Quantum Conformal de Sitter Inflation:
Linde has written a good current overview of inlationary cosmology. The quantum conformal fluctuation approach of Narlikar and Padmanabhan (1986) and Gunzig, Geheniau, and Prigogine (1987) is compatible with the natural structure of the D4-D5-E6 model, whose spacetime has a fundamental underlying light-cone causal structure in both 8 and 4 dimensions. Quantum conformal fluctuation quantization gives a lower bound on the order of the Planck length to the proper interval between any two events in spacetime (section 13.4 of Narlikar and Padmanabhan (1986)) and provides for cosmogenesis from vacuum instability (section13.8 of Narlikar and Padmanabhan (1986) and Gunzig, Geheniau, and Prigogine (1987)). A quantum conformal fluctuation can be interpreted as creation of virtual particles in the background spacetime. The only particles in the D4-D5-E6 model that could be massive enough to have an effect as large as creating a universe out of a preexisting Minkowski background are virtual black holes, whose mass must be at least Planck-mass, about 10^19 GeV. Creation of virtual black holes in a spacetime while preserving the fundamental light-cone causal structure can be described by quantum conformal fluctutations, as in chapters 12, 13, and 14 of Narlikar and Padmanabhan (1986), because quantum conformal fluctuations preserve the light-cone causal structure of spacetime. 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)) The D4-D5-E6 model universe begins with a flat Minkowskian vacuum, with initial dimensionality taken to be 4 since the expansion would occur after dimensional reduction from 8 dimensions. The flat Minkowskian vacuum then undergoes a quantum conformal fluctuation causing creation of black holes and a phase transition to an inflationary de Sitter universe. (Here, the term de Sitter universe is to include anti-de Sitter universes as well.) For a flat Minkowski vacuum to be unstable, the black holes of the quantum conformal fluctuation must be on the order of 100 times as massive as the Planck mass, or approximately 10^21 GeV. Narlikar and Padmanabhan (1986), in section13.8.1, show how that works. Begin with an action that is a conformal transformation of gravitation, a scalar field of mass m, and a coupling (1/6)RB^2 between gravity curvature R and scalar field B: S = (1/2)INT(f^i f_i - f^i f_i - aG^2 f^2 f^2) d^4 x , where aG^2 = 4 pi Gm^2 / 3. The Euler-Lagrange equations for dS = 0 are k f + a G^2 f^2 h = 0 and k f - a G^2 f^2 h = 0 , where f is treated as a quantum field and h is treated as a classical variable determining the metric by the conformal transformations. Then k f - a G^2 f^2 h = 0 can be interpreted as k f - aG^2 { 0|f^2|0 } f = 0 and the flat vacuu Minkowski spacetime corresponds to f = m / aG and { 0|f^2|0 } = 0. Then perturb the spacetime by f(t) = m / aG + e(t) , for t}0, and , to first order in e(t), k f + aG^2 [m^2 / aG^2 + 2m e(t) / aG ] = 0 . Then {0|f^2|0} = (m aG/(2 pi)^3) INT(d^3k / 2 f_k) INT(0,t)e'(t')cos[2w_k(t-t')]dt' and, by Laplace transforms, e"(s) = (m^2 aG^2 / 8 pi^2) e'(0) { LL(s) / (1 - (m^2 aG^2 / 8 pi^2)LL(s)} , where LL(s) = INT(0,oo) (k^2 dk / w_k^4) INT(0,oo) exp(-st) sin(2wt) dt = = INT(0,oo) 2k^2 dk / w_k^3 (s^2 + 4w_k^2) . LL(s) is a decreasing function of |s| with a maximum at s=0, and LL(0) = INT(0,oo) k^2 dk / 2(k^2 + m^2)^(5/2) = 1 / 6 m^2 . From Laplace transform theory e'(t) will grow without bound if e"(s) has poles for real s, which exist if (m^2 a G^2 / 8 pi^2) LL(0) = (aG^2 / 48 pi^2) } 1 . Therefore a flat vacuum is unstable to perturbations if m^2 } 36 pi (hbar c / G) . If hbar = c = 1 and G = 1/mPL^2 then m^2 }113.1 mPL^2 , and m } 10.6 mPL . m = 100 mPL is due to more degrees of freedom in the standard model boson and fermion products of Hawking radiation from the black hole of mass m. The subsequent evolution of the universe process is outlined below following Gunzig, Geheniau, and Prigogine (1987), and using Narlikar and Padmanabhan (1986) (particularly section 13.8.1) and Kolb and Turner (1990) (particularly section 3.5, section 11.1, and Appendix A). As there are about (10^(-13) /10^(-33)^)3 = 10^60 spacelike vertices per cubic fermi, the energy density at the phase transition to the inflationary de Sitter phase should be about pdS = 10^81 GeV / fm^3 = 10^62 mPL / fm^3 = 10^101 mPL / cm^3 = 10^96 gm/cm^3. The time of the phase transition to the de Sitter phase is taken to be one lattice step in time, or the Planck time: tdS = 10^(-43) sec. Then, the temperature is TdS = 0.55 mPL / g*^(1/4) , where g* = 106.75 is the number of effectively massless degrees of freedom of bosons (weighted by 1) and of fermions (weighted by 7/8) for the standard model and temperatures above the weak boson range of about 300 GeV. Therefore TdS = 0.55 mPL / g*^(1/4) = 10^18 GeV = 10^31 degK. The size of the universe is then RdS = 10^(-4) to 10^(-2) cm. The 100 mPL black holes then begin to decay by Hawking radiation, emitting standard model bosons and fermions, all of which are effectively massless because the most massive of them, the Higgs scalar, is only 261 GeV in the D4-D5-E6 model. During the decay time of the black holes down to a stable Planck mass black hole state, the universe remains in the inflationary de Sitter phase. During the inflationary de Sitter phase, quantum density fluctuations dp are generally on the order of a few of the standard model bosons and fermions, so that dp is no more than about 1000 GeV. Since the primordial black holes are decaying down to the stable Planck mass, they are always at least that massive, so that at all times during the inflationary de Sitter phase dp / p { 10^3 GeV / 10^19 GeV = 10^(-16). Such density fluctuations are not able to cause structure formation by the standard mechanism, but the standard mechanism is not needed in the D4-D5-E6 model with the Layzer critical temperature cold dark matter mechanism of structure formation, described later herein. Such density fluctuations are small enough that the cosmic microwave background radiation should appear to be isotropic (except for the observed and understood dipole anisotropy) to at least dT/T { 10^(-16), and should not be observable by COBE. During the de Sitter inflationary phase, the universe consists of two components: the primordial black holes; and the emitted bosons, leptons, and hadrons. The black holes should be cold, and the emitted bosons, leptons, and hadrons hot, because if momentum is conserved during emission of, for example, a proton with mass m = 1 GeV from a black hole with at least Planck mass mPL = 10^19 GeV, then the velocity of the proton vp is at least 10^19 the velocity vPL of the black hole. As temperature is determined by kinetic energy, which in turn is proportional to mv^2, the proton kinetic energy should be at least 10^19 that of the black hole. The black holes are small and interact only gravitationally, so the components will not get in thermal equilibrium. The ordinary matter and radiation that is emitted by the black holes is hot, because the temperature of the black hole is T = 1 / 8 pi GM, a quantity that increases as the black hole shrinks to a maximum value at the stable Planck mass: TbhmPL = mPL^2 / 8 pi mPL = mPL / 8 pi = 4 x 10^17 GeV = 4 x 10^30 degK. Therefore there is no reheating problem at the end of inflation, and the inflationary universe consists of two components: cold dark matter black holes and hot ordinary matter (including radiation) The lifetime of a black hole of mass M (in grams) is abou (2560 pi / g*) G^2 M^3 sec, so that the lifetime of the primordial black holes with M = 100 mPL is (2560 pi / 106.75) G^2 M^3 = (2560 pi / 106.75) mPL^(-4) M^3 = = 75.3 x 10^6 / mPL = 75 x 10^(-13) GeV^(-1) = =75 x 10^(-3) x 6.6 ╨ 10^(-25) sec = 5 x 10^(-36) sec Then, at time tRW = 5 x 10^(-36) sec, the universe has a phase transition from the inflationary de Sitter phase to the present Robertson-Walker phase. At tRW, the temperature of the universe is TRW = 10^27 degK = 10^15 GeV and the size of the universe RRW = 10 cm. The density has then declined to about pRW = 10^75 gm/cm^3. The de Sitter inflationary phase can be considered as the decay of the initial black holes by Hawking radiation particle production with a consequent reduction of the de Sitter cosmological term to zero, at which time there occurs a phase transition to our present open matter-radiation Robertson-Walker universe. The decay of the primordial black holes in the inflationary phase is a non-equilibrium process with CP violation and baryon nonconservation, and could account for the particle-antiparticle asymmetry and the baryon-photon ratio of 5 x 10^(-10) that is observed now (Turner (1979) and Dolgov (1980)). Another possible mechanism for particle-antiparticle asymmetry is the weak force phase transition. The Robertson-Walker universe is open, and consists of two components: cold dark matter, stable Planck-mass residual black holes, and hot ordinary matter (including radiation, which dominates at this time tRW). The residual Planck-mass black holes left over after evaporation of the primordial black holes may constitute enough cold dark matter for the density of the universe to be the critical flat value. Since the cold black holes interact with the ordinary matter only gravitationally, their evolutions in the Robertson-Walker universe are discussed separately.Hot Ordinary Matter:
At T = 100 GeV = 10^15 degK; t = 10^(-10) sec; p = 10^28 gm/cm^3; and R = 10^14 cm = 10^9 km = 6 AU; the Higgs mechanism has been effective and the SU(2) weak force symmetry breaking has occurred. Farrar and Shaposhnikov have suggested that first order phase transition processes at this stage might account for particle-antiparticle asymmetry, but Huet and Sather, and Gavela, Hernandez, Orloff, and Pene say that QCD damping effects in bubble walls would reduce the asymmetry to a negligible amount. However, Nasser and Turok point out that when such other processes as formation of longitudinal Z condensate are taken into account the observed asymmetry might indeed be produced, and Farrar and Shaposhnikov have replied to Gavela et. al. and Huet et. al., stating that the Gavela-Huet calculational scheme violates unitarity and is unreliable. A nice overview is Farrar's 1994 invited talk at Stockholm. At T = 100 MeV = 10^12 degK; t = 10^(-3) sec; p = 10^10 gm/cm^3; and R = 10^17 cm = 10^12 km = 6 x 10^3 AU hadrons, such as protons and pions, can form and there is an SU(3) color force phase transition from quark-gluon plasma to a hadronic gas. At T = 1 MeV = 10^9 degK; t = 10 sec; p = 100 gm/cm^3; and R = 10^19 cm = 10^14 km = 6 x 10^5 AU; nucleosynthesis occurs; and neutrinos decouple before the temperature drops below the electron mass of 0.51 Mev, so that electron-positron annihilation entropy goes to photons and not neutrinos. At about T = 1 eV = 10^4 degK; t = 10^11 sec = 3 x 10^3 yr; p = 10^(-17) gm/cm^3; and R = 10^24 cm = 10^19 km = 3 x 10^5 pc; the density of matter has exceeded the density of radiation; photons decouple and the sky is transparent; matter recombines into atoms; a residual ionization freezes in; matter is dominant; and Jeans mass density fluctuations = 10^5 - 10^6 Msun can grow to form globular clusters (Narlikar and Padmanabhan (1986) section 8.4.2; Weinberg (1972)). At T = 10^(-3) eV = 3 degK; t = 10^18 sec = 10^10 yr; p = 10^(-29) gm/cm^3; and R = 10^28 cm = 10^23 km = 3 x 10^3 mpc; In certain regions (accretion disks of black holes, particle collisions, centers of stars, etc.) the local temperature is much higher The present value of p = 10^(-29) includes the cold black holes. More precisely, p should be about 4.5 x 10^(-30) gm cm^(-3) = 1.3 x 10^26 gm pc^(-3) that is accepted as the critical value for our universe to be flat (MacGibbon (1987); Kolb and Turner (1988)). With respect to the cosmological problems cited in section 5 of Linde (1984), it is evident that this approach to the D4-D5-E6 model has solved the singularity problem, the flatness problem, the homogeneity and isotropy problem, the horizon problem, and the baryon asymmetry problem. The D4-D5-E6 model breaks symmetry only at the Planck scale, for Spin(5) gravitation, and at the weak boson scale, for the SU(2) weak force and the Higgs mechanism. The D4-D5-E6 model has an 8-dimensional spacetime that is reduced geometrically to 4-dimensional spacetime. The D4-D5-E6 model has no domain structure for domain walls, no monopoles, and no gravitinos As to the vacuum energy (cosmological constant) problem, the D4-D5-E6 model may be ultraviolet finite to all orders in perturbation theory due to its octonionic structure (Kugo and Townsend (1983)), and the D4-D5-E6 model fundamental nonperturbative effects do not include particles other than Planck-mass black holes. Therefore the vacuum energy density of the D4-D5-E6 model may be exactly zero, consistent with the observed cosmological constant vacuum energy value of zero to an accuracy of one part in 10^118 (for theories that include general relativistic gravitation vacuum energy) or one part in 10^41 (for QCD alone) (Weinberg (1989)). The structure formation problem may be solved by magnetic structures in the Radiation Era of the universe, prior to recombination, and the Layzer mechanism of structure formation in a cold universe, as applied to the component of the universe consisting of cold Planck mass black holes. In the future, when the open Robertson-Walker universe has expanded enough to become very dilute, it may be enough like the original flat Minkowskian vacuum to repeat the quantum conformal fluctuation process. (Gunzig, Geheniau, and Prigogine (1987)Magnetic Structure in Radiation Era:
Battaner, Florido, and Jimenez-Vicente have considered that magnetic fields during the Radiation Era prior to recombination could be a source of structure formation. For many years, Anthony Peratt (see his book "Physics of the Plasma Universe", Springer-Verlag (1992)) has advocated electomagnetic processes as important in structure formation, as well as in formation of stars, where the problem of transfer of angular momentum to the planets and the problem of loss of magnetic fields in protostellar cloud condensation could both be explained by electromagnetic processes.Cold Black Holes and Layzer Structure Formation:
Assume that, after inflation, the universe evolves as a K=0 spatially flat Friedman universe such that any inhomogeneity can be contained in a spherical region within which the average density of mass is the same as the average density of the entire universe. At all times during the expansion of the Robertson-Walker universe, the cold dark Planck mass black holes constitute a critical point gas, and therefore unstable against fluctuations on all scales, particularly unstable against density fluctuations on the scale of the entire univers at that time (Layzer (1984)). The result is structure formation at all scales, as is observed, and no pre-existing perturbation anisotropy is needed or predicted. In the cold universe model of Layzer, in an expanding universe with zero curvature there is cluster formation on all scales and the clustering process continues forever. Although Layzer bases his cold universe model on hydrogen, it should be possible to base such a model on Planck-mass black holes as the cold dark matter in a manner consistent with the D4-D5-E6 model. Layzer's model begins with the Clausius equation 2K + (B - 1)U = 3PV , where K=kinetic energy, U=potential energy, P=pressure, V=volume, and B=2 for gravity, with an inverse square force law. In adiabatic expansion, d(K + U)/ dt + P dV/dt = 0. Then: d(K + U)/dt + (1/3) ((2K + U) / V) dV/dt = 0. If V is proportional to a^3, where a(t) is the cosmic scale factor, then (1/V) dV/dt = (1/a^3) da^3/dt = 3a'/a = 3H so that d(K + U)/dt + H(2K + U) = 0 Let U = SUM(i,j) -(1/2) G m'_i m'_j / r_ij , where G is Newton's constant, m'_i is the excess mass in a cell of volume dV_i, and r_ij is the distance between cell i and cell j. Let p" be the mean density, A = {p - p"} / p" be the relative amplitude of density fluctuations, and L be the average scale of density variations. Then, consider V to be a spherical region enough larger than the size L^3 that any fluctuations inside V can be considered to be contained entirely within V. In particular, the part of the universe outside V can then be considered to be of uniform density and its gravitational influence inside V can be ignored. Then U = SUM(i,j) -(1/2) G m'_i m'_j / r_ij = -2 pi G p" A L^2 p" V because INT(theta) INT(phi) INT(r) = 4 pi INT(r) , SUM(i in V) m'i = SUM(i in V) {p - p"} dVi = = SUM(i in V) p" A Vi = p" A Lú , {r_ij} = L , and SUM(j in V) dVj = V . If O is the temperature and N is the number of particles, P = (2K+U) / 3V = (N O / V) - (2 pi / 3) G A p"^2 L^2 . Now assume that V is such that, if V is compressed by dV, p" V remains constant, A = {p - p"} / p" remains constant, and L =prop= V^(1/3). Then dV/V = -dp"/p" = 3dL/L and dA = 0 , and dP = ( (N O / V) - (4/3)(2 pi /3) G A p" L^2 )(-dV/V) = = (P - (1/9) 2 pi G A p"^2 L^2) (-dV/V) Layzer's model is based on the expanding universe being like a vapor at its critical point, dP = 0, unstable against the growth of fluctuations at all scales. This requires a cold universe, so that |K| { |U| while 2K+U } 0. Since d(K + U)/dt + H(2K + U) = 0 if K+U is negative and 2K+U is positive, expansion causes K+U to decrease further, so that the magnitude of the (negative) potential energy U increases still further. If the magnitude of U increases enough so that 2K+U becomes negative, K+U increases. Physically, the increase of the magnitude of the potential energy U causes clusters of clumps of matter to form. The clumps within a cluster are accelerated by the fluctuating gravitational field due to the increase in the magnitude of the potential energy U. The motion of the clumps then increases the kinetic energy K and the pressure, quenching the instability. The processes act to keep the cold universe in its critical state, in which 2K+U = 0 and dP = 0. The critical value for the pressure, Pcrit, at dP = 0 , is Pcrit = (1/9) 2 pi G A p"^2 L^2. The total energy at Pcrit is E = K+U = U/3. Then: K =prop= a(t) ; U =prop= a(t) ; and E =prop= a(t) . The size of the clumps is of the scale L =prop= a^2 , because p"V is constant in time, p" =prop= a^(-3), U =prop= a, A is constant, and U = -2 pi G p" A L^2 p V. The mass M of clumps is proportional to p" L^3, so that M =prop= a^3. In the expanding universe, a heirarchy of larger and larger self-gravitating clusters forms, with the self-gravitating clusters of one stage forming the clumps in the clusters of the next stage. The diameter of the clusters is L =prop= M^(2/3). Layzer estimates that at the onset of instability against formation of self-gravitating clusters of clumps of matter, the relative amplitude of density fluctuations A = {p - p"} / p" is of the order 1/10 to 1/100. The energy per unit mass e of the cluster is given by e = (K+U) / p"V = (-(2/3)U + U) / p"V = = U / 3 p" V = (1/3)(-2 pi) p" A L^2 G . Since p" =prop= 1/V =prop= a^(-3) and L^2 =prop= a^4 : e =prop= a =prop= M^(1/3). Layzer notes that the relationship e =prop= M^(1/3) is consistent with observation from the scale of Jupiter and its satellites to the scale of clusters of galaxies. The clusters of clumps of matter are of the scale of volume V =prop= a^3, while the clumps of matter within self-gravitating cluster are of the scale of volume L^3 =prop= (a^2)^3 = a^6. Therefore, at some time after the beginning of the Friedman Robertson-Walker expansion, L will grow large enough to equal V. So, on very large scales, larger than clusters of galaxies, structures are formed after the universe has expanded enough so that the clumps are so large that they will not all fall as spherical units into a cluster in the potential wells of the Layzer process, but some will be stretched and pulled among nearby clusters, thus forming luminous filaments and sheets as well as voids.Mass Distribution Within Galaxies:
Consider the stage of the Layzer clustering heirarchy at which the self-gravitating clusters are the size of glaxies. The galactic-size cluster should be a self-gravitating spherical region that is gravitationally dominated by cold dark Planck mass black holes. Since the Planck mass black holes have very small (10^(-66) cm^2) cross section, they can be considered to be collisionless within the cluster. The cluster of dark matter can be considered to be an isothermal ideal gas of pressure pr, density p, and equation of state pr =prop= p. As it is self-gravitating, its equation of hydrostatic support is dpr/dr = (kT/m) dp/dr = -p GM(r) / r^2 , where k is Boltzmann's constant, T is temperature, and m is the Planck mass of the black hole, or d (r^2 dlnp)/dr) /dr = -(Gm/kT) 4pi r^2 p , which is equivalent to a collisionless system with distribution function (p_1/(2 pi kT/m)^(3/2)) exp((F - (1/2)V^2) / (kT/m)) , which gives p = p_1 exp(F / (kT/m)) as shown in sectiion 4.4.3(b) of Binney and Tremaine (1987). As they show, a nonsingular solution for this isothermal sphere is given by d (r'^2 dlnp'/dr') /dr' = -9 r'^2 p' where p' = p/p_0 , r' = r/r_0 , and r_0 = Sqrt(9 kT / m 4 pi G p_0) is the core radius. At r { 2 r_0 , p'(r') = 1/(1 + r'^2)^(3/2) , correct to about 5%. At r } 15 r_0 , p'(r') = (2/9) r'^(-2) , and the nonsingular isothermal sphere solution approaches the singular isothermal sphere solution p(r) = kT / m 2 pi G r^2 . The circular speed Vc at r is Vc^2 = G M(r) / r , where M(r) is the mass inside a sphere of radius r. From d (r^2 dlnp/dr) /dr = -(Gm/kT) 4 pi r^2 p , Vc^2 = -(kT/m) dlnp / dlnr . The circular speed Vc curve for the nonsingular isothermal sphere is similar to observed galactic rotation curves (figure 4-8, figure 10-1, and figure 10-2 of Binney and Tremaine (1987)). In section 10.1.6, Binney and Tremaine (1987) state that the density distribution of a dark halo that would give the observed flat rotation curves at large r "is also the density distribution for the isothermal sphere at large radii ... . However, there is no compelling theoretical argument to suggest why the dark halo should resemble an isothermal sphere." I disagree: Layzer clustering of cold dark Planck mass black holes is such a compelling theoretical argument. Binney and Tremaine (1987, section 4.4.3(b)) state "From the astrophysical point of view, the isothermal sphere has a very serious defect: its mass is infinite. Thus from equations 4-127 and Figure 4-7, we have that M = 2 s^2 r / G [s^2 = kT / m] at large r. Clearly no real astrophysical system can be modeled over more than a limited range of radii with a divergent mass distribution. On the other hand, the rotations curves of spiral galaxies (section 10.1.6 and MB section 8-3) are often remarkably flat out to great radii, and this suggests that we try to construct models that deviate from the isothermal sphere only far from their cores." I disagree with the statement that the isothermal sphere mass distribution is a defect. The dark Planck mass black holes should exist throughout the universe at a density sufficient to make Omega =1. That density is about 1.88 x 10^(-29) h^2 gm/cm^3 (Kolb and Turner (1990)). The galactic rotation curve halo density is on the order of at least (it could be about an order of magnitude greater) 0.01 Msun/pc^3 (Binney and Tremaine (1987), section 10.1.6), or about 0.01 x 2 x 10^33 / (3 x 10^18)^3 = = .0007 x 10^(-21) = 7 x 10^(-25) gm/cm^3. The minimum rotation curve halo density is therefore at least about 3 x 10^4 times greater than the Omega = 1 critical density. In the Layzer clustering model, the isothermal sphere density p at large r varies as p =prop= 1 / r^2. In it, p at r = 3 r_0 = 10 kpc (roughly the 8.5 kpc distance from the sun to the center of our galaxy) is 4 x 10^4 times greater than p at r = 600 r_0 = 2 Mpc (the median radius of clusters of galaxies is about 3 h^(-1) Mpc (Binney and Tremaine (1987), table 1-4)). As the bulk of the mass in the universe is in the cold dark matter, Layzer's model should describe structure formation on scales large enough that gravity is the dominant force (structures at planetary scale or larger). On smaller scales, where electromagnetism or other forces are stronger, the cold dark matter (being very weakly interacting with respect to forces other than gravity) should be ignored or considered as a background, with the standard hot big bang model applying to the small scale processes. Except for gravitational interaction, the cold dark matter would be decoupled from the hot ordinary matter and radiation at all times after the end of inflation. The radiation would decouple from the ordinary matter about 200,000 years after the end of inflation. Structure in the Layzer process is always subhorizon in size, so that anisotropy of the microwave background is small-angular scale, O {{ 1deg = decoupling Hubble scale (Kolb and Turner (1990), section 9.6.2), and not measurable by COBE. With two classes of matter (cold dark matter forming structure according to Layzer's theory and ordinary matter having a lesser role to play on gravitational scales because it is much less massive), the fact that the ordinary Jeans mass after decoupling is about the mass of a globular cluster indicates an ordinary process of globular cluster formation within the structures already formed at that time by Layzer's cold matter process. As was stated in discussion about ordinary matter, in the future, when the open Robertson-Walker universe has expanded enough to become very dilute, it may be enough like the original flat Minkowskian vacuum to repeat the quantum conformal fluctuation process. (Gunzig, Geheniau, and Prigogine (1987))COBE - Hubble Constant:
COBE and other observations can be accounted
for by a Hubble constant of H_0 = 30 km/sMpc,
according to a review of experimental observations
by Liddle, Lyth, Schaefer, Shafi, and Viana.
Bartlett, Blanchard,Silk, and Turner had earlier
proposed H_0 = 30 in a flat universe
with Omega_b = 0.1.
H_0 = 30 gives an age of the universe of 18 Gyr.
(The Bartlett et. al. article has a misprint of 1.8 Gyr.)
An alternative is to use a high H_0 of 80 and
add a cosmological constant.
H_0 = 30 gives a CDM power spectrum with shape
that agrees with observations.
H_0 = 30 gives abundance of clusters of galaxies
that agrees with cluster x-ray observations.
H_0 = 30 and Omega_b = 0.1 gives a baryonic mass
ratio that agrees with cluster x-ray observations.
Degree-scale CBR anisotropy in the H_0 = 30 model
should be about 1.5 times that of standard CDM.
Experiments that "directly" measure H_0 ,
including Hubble Space Telescope observations
to be made of Cepheid variables, depend
on the cosmological "distance ladder" whose
lower rungs may contain systematic errors.
They also note that, if we live in a part of
the universe that is underdense by 70% out
to 20 h^-1 Mpc, our present observational
methods would measure H_0 to be 2.5 times true H_0.
Linde,
Linde, and Mezhlumian consider a stationary self-reproducing
inflationary universe, and conclude that, if we are "typical
observers", we should see ourselves as living at the center
of a universe in which the density where we are appears to be
less than the density far out at the horizon. Their model
is therefore consistent with a locally high value of
H_0 (such as 85) and a globally low value (such as 30).
Di Nella and
Paturel at Lyon observe that "The distribution of galaxies up
to a distance of 200 Mpc (650 million light-years) is flat and
shows a structure like a shell roughly centered on the
Local Supercluster (Virgo cluster). This result clearly
confirms the existence of the hypergalactic large scale
structure noted in 1988. This is presently the largest
structure ever seen."
Big Bang Gravitational Radiation:
Gravity waves might account for some or even all of the anisotropy of the cosmic background radiation, but they should be seen more at angular scales of more than about 3 degrees, and much less at one degree or smaller scales. (Taubes 1994) Gravitational radiation can account for all observed anisotropy of the cosmic background radiation if the vacuum energy during inflation were about 10^16 GeV, which could well be the case for an inflationary de Sitter universe starting at Planck energy 10^19 GeV (Gott (1982)) and continuing to a phase transition to a Robertson-Walker universe at 10^16 GeV.The inflationary de Sitter 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)
Such gravity waves should be seen more at angular scales of more than about 3 degrees, and much less at one degree or smaller scales. (Taubes 1994) Narlikar and Padmanabhan (1986), section 13.8.2, discuss inflation due to quantum conformal fluctuations such as should arise in the D4-D5-E6 model. Kolb and Turner (1990), section 8.4, discuss the production of gravitons by de Sitter inflation, also natural for the D4-D5-E6 model. They also discuss the possibility of de Sitter fluctuations in other light fields, particularly the photon field that might produce the primeval magnetic fields needed to seed the astrophysical magnetic fields observed today.