The Inflationary Universe begins with an empty universe and a non-zero cosmological term, which is mathematically equivalent to a negative pressure, so the origin of the universe is a lot like the Bhuddist picture of the void torn apart by the Chinese hermit Ryu playing his iron flute in the reverse direction. (See "The World is Sound: Nada Brahma" by Joachim-Ernst Berendt, Destiny (1987, 1991), p. 170)
After the Universe has expanded to a very dilute state, a New Inflationary Universe can form from a Quantum Fluctuation.
The first of the above 7 images is adapted from Figure 3.7 of The Early Universe, by Edward W. Kolb and Michael S. Turner (paperback edition, Addison-Wesley 1994), and the other 6 of the above 7 images are adapted from the article The Future of the Universe, by Fred C. Adams and Gregory Laughlin, Sky and Telescope Magazine, August 1998, pages 32-39.
Some Interesting Times:
The paper gr-qc/0007006 by Paola Zizzi shows that
... This is also the number of superposed tubulins-qubits in our brain ... leading to a conscious event. ...".
In a subsequent paper, gr-qc/0103002, Paola Zizzi says:
"... We consider a quantum gravity register that is a particular quantum memory register which grows with time, and whose qubits are pixels of area of quantum de Sitter horizons. At each time step, the vacuum state of this quantum register grows because of the uncertainty in quantum information induced by the vacuum quantum fluctuations. The resulting virtual states, (responsible for the speed up of growth, i.e., inflation), are operated on by quantum logic gates and transformed into qubits. ... We also show that the bound on the speed of computation, the bound on clock precision, and the holographic bound, are saturated by the QGN. ...... The model of quantum growing network (QGN) described here is exactly solvable, and (apart from its cosmological implications), can be regarded as the first attempt toward a future model for the quantum World-Wide Web. ... A quantum Web could even undergo conscious experiences, if we believe ... that conscious experiences are due to decoherence of tubulins-qubits ... The idea of a conscious quantum Web is quite in agreement with the Global Brain idea ... ( the Net becoming the brain of a superorganism of which humans are just a component ). ...
... One could argue that the QGN discussed in this paper, is one of the attractors of some self-organizing system. That self-organizing system might be some kind of non local and non causal space-time structure made up of entangled qubits ... Although that system does not represent any physical space-time, it can be considered as a proto space-time, which is the seed of physical quantum space-time. ... we think that ... a random and non-local structure exists just below the Planck scale. At the Planck scale, the random network has already self-organized into the QGN. Indeed, we believe that the quantum beginning of physical space-time took place at the node 0 (the Hadamard gate) of the QGN. Quantized time appears as the result of the transformation of virtual states (vacuum energy) into qubits (quantum information) at the nodes of a quantum network. ...
... The speed up of the growth of the QGN, is due to virtual states and it is responsible for quantum inflation. If virtual states were absent in the quantum network, the growth would be much slower. In that case, the early universe could be interpreted as a 2^n lattice (n=0,1,2…), represented by the regular tree graph ...
... we have three "degrees" (or phases) for the beginning of the universe:
- The (perhaps eternal) presence of the proto space-time below the Planck scale.
- The beginning of (quantum) inflation at the Planck time.
- The end of inflation and beginning of existence.
... The beginning of existence of the universe (at the end of inflation due to decoherence) coincided with a cosmic conscious event ... of which our brain structure is still reminiscent. ...".
[ My view of what happens next, after decoherence and the end of inflation, may not be exactly the same as that of Paola Zizzi, but I think that it is in the spirit of her work. My view is:
A few months after writing gr-qc/0103002, Paula Zizzi wrote gr-qc/0110122, in which she said:
"... In a previous paper (gr-qc/0103002), the inflationary universe was described as a quantum growing network (QGN). Here, we propose our view of the QGN as the "ultimate Internet", as it saturates the quantum limits to computation. ... The QGN can be ... divided into two sub-systems:
- ... the connected part, made of connecting links and nodes, (quantum fluctuations ...) ... the quantum foam ...[which]... can be thought of as the "environment" ...
- ... the disconnected part ...[which]... can be thought of as the quantum state ...
... Also, we ...[discuss]... some features of the QGN which are related to:
- ... the cosmological constant problem ... and ... the quantum computational aspects of spacetime foam and decoherence ...
... as the QGN describes the early inflationary universe, the decohence time corresponds to the end of inflation, and the decoherence energy corresponds to the reheating energy. ... We can visualize the QGN after decoherence as a regular lattice, the connected part of the QGN itself. ...
... inflation ... is due to the presence of virtual qubits in the vacuum state of the quantum memory register. Virtual quantum information is created by quantum vacuum fluctuations, because of the inverse relation [... gr-qc/0103002 ...] between the quantized cosmological constant [... hep-th/9808180 ...] and quantum information I : ...
/\_n = 1 / I (L_planck)^2 where: n = 0,1,2,3... and the quantum information I is [... gr-qc/9907063 ...] : ...
I = N = (n+1)^2 ... [leading] to: ...
delta_I = - delta_/\ / ( (L_planck)^2 /\^2 ) = 2n +3 ... That is, at each time step t_n, there are 2n+3 extra bits (virtual states) in the vacuum state of the quantum memory register, where: ...
t_n = (n+1) t_planck is the quantized time, and t_planck = 10^(-43) sec . is the Planck time. ...
... We calculate the present value of the quantized cosmological constant ... with n_now = 9 x 10^60, and we get: ...
/\_now = 1.25 x 10^(-52) m^(-2) Also, we obtain: ...
OMEGA_/\ = /\ c^2 / 3 H_o^2 = (1/3) /\ c^2 (t_now)^2 Where ... t_now = H_o^(-1) = 3 x 10^17 h^(-1) sec
H_o being the Hubble constant and h a dimensionless parameter in the range: 0.58 < h < 0.72 . By choosing h = 0.65, we get: ...
OMEGA_./\ = 0.7 ... quite in agreement with the Type Ia SN observation data ...
From this result, the connecting links (virtual states) of the QGN look like to be still active. But the value of the total entropy is too big, for n_now = 10^60 : it would be S_now = 10^120 ln(2) , indeed a huge amount of entropy. We believe that ... at some earlier time, the QGN decohered ...[and]... the free links were not activated anymore by the nodes, since the decoherence time. We can visualize the QGN after decoherence as a regular lattice, the connected part of the QGN itself. ...
... The speed of computation v of a system of average energy E , is bounded as ... : ...
v < 2 E / pi hbar ... The energy of node "n" is ... the energy ... of the nth quantum fluctuation of the ... connected ... nodes ... : ..
E = E_planck / (n+1) ... E_planck = 10^19 GeV is the Planck energy ... we have : ...
E_now(nodes) = E_planck / n_now = 10^(-41) GeV = 10^(-51) J for n -> infinity, quantum information I will grow to infinity as n^2, while the energy of the nodes will decrease to zero as 1 / n . ... a low energy just reflects ... a low speed of computation v but not ... a low amount of information. ... it follows : ...
v_now = 10^(-17) sec^(-1) ... in our case, v_now^(-1) is the age of the universe:
v_now^(-1) = 10^17 sec ... Ng showed [... hep-th/0010234 ... gr-qc/0006105 ...] ... the bounds on speed of computation v and information I can be reformulated respectively as : ...
v^2 < P / hbar I < hbar / P t_planck^2
where P is the mean input power ...[leading]... to a simultaneous ... bound on the information I and the speed of computation v : ...
I v^2 < 1 / t_planck^2 ... from the simultaneous bound ... we get : I_now < 10^120 ...
... The quantum entropy of N = I qubits is: S = I ln(2). ...[if the bound were saturated]... We would get .. a huge total entropy S_now = 10^120 ln(2) ...
... to get the actual entropy [now], one should compute it as: ...
S_now = 10^120 ln(2) / S_decoherence = 10^120 / I_max If one agrees with Penrose [... The Emperor's New Mind, Oxford University Press (1989). in which Penrose says:
- "... let us consider what was previously thought to supply the largest contribution to the entropy of the universe, namely the 2.7 K black-body background radiation. ... The background radiation entropy is something like 10^8 for every baryon (where I am now choosing 'natural units', so that Boltzmann's constant, is unity). (In effect, this means that there are 10^8 photons in the background radiation for every baryon.) Thus, with 10^80 baryons in all, we should have a total entropy of 10^88 for the entropy in the background radiation in the universe. Indeed, were it not for the black holes, this figure would represent the total entropy of the universe, since the entropy in the background radiation swamps that in all other ordinary processes. The entropy per baryon in the sun, for example, is of order unity. On the other hand, by black-hole standards, the background radiation entropy is utter 'chicken feed'. For the Bekenstein-Hawking formula tells us that the entropy per baryon in a solar mass black hole is about 10^20, in natural units, so had the universe consisted ... of ... galaxies ...[consisting]... mainly of ordinary stars - some 10^11 of them - and each to have a million (i.e. 10^6) solar-mass black hole at its core ... Calculation shows that the entropy per baryon would now be actually ... 10^21, giving a total entropy, in natural units, of 10^101 ...]
... that the entropy now should be of order 10^101, this corresponds to the maximum amount of quantum information at the moment of decoherence: ...
I_max = 10^19 (n_cr = 10^9) where n_cr stands for the critical number of nodes which are needed to process the maximum quantum information, I_max ... it follows that the early quantum computational universe decohered at ...
t_decoherence = 10^(-34) sec. Moreover ... we find that the mean energy at the moment of decoherence ( n = 10^9) is: ...
E_decoherence = 10^10 GeV = 1 J corresponding to a rest mass m_decoherence = 10^(-13) g
... we get, for n = 10^9 : ...[the average speed of computation up to decoherence (i.e., during inflation) vbar_decoherence is given by]...
vbar_decoherence = I_ max / t_decoherence = 10^53 sec^(-1) ...
- ... the "information loss" puzzle ...[and]... the problem of causality at the Planck scale ...
... the semiclassical arguments of black holes evaporation might fail at the Planck scale. When the black hole reaches the Planck mass [about 10^19 proton masses], strong quantum gravity effects might stop the evaporation process ...[and]... there would be a remnant, which should store all the information collapsed in the original black hole. ... the remnant Planckian black hole gives rise to a QGN ... This idea is similar to the original one of Dyson [... Institute of Advanced Study preprint, 1976, unpublished...], that the black hole disappears completely, but one or more new universes branch off and carry away the information. ... the "unphysical time" t_(-1) = 0 (corresponding to a singularity in the classical theory) is unphysical for the new born universe, but not for the mother universe. ... in the mother universe, t_(-1) is the latest instant of evaporation of the black hole which will originate the child universe. The fact that there is this "leap" from physical time to unphysical time, in the passage from one universe to another, means that the two universes are not causally related. ...
The resulting picture is a self-organizing system ...".
[ My view of evaporating black holes differs from that of Paola Zizzi in gr-qc/0110122 in at least one important respect:
Paola Zizzi says:
"... There is no fundamental reason that the number of qubits at which our inflationary universe self-decohered should be 10^19. This was just the number of bits lost in the evaporation of a black hole in our mother universe. ... We wish to make a distinction here between oblique universes and parallel universes. We name oblique universes those which were generated by black holes evaporation with different information loss, and which will have totally different evolutions. ... we are not only causally unrelated, but also logically unrelated, to oblique universes. ... we call parallel universes those which were generated from black holes evaporation with the same information loss, and which will have similar evolutions. ...".
My opinion is that the number of bits lost in the evaporation of a black hole in a mother universe is NOT arbitrary, but MUST be 10^19, because the final stage in the evaporation is the evaporation of a Planck-mass black hole whose mass is 10^19 GeV = 10^19 proton masses.
The information just prior to the birth-evaporation is coded in the protons within the Planck-mass black hole, one bit per proton, so that the number of bits lost in the evaporation of a black hole in a mother universe MUST be 10^19, so that the "oblique universes" described by Paula Zizzi do not exist. ]
Here are some more details of Zizzi's Inflationary Cosmolgy, in the form of an edited summary of the paper gr-qc/0007006 by Paola Zizzi, and some comments (set off by brackets [ ] ) that I think are relevant:
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 ) there 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 ] ...".
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) Clifford algebra, which can be described by 2^8 qubits.
Our inflationary universe decoheres when it has Ndecoh = 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
we have:
= Cl(8) x Cl(8) x Cl(8) x Cl(8) x Cl(8) x Cl(8) x Cl(8) x Cl(8)
Therefore,
Cl(64) is the first ( lowest dimension ) Clifford algebra at which we can reflexively identify each component Cl(8) with a vector in the Cl(8) vector space.
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 of magnitude larger than the number of tubulins Ntub = 10^18 of the human brain. In my model of Quantum Consciousness ( and that of Jack Sarfatti ), conscious thought is due to superposition states of those 10^18 tubulins. Since a brain with Ndecoh = 10^19 tubulins would undergo self-decoherence and would therefore not be able to maintain the superposition necessary for thought, it seems that the human brain is about as big as an individual brain can be. The Zizzi Self-Decoherence can be compared to GRW decoherence.
... This value for the maximum number of e-foldings is close to the value necessary to solve the "horizon problem". It is interesting to note that a small value for the number of e-foldings may have observable implications for the low values of l in the spectrum of fluctuations of the microwave background. ...".
Since S3=SU(2), the Inflationary Universe has a boundary whose global Lie group structure is isomorphic to the SU(2) of the Higgs mechanism, so that the Inflationary Universe looks like an Expanding Instanton:
The New Universe can be regarded as being created in a Quantum Fluctuation Black Hole as described in hep-th/0103019 by Damien A. Easson and Robert H. Brandenberger, who study "... consequences of cosmological scenarios in which our universe is born from a black hole resting in a parent universe ...
Such Universe Creation by Quantum Fluctuation may be consistent with the view of Dyson, Kleban, and Susskind in hep-th/0208013, where they say:
"... The conventional view is that the universe will end in a de Sitter phase with all matter being infinitely diluted by exponential expansion. ... In the following we will assume the usual connections between quantum statistical mechanics and thermodynamics. These assumptions{together with the existence of a final cosmological constant - imply that the universe is eternal but finite. Strictly speaking, by finite we mean that the entropy of the observable universe is bounded, but we can loosely interpret this as saying the system is finite in extent. On the average it is in a steady state of thermal equilibrium. This is a very weak assumption, because almost any large but finite system, left to itself for a long enough time, will equilibrate (unless it is integrable). However, intermittent fluctuations occur which temporarily disturb the equilibrium. It is during the return to equilibrium that interesting events and objects form. ... Let S be the final thermodynamic entropy of the gas. Then on time scales of order Tr = exp( S ) the system will undergo Poincare recurrences ... On such long time scales the second law of thermodynamics does not prevent rare events, which effectively reverse the direction of entropy change. Obviously, the recurrence allows the entire process of cosmology to begin again ... What is more, the sequence of recurrences will stretch into the infinite past and future. ... Starting in a high entropy, "dead" configuration, if we wait long enough, a fluctuation will eventually occur in which the inflaton will wander up to the top of its potential, thus starting a cycle of inflation, re-heating, conventional cosmology and heat death. The frequency of such events is very low. The typical time for a fluctuation to occur is of order Tr = exp( S - S0 ) ... where S is the equilibrium entropy and S0 is the entropy of the fluctuation. The fluctuations we have in mind correspond to early inflationary eras during which the entropy is probably of order 10^10, while the equilibrium entropy is of order 10^120. Thus Tr = exp( 10^120 ) ... dismissing such long times as "unphysical" may be a symptom of extreme temporal provincialism. ...... the entropy in observable matter in today's universe ... is of order 10^100. This means that the number of microstates that are macroscopically indistinguishable from our world is exp( 10^100 ).
[ As to the Dyson-Kleburn-Susskind view as stated so far, I agree. However, I disagree with their following statements: ]
But only exp( 10^10 ) of these states could have evolved from the low entropy initial state characterizing the usual inflationary starting point. ... imagine running these states backward in time until they thermalize in the eventual heat bath with entropy 10^120. Among the vast number exp( 10^120 ) of possible initial starting points, a tiny fraction exp( 10^100 ) will evolve into a world like ours. However, all but exp( 10^10 ) of the corresponding trajectories (in phase space) are extremely unstable to tiny perturbations. Changing the state of just a few particles at the beginning of the trajectory will lead to completely different states. ... As an example, consider a state in which we leave everything undisturbed, except that we replace a small fraction of the matter in the universe by an increase in the amount of thermal microwave photons. In particular, we could do this by increasing the temperature of the CMB from 2.7 degrees to 10 degrees. ... It is ... possible that we are missing some important feature that picks out, or weights disproportionally, the recurrences which go through a conventional evolution, beginning with an inflationary era. However, we have no idea what this feature would be. ...".
I, however, do have an idea what such a feature would be: It would be that all universes follow the physics model of D4-D5-E6-E7-E8 VoDou Physics and evolve in accord with Zizzi Quantum Inflation.
Many Universes might be so created
each corresponding to a Timelike Brane in 27-dimensional J3(O) = J4(Q)o M-theory and a Spacelike Brane in 28-dimensional J4(Q) F-theory.
The Inflationary Universe could be based on Complex Structure with Conformal Symmetry: If the R4 neighborhood (in which the Expanding Instanton is considered to be embedded) is complexified into 8-real-dimensional C4, then the Instanton becomes a bounded complex homogeneous domain. If the Instanton has the Conformal symmetry of 15-6-1= 8-real-dimensional Spin(6) / (Spin(4)xU(1)) then the Instanton has as its Shilov boundary RP1 x S3 which is the spacetime structure of the D4-D5-E6-E7-E8 VoDou Physics model.
As the New Universe of the HyperDiamond Feynman Checkerboard discrete version of the D4-D5-E6-E7-E8 VoDou Physics model grows, its boundary is always the discrete version of a 3-sphere S3:
A Virtual Graviton can produce links (shown in green) that can reconnect the Parent Universe to the Spacetime Lattice Vertex at which the Instanton created the New Universe. Such a Virtual Graviton would exist only in some of the Worlds of the Many-Worlds, but the MacroSpace structure of the Many-Worlds might allow communication.
The boundary could be RP3 instead of ordinary S3: As Jeffrey Weeks says in The Shape of Space, Real Projective 3-space RP3,which can be made by identifying antipodal points of S3, has Elliptic Geometry.
The boundary could be the Quaternionic Manifold instead of ordinary S3: As Jeffrey Weeks says in The Shape of Space, the Quaternionic Manifold, which can be made by opposite faces of a Cube with a 1 / 4 clockwise turn, has Elliptic Geometry. It is called the Quaternionic Manifold because it has Quaternionic Symmetry.
The boundary could be T3 instead of ordinary S3: As Jeffrey Weeks says in The Shape of Space, the 3-Torus T3, which can be made by opposite faces of a Cube with no turn, has Euclidean Geometry.
The boundary could be Seifert-Weber Space instead of ordinary S3: As Jeffrey Weeks says in The Shape of Space, Seifert-Weber Space, which can be made by opposite faces of a Dodecahedron with a 3 / 10 clockwise turn, has Hyperbolic Geometry, as do most closed 3-manifolds.
The boundary could be the S3# Poincare Dodecahedral Space instead of ordinary S3: S3# is made by taking the quotient of S3 = Spin(3) = SU(2), the double cover of SO(3), by the 120-element binary icosahedral group. You can make an S3# by identifying opposite faces of a Dodecahedron with a 1 / 10 clockwise turn, as described in Chapter 16 of The Shape of Space, by Jeffrey R. Weeks (Marcel Dekker 1985). S3#, like S3, has Elliptic Geometry. S3# is a natural spinor space, in that you have to do a 720 degree rotation to get back to the initial state. Jean-Pierrre Luminet, in astro-ph/0501189, entitled "The Shape of Space after WMAP data", says:
"... the recent analysis of CMB data provided by the WMAP satellite suggest a finite universe with the topology of the Poincar´e dodecahedral spherical space. Such a model of a "small universe", the volume of which would represent only about 80 % the volume of the observable universe, offers an observational signature in the form of a predictable topological lens effect on one hand, and rises new issues on the early universe physics on the other hand ...... cosmic crystallography looks at the 3-dimensional apparent distribution of high redshift sources (e.g. galaxy clusters, quasars) in order to discover repeating patterns in the universal covering space, much like the repeating patterns of atoms observed in a crystal. "Pair Separation Histograms" (PSH) are in most cases able to detect a multiconnected topology of space, in the form of sharp spikes standing out above the noise distribution that is expected in the simply-connected case. ... However ... PSH may provide a topological signal only when the holonomy group of space has Clifford translations, a property which excludes all hyperbolic spaces. ...
... The main limitation of cosmic crystallography is that the presently available catalogs of observed sources at high redshift are not complete enough to perform convincing tests ... Fortunately, the topology of a small Universe may also be detected through its effects on such a "Rosetta stone" of cosmology as is the CMB fossil radiation ...
... The "concordance model" of cosmology describes the Universe as a flat infinite space in eternal expansion, accelerated under the effect of a repulsive "dark energy". The data collected by the NASA satellite WMAP ... combined with other astronomical data ... is marginally compatible with strictly flat space sections. ... Presently ... taken at their face value, WMAP data favor a positively curved space, necessarily of finite volume since all spherical spaceforms possess this property. ...
Now what about space topology ? ... WMAP data ... power spectrum of temperature anisotropies ... exhibits a set of "acoustic" peaks when anisotropy is measured on small and mean scales ... These peaks are remarkably consistent with the infinite flat space hypothesis.
However, at large angular scale ( for CMB spots typically separated by more than 60 degrees ), there is a strong loss of power which deviates significantly from the predictions of the concordance model. ... WMAP has observed a value of the quadrupole 7 times weaker than expected in a flat infinite Universe. ... The octopole ... is also weaker (72 % of the expected value). For larger wavenumbers ... which correspond to temperature fluctuations at small angular scales ... observations are remarkably consistent with the standard cosmological model.
The unusually low quadrupole value means that long wavelengths are missing. ... A ... natural explanation may be because space is not big enough to sustain long wavelengths. ...
... the long wavelengths modes tend to be relatively lowered only in a special family of closed multiconnected spaces called "well-proportioned". ...
... Among the family of well-proportioned spaces, the best fit to the observed power spectrum is the Poincare Dodecahedral Space (hereafter PDS) ... PDS may be represented by a dodecahedron ... whose opposite faces are glued after a 36 degree twist ... Such a space is positively curved, and is a multiconnected variant of the simply-connected hypersphere S3, with a volume 120 times smaller. ... The associated power spectrum, ... strongly depends on the value of the mass-energy density parameter. ... There is a small interval of values within which the spectral fit is ... in agreement with the value of the total density parameter deduced fromWMAP data ( 1.02 +/- 0.02 ). The best fit is obtained for OMEGA_0 = 1.016 ... The result is quite remarkable because the Poincare space has no degree of freedom. ...
... the curvature radius Rc is the same for the simply-connected universal covering space S3 and for the multiconnected PDS. ... a cosmological model with OMEGA_0 = 1.02 is far from being "flat" (i.e. with Rc = 1) ... For the same curvature radius, PDS has a volume 120 times smaller than S3. Therefore, the smallest dimension of the fundamental dodecahedron is only 43 Gpc, and its volume about 80% the volume of the observable universe (namely the volume of the last scattering surface). This implies that some points of the last scattering surface will have several copies. Such a lens effect is purely attributable to topology and can be precisely calculated in the framework of the PDS model. It provides a definite signature of PDS topology ...
... To be confirmed, the PDS model ... must satisfy two experimental tests :
1) A finer analysis of WMAP data, or new data ... will be able to determine the value of the energy density parameter with a precision of 1 %. A value lower than 1.01 will discard the Poincare space as a model for cosmic space, in the sense that the size of the corresponding dodecahedron would become greater than the observable universe and would not leave any observable imprint on the CMB, whereas a value greater than 1.01 would strengthen its cosmological pertinence.
2) If space has a non trivial topology, there must be particular correlations in the CMB, namely pairs of "matched circles" ... The PDS model predicts 6 pairs of antipodal circles with an angular radius less than 35 degrees. ... Cornish et al. (2004) claimed to have found no matched circles on angular sizes greater than 25 degrees, and thus rejected the PDS hypothesis. ... This is a wrong statement because they searched only for antipodal or nearly-antipodal matched circles. However ... for generic topologies ( including the well-proportioned topologies .... ), the matched circles are not back-to-back and space is not globally homogeneous, so that the positions of the matched circles depend on the observer's position in the fundamental polyhedron. The corresponding larger number of degrees of freedom for the circles search in the WMAP data generates a dramatic increase of the computer time, up to values which are out&endash;of&endash;reach of the present facilities. On the other hand, ... the same analysis for smaller circles ... found six pairs of matched circles distributed in a dodecahedral pattern, each circle on an angular size about 11 degrees. This implies OMEGA_0 = 1.010 +/- 0.001 for OMEGA_m = 0.28 +/- 0.02, values which are perfectly consistent with the PDS model. ... Eventually, the second&endash;yearWMAP data, originally expected by February 2004 but delayed for at least one year due to unexpected surprises in the results, may soon bring additional support to a spherical multiconnected space model. ...
... positive curvature ... implies a finite space and sets strong constraints on the number of e-foldings that took place during an inflation phase. It is possible to build models of "low scale" inflation where the inflationary phase is short and leads to a detectable space curvature ... It turns out that, if space is not flat, the possibility of a multiconnected topology is not in contradiction with the general idea of inflation ...
In most cosmological models, it is generally assumed that spatial homogeneity stays valid beyond the horizon scale. ... On this respect, the PDS model .... requires only one expanding bubble universe, of size sufficiently small to be entirely observable. ... spatially closed universes had the advantage to eliminate boundary conditions ... the PDS or a well&endash;proportioned ... universe ... is the only type of model in which the astronomical future could be definitely predicted ...
Maybe the most fundamental issue is to link the present&endash;day topology of space to a quantum origin, since classical general relativity does not allow for topological changes during the course of cosmic evolution. ... some simplified solutions of Wheeler-de Witt equations show that the sum over all topologies involved in the calculation of the wavefunction of the universe is dominated by spaces with small volumes and multiconnected topologies ...".
The D4-D5-E6-E7-E8 VoDou physics model has a natural process for Inflationary Universe Creation.
In the D4-D5-E6-E7-E8 VoDou physics model picture, the initial Inflationary Universe Quantum Fluctuation is very small and very hot, with a Planck Energy temperature in its Planck-size volume. As the Instanton expands, it cools so that its temperature is, like a Black Hole, inversely proportional to its radius. (Unlike a Black Hole, which has maximal mass for its volume, the Instanton temperature is not inversely proportional to its mass.) This produces the hot Big Bang necessary for nuceosynthesis.
Prior to dimensional reduction of spacetime from 8-dimensional to 4-dimensional, the Lagrangian for the D4-D5-E6-E7-E8 VoDou physics model is
where the three terms represent the adjoint, scalar, and half-spinor representations of Spin(8) and the base manifold over which the Lagrangian is integrated represents the vector representation,
The Pontrjagin term represents Instantons in 8-dimensional spacetime that is locally R8, so that the Instantons have as boundary the 7-sphere S7.
After dimensional reduction to 4-dimensional spacetime, the S7 Instanton boundary is factored by the Hopf fibration S3 -> S7 -> S4 into an Instanton with S3 boundary in 4-dimensional spacetime that is locally R4, plus an S4 part related to 4-dimensional Internal Symmetry Space.
In addition to the Standard Model, 3 generations of fermions, and a complex U(1) propagator phase,
that is a compact version of the 15-dimensional Conformal Group Spin(4,2), which is generated by 4 conformal transformations, 1 scale transformations, and 10 Spin(5) = Sp(2) deSitter transformations.
Conformal changes in the spacetime metric can be lifted to the fermion spinor bundle as described in Theorem 5.24 of Lawson and Michelsohn (1989), saying that the Atiyah-Singer Dirac operator remains essentially invariant under all changes of the metric by the conformal group C(n) = {g in GL(n,R) : g = Lg' for L in R+ and g' in SO(n)}. The conformal group C(n) = Spin(n,2) is in a sense the largest group that respects the spinor bundle on an n-dimensional manifold, which itself depends on the choice of Riemannian metric. The introduction of a Riemannian metric amounts to a simultaneous reduction of the structure group GL(n,R) of the tangent bundle, the cotangent bundle, and their tensor products to SO(n). (Lawson and Michelsohn (1989))
To get Gravity from the Spin(6) Conformal Group,
first gauge-fix the 4 dimensions of conformal transformations (thus linking the 4-dimensional SU(2) Higgs scalar to Gravity) and
then gauge-fix the 1-dimensional scale transformation (thus setting the Higgs mechanism mass scale).
After the conformal and scale gauges have been fixed, the Spin(6) = SU(4) conformal Lagrangian becomes a Spin(5) = Sp(2) de Sitter Lagrangian, from which gravity is obtained by the mechanism of MacDowell and Mansouri (Phys. Rev. Lett. 38 (1977) 739).
As Nieto, Obregon, and Socorro showed in gr-qc/9402029, the MacDowell-Mansouri Spin(0,5) = Sp(2) de Sitter Lagrangian for gravity plus
a Pontrjagin topological term
is equal to
the Lagrangian for gravity in terms of the Ashtekar variables plus
a cosmological constant term - which may vary during Expansion of the Instanton Universe (Overduin and Cooperstock, in astro-ph/9805260, have described some other cosmological models with variable cosmological constant), plus
an Euler topological term - which counts the number of handles of a maniforld and for 4-dim spacetime is a 4-form that is proportional to the square root of the determinant of the 4x4 matrix representing the curvature 2-form (see sec. 11.4 of Nakahara, Geometry, Topology, and Physics, Adam Hilger 1990).
WMAP observation of the Cosmic Background Radiation indicates that live in a Flat Expanding Universe with three types of stuff:
- According to a New Scientist (22 March 2003 pp. 41-42) article by Govert Schilling:
"... Only around a quarter (1%) of the baryonic mass is ... in objects we can see ... stars, galaxies, and gas clouds ... Up to another quarter (1%) .. may be ...[in]... objects too faint for our telescopes too pick up, such as burned-out stars, small planets, or stars that failed to ignite ... The lost baryons ...[may be]... strung out like cobwebs throughout the cosmos ...... the Virgo cluster of galaxies ...[is]... beaming out far more extreme-ultraviolet radiation than expected. ...[because]... galaxy clusters ...[are].. filled with gas as hot as 10 million kelvin ...[which]... gives off high-energy X-rays, not lower-energy ultraviolet radiation ... Richard Lieu ... suspected that much cooler gas was being sucked into the galaxy cluster from intergalactic space. ...[if so]... intergalactic space ... is filled with a wispy gas of baryons ...
... Long before galaxies began to form, 3 billion years after the big bang, baryonic matter was spread throughout the universe ... the gas was dominated by hydrogen ... in today's Universe, [some of] the clouds of hydrogen ...[has been]... eaten up during galaxy formation ...
... Computer simulations ... show that ... dark matter ... tends to be ... eventually drawn out into filaments ...[that]... crisscross each other to form a giant cosmic cobweb. ... the densest knots in the web turn into ... congregations of galaxies ... According to Cen and Ostriker's [computer] simulations ... Most of the baryons ... are still in intergalactic space, but ... are too hot to spot easily. ... the process of galaxy formation sends shock waves through intergalactic space, heating the gas to about 1 milion kelvin. ... [the] baryons [are] spread so thinly ... that they cannot transfer heat to each other ...[or]... cool efficiently. ... they .... would beam out low-energy X-rays and extreme-ultraviolet radiation. ...
... theory predicts ... that ... highly ionized oxygen ... produced in the first generation of stars, which later exploded, scattering their contents like confetti throughout the Universe ...[among the lost baryons] ... Tripp and Savage ... found that ... radiation from ... quasars was being absorbed by oxygen ions ... in intergalactic space. ...".
a Cosmological Constant L(t) - 73% .
In the D4-D5-E6-E7-E8 VoDou Physics model, Gravity and the Cosmological Constant come from the MacDowell-Mansouri Mechanism 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&endash;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&endash;direct product between Lorentz and special conformal transformation groups, and both de Sitter spaces are reduced to the cone&endash;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&endash;constant limit and the Q-symmetry of the strong cosmological&endash;constant limit can be considered as limiting cases of the fundamental symmetry.
Minkowski and the cone&endash;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&endash;space N. The points at infinity of M are concentrated in the vertex of the cone&endash;space N, and those on the light&endash;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&endash;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 Cosmological Constant 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 of the 15-dimensional Conformal Group Spin(2,4) = SU(2,2) through the MacDowell-Mansouri Mechanism (in which the generators corresponding to the 3 Rotations and 3 Boosts do not propagate), the fractional part of our Universe of Dark Matter Primordial Black Holes should be about 4 / 15 = 27%.
Since Ordinary Matter gets mass from the Higgs mechanism which is related to the 1 Scale Dilatation of the 15-dimensional Conformal Group Spin(2,4) = SU(2,2), the fractional part of our universe of Ordinary Matter should be about 1 / 15 = 6%.
Therefore, our Flat Expanding Universe should, according to the cosmology of the D4-D5-E6-E7-E8 VoDou Physics model, have, roughly:
In my opinion,
Also, there may be gravitational interaction from other Worlds of the Many-Worlds.
Aldrovandi and Pereira, in gr-qc/9809061, show that de Sitter groups of the MacDowell-Mansouri Gravity mechanism can describe Special Relativity in SpaceTimes with varying Cosmological Constant. They use Inonu-Wigner contractions of de Sitter groups and spaces to show that in a weak cosmological-constant limit the de Sitter groups are contracted to the Poincare group, and the de Sitter spaces are reduced to the Minkowski space, while in the strong cosmological-constant limit the de Sitter groups are contracted to another group which has the same abstract Lie algebra of the Poincare group, and the de Sitter spaces are reduced to a 4-dimensional cone-space of infinite scalar curvature, but vanishing Riemann and Ricci curvature tensors, in which the special conformal transformations act transitively and the equivalence between inertial frames is that of special relativity. 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. Minkowski and the cone-space can be considered as dual to each other, in the sense that their geometries are determined respectively by vanishing and infinite cosmological constants. The same can be said of their kinematical group of motions.
The creation of the Inflationary Universe by Quantum Fluctuation has some similarities to the quantum conformal fluctuation approach of Narlikar and Padmanabhan (1986) and Gunzig, Geheniau, and Prigogine (1987) and Gunzig (1997)).
For a movie that shows the creation of a new universe from our universe, see Akira.
Since, after dimensional reduction of spacetime from 8 to 4 dimensions, the Pontrjagin term goes into the Spin(6) conformal gravity sector of the D4-D5-E6-E7-E8 VoDou Physics model, it does not go to the SU(3) color force sector. Therefore, the SU(3) color force Sector has no THETA-term and the D4-D5-E6-E7-E8 VoDou Physics model has no theoretical THETA-CP problem.
The relationship between the Einstein curvature tensor G of Gravity, the stress-enregy tensor T of the particles and fields of the Standard Model, and a variable cosmological constant LAMBDA can be seen from the Einstein equation
Overduin and Cooperstock, in astro-ph/9805260, have described some other cosmological models with variable cosmological constant.
During its Inflationary Era, the Inflationary Universe has an effective Cosmological Constant L(t) that causes particle creation (qualitatively somewhat similarly to the C-field of Hoyle's Steady-State cosmology).
From the fundamental Planck-length HyperDiamond Lattice spacetime point of view, during the Inflationary Era, new lattice vertices appear uniformly distributed among the old lattice vertices.
Without the new vertices due to Expansion, virtual Quantum Fluctuation particle-antiparticle pairs appear, move apart for a while, and then come back together and annihilate each other.
If a new vertex alters spacetime near the path of one of such a pair, and thus alters its path so that it does not annihilate the other member of the pair, then the virtual Quantum Fluctuation can create new real pairs of Planck-Mass Black Holes, which can merge with pre-existing Black Holes to form larger Black Holes, which can then decay and produce various real particles and antiparticles.
If a Black Hole has greater than the stable minimum Planck mass, it will decay with a lifetime that is proportional to the cube of its mass. For a Black Hole to survive about 20 billion years, it must have a mass of at least 2 x 10^14 grams. For comparison, the Earth has mass of 6 x 10^27 grams and the Sun has a mass of 2 x 10^33 grams. A Black Hole of the mass of the Sun would have a radius (proportional to its mass) of about 10^5 cm, or 1 km.
The temperature of a Black Hole increases as it evaporates, with a temperature that is inversely proportional to its mass, and, equivalently, inversely proportional to its radius. A Black Hole of the mass of the Sun would have a temperature of 10^(-6) degrees K.
Since small Black Holes are hot, any particles (fermions, bosons, or Higgs scalars) emitted by small Black Holes would be emitted at high temperature.
To produce particle/antiparticle asymmetry, you need processes that are non-equilibrium and that are also CP-violating. Two such processes are:
The decay of Black Holes. According to Turner (1979) and Dolgov (1980), Black Hole decay could account for the particle-antiparticle asymmetry and the baryon-photon ratio of 5 x 10^(-10) that is observed now.
Another possible mechanism for particle-antiparticle asymmetry is the set of interactions that may occur at the weak force phase transition.
Since cold Black Holes interact with the ordinary matter only gravitationally, their evolution is discussed separately from the evolution of hot ordinary matter (fermions, bosons, and Higgs scalars).
Each qubit at the end of inflation corresponds to a Planck Mass Black Hole, which in the D4-D5-E6-E7-E8 VoDou Physics model undergoes decoherence and,
each qubit transforms into 2^64 = 10^19 elementary first-generation fermion particle-antiparticle pairs.
The resulting 2^64 x 2^64 = 2^128 = 10^19 x 10^19 = 10^38 fermion pairs populating the Universe Immediately After Inflation constitutes a Zizzi Quantum Register of order n_reh = 10^38 = 2^128.
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 Reheating:
Since each qubit at Reheating should correspond, not to Planck Mass Black Holes, but to fermion particle-antiparticle pairs that average about 0.66 GeV, we have the result that
After Reheating, our Universe enters the Radiation-Dominated Era, and, since there is no continuous creation, particle production stops, so
and will continue to be mostly constant until Proton Decay.
In the paper gr-qc/0007006, Paola Zizzi says [with changes by me enclosed in square brackets - the paper states that at the end of inflation En = Eplanck / 10^9 = 10^11 GeV, but since I consider Eplanck to be 10^19 GeV, I use the value 10^10 GeV]: "... The discrete energy spectrum of the de Sitter horizon states at time Tn = ( n+1 ) Tplanck ... is En = Eplanck / ( n+1 ) where Eplanck = 1.2 x 10^19 GeV is the Planck energy ...[so that at]... the decoherence time ... Tn = 10^(-34) sec ... the time when inflation ends ... the corresponding energy is [ Edecoh = Eplanck / 10^9 = 10^10 GeV ] ...".
However, the Reheating process raises the energy/temperature at Reheating to Ereh = 10^14 GeV, the geometric mean of the Eplanck = 10^19 GeV and Edecoh = 10^10 GeV:
In the D4-D5-E6-E7-E8 VoDou Physics model,
according to Hawking and his students who have studied the physical consequences of creation of virtual pairs of Planck-energy Black Holes,
and
John Gribbin, in his book In Search of the Big Bang (Bantam 1986, page 374), says that Einstein was stopped in the street because George Gamow had just told Einstein about the idea of ceating the Universe from Nothing, which had been just then (in the 1940s) been thought of by Pascual Jordan. See the autobiography My World Line of George Gamow.
......
