is not in the galaxies themselves, but in hot X-ray emitting intergalactic gas. As the two clusters passed through each other, the hot gas in each smacked into the gas in the other, while the individual galaxies and the dark matter (presumed to be collisionless) passed right through. ...

[ I think that an animation sequence of what is happeningwould look like this

in which

In my D4-D5-E6-E7-E8 VoDou Physics model:

In tightly bound systems like our Solar System within the orbit ofUranus, the Special Conformal Degrees of Freedom are completelyfrozen out and are not observed by experiments.

However, in Swiss-Cheese systems such as Galaxies which havesubstantial regions in which the Special Conformal Degrees of Freedomare not frozen, but the total system of the Galaxy is bound and doesrotate, the Special Conformal Degrees of Freedom do not expand theGalaxy, but act to modify the rotation of the Galaxy in a wayequivalent to MOND.

In more detail, in my D4-D5-E6-E7-E8 VoDou Physics model, Gravityand the Cosmological Constant come from the MacDowell-MansouriMechanism and the 15-dimensional Spin(2,4) = SU(2,2) Conformal Group,which is made up of:

According to gr-qc/9809061 by R. Aldrovandi and J. G.Peireira:

"... By the process of Inonu-Wigner group contraction with R -> oo ...[where R ]... the de Sitter pseudo-radius ... , both de Sitter groups ... with metric ... (-1,+1,+1,+1,-1) ...[or]... (-1,+1,+1,+1,+1) ... are reduced to the Poincare group P, and both de Sitter spacetimes are reduced to the Minkowski space M. As the de Sitter scalar curvature goes to zero in this limit, we can say that M is a spacetime gravitationally related to a vanishing cosmological constant.

On the other hand, in a similar fashion but taking the limit R -> 0, both de Sitter groups are contracted to the group Q, formed by a semi-direct product between Lorentz and special conformal transformation groups, and both de Sitter spaces are reduced to the cone-space N, which is a space with vanishing Riemann and Ricci curvature tensors. As the scalar curvature of the de Sitter space goes to infinity in this limit, we can say that N is a spacetime gravitationally related to an infinite cosmological constant.

If the fundamental spacetime symmetry of the laws of Physics is that given by the de Sitter instead of the Poincare group, the P-symmetry of the weak cosmological-constant limit and the Q-symmetry of the strong cosmological-constant limit can be considered as limiting cases of the fundamental symmetry. ...

... N, whose geometry is gravitationally related to an infinite cosmological constant, is a 4-dimensional cone-space in which ds = 0, and whose group of motion is Q. Analogously to the Minkowski case, N is also a homogeneous space, but now under the kinematical group Q, that is, N = Q/L. In other words, the point-set of N is the point-set of the special conformal transformations. Furthermore, the manifold of Q is a principal bundle P(Q/L,L), with Q/L = N as base space and L as the typical fiber. The kinematical group Q, like the Poincare group, has the Lorentz group L as the subgroup accounting for both the isotropy and the equivalence of inertial frames in this space. However, the special conformal transformations introduce a new kind of homogeneity. Instead of ordinary translations, all the points of N are equivalent through special conformal transformations. ...

... Minkowski and the cone-space can be considered as dual to each other, in the sense that their geometries are determined respectively by a vanishing and an infinite cosmological constants. The same can be said of their kinematical group of motions: P is associated to a vanishing cosmological constant and Q to an infinite cosmological constant.

The dual transformation connecting these two geometries is the spacetime inversion x^u -> x^u / sigma^2 . Under such a transformation, the Poincare group P is transformed into the group Q, and the Minkowski space M becomes the cone-space N. The points at infinity of M are concentrated in the vertex of the cone-space N, and those on the light-cone of M becomes the infinity of N. It is interesting to notice that, despite presenting an infinite scalar curvature, the concepts of space isotropy and equivalence between inertial frames in the cone-space N are those of special relativity. The difference lies in the concept of uniformity as it is the special conformal transformations, and not ordinary translations, which act transitively on N. ...

... in the light of the recent supernovae results ... favoring possibly quite large values for the cosmological constant, the above results may acquire a further relevance to Cosmology ...".

Since the Cosmological Constant comes from the 10 Rotation, Boost,and Special Conformal generators of the Conformal Group Spin(2,4) =SU(2,2), the fractional part of our Universe of the CosmologicalConstant should be about 10 / 15 = 67%.

Since Black Holes, including Dark Matter Primordial Black Holes,are curvature singularities in our 4-dimensional physical spacetime,and since Einstein-Hilbert curvature comes from the 4 Translations ofthe 15-dimensional Conformal Group Spin(2,4) = SU(2,2) through theMacDowell-Mansouri Mechanism (in which the generators correspondingto the 3 Rotations and 3 Boosts do not propagate), the fractionalpart of our Universe of Dark Matter Primordial Black Holes should beabout 4 / 15 = 27%.

Since Ordinary Matter gets mass from the Higgs mechanism which isrelated to the 1 Scale Dilatation of the 15-dimensional ConformalGroup Spin(2,4) = SU(2,2), the fractional part of our universe ofOrdinary Matter should be about 1 / 15 = 6%.

Therefore, our Flat Expanding Universe should, according to thecosmology of the D4-D5-E6-E7-E8 VoDou Physics model, have,roughly:


As Dennnis Marks pointed out to me, since:

the ratio of their overall average densities must vary with time,or scale factor R of our Universe, as it expands so that the abovecalculated ratio 0.67 : 0.27 : 0.06 is valid only for a particulartime, or scale factor, of our Universe, and

that is a time near our present time at which WMAP measures thatratio to be 0.73 : 0.23 : 0.04 (in my opinion very close to the abovecaculated ratio).

His remarks are substantially equivalent to a question thatMichael S. Turner, in astro-ph/0202005, calls "... The Nancy KerriganProblem ... in the past dark energy was unimportant and in the futureit will be dominant! We just happen to live at the time when darkmatter and dark energy have comparable densities. In the words ofOlympic skater Nancy Kerrigan, "Why me? Why now?". In otherwords:

WHEN is the above calculated ratio 0.67 : 0.27 : 0.06?

Since WMAP observes Ordinary Matter at 4% NOW,

the time WHEN Ordinary Matter was 6% would be at redshift z suchthat 1 / (1+z)^3 = 0.04 / 0.06 = 2/3 , or (1+z)^3 = 1.5 , or 1+z =1.145 , or z = 0.145. To translate redshift into time, in billions ofyears before present, or Gy BP, use this chart

from a file SNAPoverview.pdf. to seethat

the time WHEN Ordinary Matter was 6% would have been a bit over 2billion years ago, or 2 Gy BP.

In the diagram, there are four Special Times in the history of ourUniverse:

Those four Special Times define four Special Epochs:

NOW happens to be about 2 billion years into the Late AcceleratingExpansion Epoch.

The Copernican insight that Earth, the home of Humanity and itsprecursor Life, is Not Special in our Solar System (and also itsplace among the stars of our Milky Way Galaxy) led us to understandthe true structure of our Solar System and our Milky Way Galaxy.

Our present insight that the Time of Life on Earth, from theProterozoic begining of Eukaryotic Life to Present-Day Humanity,covers the 2 billion years beginning with a Special Time in theTime-History of our Universe leads us to a better understanding ofthe Unification of Gravity / Particle Physics / Mathematics /Information / Consciousness, and perhaps to a better understandingour our ultimate Fate.


the above calculated ratio 0.67 : 0.27 : 0.06 of about 2billion years ago corresponds to the WMAP measured ratio 0.73 : 0.23: 0.04 for the time NOW.

What about Dark Energy /\ and Cold Dark Matter during the past 2Gy ?

Since Cold Dark Matter = Primordial Black Holes (PBH):

The above calculation of 2 Gy BP for the ratio 0.67 : 0.27 : 0.06is based only on the decline in the Ordinary Matter component withexpansion of Space, so it is only a rough estimate, in that itignores such things as decay of Ordinary Matter protons by GUT (10^31year lifetime) or by Black Hole processes (10^64 year lifetime),which would be less important during the relevant time periods nearNOW than in the Black Hole and Dark Eras of the distant future.

Jack Sarfatti said (in the context of his physics/cosmology model): "... "... I am also saying that lepto-quarks [leptons and quarks] have dark matter cores on small scale. It's /\zpf < 0 that keeps electron stable. Think, naively for the nonce, of electron as a shell of electric charge with an inner /\zpf < 0 core. It looks like a "point" from huge effective curvature of /\zpf. ...".

That idea is not only interestingly similar to the idea of /\zpf < 0 haloes helping to hold galaxies together, but also seems very much like the Compton Radius Vortex model of leptons and quarks as Kerr-Newman black holes with no cosmic censorship of their naked singularities.

Also, perhaps the concept of Primordial Black Holes as Cold Dark Matter might be a particle manifestation of the part of /\zpf < 0 that is not found in the center of /\ = 0 Ordinary Matter leptons and quarks. If that viewpoint is correct, in view of the WMAP ratio of 73% - 23% - 4% of /\ > 0 , /\ < 0, /\ = 0, there should be a lot more mass in /\ < 0 Primordial Black Holes than in /\ = 0 leptons and quarks.

Further, Cold Dark Matter cores of leptons and quarks seems consistent with an association of Ordinary Matter with production of Cold Dark Matter in early times of our Universe.

As to how the Dark Energy /\ and Cold Dark Matter terms haveevolved during the past 2 Gy, a rough estimate analysis would be, forCold Dark matter = PBH:

The Ordinary Matter excess 0.06 - 0.04 = 0.02 plus the first-orderCDM excess 0.27 - 0.18 = 0.09 should be summed to get a totalfirst-order excess of 0.11, which in turn should be distributed tothe /\ and CDM factors in their natural ratio 67 : 27, producing, forNOW after 2 Gy of expansion:

for a total calculated ratio for NOW of 0.75 : 0.21 : 0.04

so that the present ratio of 0.73 : 0.23 : 0.04 observed by WMAPseems to me to be consistent with the cosmology of the D4-D5-E6-E7-E8VoDou Physics model with Cold Dark Matter = PBH.


MOdified Newtonian Dynamics (MOND)

In my D4-D5-E6-E7-E8 VoDou Physics model, Swiss-Cheese systemssuch as Galaxies which have substantial regions in which the SpecialConformal Degrees of Freedom are not frozen, but the total system ofthe Galaxy is bound and does rotate, the Special Conformal Degrees ofFreedom do not expand the Galaxy, but act to modify the rotation ofthe Galaxy in a way equivalent to MOND.

In astro-ph/0112069, Mordehai Milgrom says:

"... In the early 1980s I proposed a modifed-dynamics ... based onthe fact that typical accelerations in galactic systems are manyorders of magnitude smaller than those encountered in the solarsystem. ... This modified dynamics, MOND, introduces a constant withthe dimensions of an acceleration, a_0, and posits that standardNewtonian dynamics is a good approximation only for accelerationsthat are much larger than a_0. ... the basic point of MOND, fromwhich follow most of the main predictions, can be simply put asfollows: a test particle at a distance r from a large mass M issubject to the acceleration a given by

a^2 / a_0 = M G r^(-2)

when a << a_0, instead of the standard expression a = M Gr^(-2) , which holds when a >> a_0. ... The value of theacceleration constant a_0 that fits all the data discussed ...[in the paper ]... is about 10^(-8) cm s^(-2) ...

... One immediate result ... is that at a large radius around amass M, the orbital speed on a circular orbit becomes independent ofradius. This indeed was a guiding principle in the construction ofMOND, which took asymptotic flatness of galaxy rotation curves as anaxiom ... When we count the mass of baryonic matter in such systems -in stars, neutral and high-T gas, etc.- the total sum does notprovide enough gravity to explain the observed accelerations in suchsystems within standard physics. If we adhere to standard dynamics,the need for dark matter is the only solution we can conceive. It is,however, possible that the laws of dynamics, proven in the laboratoryand the solar system, cannot be simply applied in the realm of thegalaxies. ... Regarding galactic systems other than galaxies, thecomparison of the systematics of the observed mass discrepancy withthe expectations from MOND are shown in Figure 2

in Milgrom (1998) [ astro-ph/9810302 , which says:

"... MOND is not a modification at large distances, but at low accelerations - which for a given mass are attained at large distances ... there is no correlation of the discrepancy with system size. ...


... in particular ... the small dwarf spheroidals and LSB discs show large discrepancies, while the large galaxy clusters evince only moderate discrepancies...." ].

... based on analyzes referenced there.

The agreement is uniform, with one exception: The cores of richx-ray clusters of galaxies show a considerable mass discrepancy,while, according to MOND there shouldn't be any, because theaccelerations there are only of the order of a_0, and not muchsmaller. ( Application of MOND to the clusters at large, say within afew megaparsecs of the center, does predict correctly the massdiscrepancy. ) The resolution, by MOND, will have to be that thesecores harbor large quantities of still undetected baryonic matter,perhaps in the form of dim stars, perhaps as warm gas. Theenvironment, and history, of these cores is so unlike others thatthis would not be surprising. ...

.. in interpreting data we equate observed accelerations with thegravitational field ... We can exemplify this point by consideringthe claimed anomaly in the motions of the Pioneer 10 and 11spacecraft. Analysis of their motion have shown an unexplained effect...[ see Anderson & al 2001, Study of the anomalousacceleration of Pioneer 10 and 11, gr-qc/0104064 ]... that can beinterpreted as being due to an unexplained constant accelerationtowards the sun of about 7 x 10^(-8) cm s^(-2) , of the order of a_0.... MOND could naturally explain such an anomalous acceleration... It may well be that the modification enters the Pioneers motion,which corresponds to unbound, hyperbolic motions, and the motion ofbound, and quasi-circular trajectories in a different way. ...

... It is worth pointing out that in such a modified-gravitytheory, the deep-MOND limit ... the deep-MOND regime ( a <<a_0 ) ... corresponds to a theory that is conformally invariant,as discussed in Milgrom (1997) [ gr-qc/9705003 which says:

"... The Poisson equation describes many physical problems in linear media such as electrostatics, magnetostatics, steady-state diffusion and other potential flows in the presence of sources and sinks, and, of course, Newtonian gravity. It can be generalized ... to describe, for example, non-linear media with a response coefficient (dielectric constant, permeability, diffusion coefficient, etc.) that is a function of the field strength. ... For example, ... as a modification of Newtonian gravity to replace the dark-matter hypothesis for galactic systems ... In the modified dynamics discussed as an alternative to dark matter, phenomenology requires just this ... conformally invariant (CI) ... Our results here apply then in the large-distance limit of this theory. ...". ]. ...


... this asymptotic rotational speed depends only on the totalmass M via V^4 = M G a_0 . This, according to MOND, is the factunderlying the observed Tully-Fisher-type relations, by which thetypical (mean) rotational velocity, V , in a disc galaxy is stronglycorrelated with the total luminosity of the galaxy, L, in a relationof the form L ...[ proportional to ]... V^alpha . The poweralpha is around 3-4, and depends on the wavelength band at which L ismeasured. The close agreement between this TF [ Tully-Fisher-type] relation and the prediction of MOND is encouraging; but, totest MOND more precisely on this count, one would have to bridgeproperly the mass-asymptotic-velocity MOND relation with the commonlypresented luminosity-bulk-velocity TF relation. One should use theluminosity in a band where it is a good representative of the stellarmass, take into account not only the stellar mass, as represented bythe luminosity, but also the contribution of gas to the mass, and usethe asymptotic velocity, as opposed to other measures of therotational velocity. It has emerged recently ... that if one does allthis one indeed obtains a tight and accurate relation of the formpredicted by MOND. ...".

Primordial Stable Planck-Mass Black Holes

If our spacetimeremains octonionic 8-dimensional throughout inflation, then thenon-associativity and non-unitarity of octonions might account forparticle creation without the need for tapping the energy of aninflaton field.

In gr-qc/0007006, Paola Zizzi says:

"... the vacuum-dominated early inflationary universe ... is a superposed quantum state of qubits. ...

... the early universe had a conscious experience at the end of inflation, when the superposed quantum state of ... [ 10^18 = N quantum qubits ] ... underwent Objective Reduction. The striking point is that this value of [ N ] equals the number of superposed tubulins-qubits in our brain ...

... [ in the inflationary phase of our universe ] ... the quantum register grows with time. In fact,

at each time step

... [ Tn = (n+1) Tplanck (where Tplanck = 5.3 x 10^(-44) sec) ] ...

a Planckian black hole, ... the n=1 qubit state 1 which acts as a creation operator, supplies the quantum register with extra qubits. ...

At time Tn = (n+1) Tplanck the quantum gravity register will consist of (n+1)^2 qubits. [ Let N = (n+1)^2 ] ...

By the quantum holographic principle, we associate N qubits to the nth de Sitter horizon ... remember that |1> = Had|0> where Had is the Hadamard gate ... the state ... [ of N qubits ] ... can be expressed as

... [ |N> = ( Had|0> )^N ] ...

As the time evolution is discrete, the quantum gravity register resembles more a quantum cellular automata than a quantum computer. Moreover, the quantum gravity register has the peculiarity to grow at each time step ( it is self-producing ). If we adopt an atemporal picture, then the early inflationary universe can be interpreted as an ensemble of quantum gravity registers in parallel ... which reminds us of the many-worlds interpretation. ...

The superposed state of quantum gravity registers represents the early inflationary universe which is a closed system. Obviously then, the superposed quantum state cannot undergo environmental decoherence. However, we know that at the end of the inflationary epoch, the universe reheated by getting energy from the vacuum, and started to be radiation-dominated becoming a Friedmann universe. This phase transition should correspond to decoherence of the superposed quantum state. The only possible reduction model in this case is self-reduction ...

during inflation, gravitational entropy and quantum entropy are mostly equivalent ...

Moreover ... The value of the cosmological constant now is

... /\N = 10^(-56) cm^(-2) ...

in agreement with inflationary theories.

If decoherence of N qubits occurred now, at Tnow = 10^60 Tplanck

( that is, n = 10^60, N = 10^120 )

here would be a maximum gravitational entropy

... [ maximum entropy Smax = N ln2 = 10^120 ] ...

In fact, the actual entropy is about

... [ entropy now Snow = 10^101 ] ...

[Therefore] decoherence should have occurred for

... [ Ndecoh = 10^(120-101) = 10^19 = 2^64 ] ...

which corresponds to ... [ n = 9 and to ] ... the decoherence time

... [ Tdecoh = 10^9 Tplanck = 10(-34) sec ] ...".

There is a fundamental reason that the number of qubits atwhich our inflationary universe experiences self-decoherence is

Ndecoh = 10^19 = 2^64

The self-reflexivity property of the 2^64-dimensional Cliffordalgebra Cl(64) causes self-decoherence !

From the point of view of my D4-D5-E6-E7-E8 Vodou Physics model,the fundamental structure is the 2^8 = 256-dimensional Cl(8) Cliffordalgebra, which can be described by 2^8 qubits.

Our inflationary universe decoheres when it has Ndecoh = 2^64qubits.

What is special about 2^64 qubits ?

2^64 qubits corresponds to the Clifford algebra Cl(64) =Cl(8x8).

By the periodicity-8 theorem of real Clifford algebras that

Cl(K8) = Cl(8) x ... tensor product K times ... x Cl(8),

we have:

Cl(64) = Cl(8x8) =

= Cl(8) x Cl(8) x Cl(8) x Cl(8) x Cl(8) x Cl(8) x Cl(8) xCl(8)


Cl(64) is the first ( lowest dimension ) Clifford algebra at whichwe can reflexively identify each component Cl(8) with a vector in theCl(8) vector space.

This reflexive identification/reduction causes decoherence.

It is the reason that our universe decoheres at N = 2^64 =10^19,

so that inflation ends at age 10^(-34) sec.

Note that Ndecoh = 2^64 = 10^19 qubits is just an order ofmagnitude larger than the number of tubulins Ntub = 10^18 of thehuman brain. In my model of Quantum Consciousness ( and that of JackSarfatti ), conscious thought is due to superposition states of those10^18 tubulins. Since a brain with Ndecoh = 10^19 tubulins wouldundergo self-decoherence and would therefore not be able to maintainthe superposition necessary for thought, it seems that the humanbrain is about as big as an individual brain can be. The ZizziSelf-Decoherence can be compared to GRW decoherence.

How Many Particles are in our Universe?

At the end of inflation:

Each qubit at the end of inflation corresponds to a Planck MassBlack Hole, which in the D4-D5-E6-E7-E8 physics model undergoesdecoherence and, in a process corresponding to Reheating in theStandard Inflationary Model, after the end of inflation and duringreheating, the fate of each Planck Mass Black Hole is governed byConformal Gravity, producing either

The 4 to 1 ratio of Special Conformal Transformations to Dilationdetermines that the fundamental ratio of Dark Matter to OrdinaryMatter will be about 4 to 1.

Here is a very rough estimate of the number of Ordinary Matterparticles in our universe, produced by reheating from a population of(2^64)^2 = 2^128 = 10^38 fermion pairs populating the UniverseImmediately After Inflation:

Since, as Paola Zizzi says in gr-qc/0007006, ( with some editing by me denoted by [ ] ):
"... the quantum register grows with time. ... At time Tn = (n+1) Tplanck the quantum gravity register will consist of (n+1)^2 qubits. [ Let N = (n+1)^2 ] ...",

we have the number of qubits at the next time step (Reheating)

Nreh = ( n_reh )^2 = ( 2^128 )^2 = 2^256 = 10^77

Since each qubit at Reheating should correspond, for the Ordinary Matter component, to fermion particle-antiparticle pairs that average about 0.66 GeV, we have the results that

the number of particles in our Universe at Reheating is about 10^77 nucleons.

After Reheating, our Universe enters the Radiation-Dominated Era, and, since there is no continuous creation, particle production stops, so

the 10^77 nucleon Baryonic Mass of our Universe has been mostly constant since Reheating, and will continue to be mostly constant until Proton Decay.

The present scale of our Universe is about R(tnow) = 10^28 cm, so that its volume is now about 10^84 cm^3, and its baryon density is now about 10^77 protons / 10^84 cm^3 = 10^(-7) protons/cm^3 = 10^(-7-19-5) gm / cm^3 = 10^(-31) gm / cm^3 = roughly the baryonic mass density of our Universe.

Since the critical density of our Universe is about 10^(-29) gm / cm^3, it is likely that the excess of the critical mass of our Universe over its baryonic mass is due to Dark Matter Primordial Stable Planck Mass Black Holes and Dark Energy.


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