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Probable approach to solution of the cosmological constant problem

Probable approach to solution of the cosmological constant problem. Vladimir Burdyuzha Miami-2009, December15, 2009. Introduction. A.Einstein introd. Λ -term as property of space G μν + Λ g μν = - 8 π G N T μν If we put Λ -term in the right side-energy form

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Probable approach to solution of the cosmological constant problem

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  1. Probable approach to solution of the cosmological constant problem Vladimir Burdyuzha Miami-2009, December15, 2009

  2. Introduction A.Einstein introd. Λ-term as property of space Gμν+ Λ gμν= - 8π GN Tμν If we put Λ-term in the right side-energy form Gμν= - 8π GN Tμν + Λ gμν The modern value of this form energy is: ρDE = ρΛ ~ 10 -47 (GeV)4 ~ 10 -29 g/cm3 In Planck epoch vacuum energy had density ρDE = ρΛ ~ 2 x 10 76 (GeV)4 ~ 1094 g/cm3

  3. Some exercises In a homogeneous, spherical system ρ = E/V where V=(4/3) π R3 MPl= (ħc/GN)1/2 ;LPl= (GNħ/c3)1/2 LPl= ħ / MPlc ρcr= (3H02)/8πGN E ~ (V/LPl3) MPlGμν≡ Rμν- (1/2)R gμν ρ ~ MPl4

  4. It is crisis of physics 123 orders unexplained difference in vacuum energy were interpreted as crisis of physics

  5. Modern cosmological paradigm A new cosmological paradigm - multiverse. It is eternally increasing fractal which consists of a much number of parts (universes) with different constants of bound, masses of particles and other constants of nature. Our Universe is one of them age of which is near 3.8x10 9 years. During this time our Universe came a thorny path ( evolution).

  6. The Universe evolution Inflation, reheating, radiation epoch, matter epoch, vacuum dominated epoch is now. Universe expands accelerated from z ~ 0.7 because of ρgr <ρDE Ωtot = 1; 4% - baryon component (Ω ), 23 % - dark matter(ΩDM), 73% - dark energy (ΩDE). Ωi= ρi /ρcrρcr= (3H02)/8πGN

  7. What is vacuum? In classical physics: vacuum is the simplest system-world without particles and this world is flat; In quantum physics: vacuum is a system of quantum condensates arising in processes of relativistic phase transitions; In geometrical physics: vacuum is a state in which geometry of space-time is not deformed.

  8. More general Vacuum is a stable state of quantum fields without excitation of wave modes (non-wave modes are condensates) w ≡ p/ρ; p = - ρ if w = -1 vacuum energy if w > -1 quintessence (time evolution) if w < -1 phantom energy

  9. DE models DE models proposed to account for the present cosmic acceleration include: (i) cosmological constant w=-1 is a special member of this class; (ii) quintessence models which are inspired by the simplest class of inflation models (a scalar field rolling down); it is dynamical model; (iii) the Chaplygin gas (CG) model (p~ - 1/ρ);

  10. DE models (iv) phantom DE; (v) oscillating DE; (vi) models with interactions between DE and DM; (vii) scalar-tensor DE models; (viii) modified gravity as alternative; (ix) DE driven by quantum effects; (x) higher dimensional “braneworld” models; (xi) holographic dark energy arXiv:0812.2768

  11. Really a vacuum dominated epoch is now ΩDE ~ 0.73 - 0.14 < 1+w < 0.12 (95% CL) Astrophys. J. Suppl. 180 330 (2009) 1+w = 0.013 +0.066–0.068 (0.11 syst) CERN COURIER, March (2009) Why vacuum energy

  12. Vacuum in the Universe is the combination of a large number of mutual connected subsystems: a gravitational condensate; ---------------------------- ---------------------------- a Higgs condensate; a quark-gluon condensate. How these subsystems were coordinated? Which influence had compactification?

  13. The total energy of vacuum A small positive value of Λ must be in our Universe Λ = ΛQF + ΛGVC Gravitation vacuum condensate (topological microdefects – wormholes; micromembranes; microstrings, monopoles). There is some analogy between the known vacuum structures and a hypothetical structures of the gravitation vacuum (condensates of the quark-gluon type consist of topological structures- instantons). It is necessary a small positive value of Λ only!

  14. Quintessence period of the vacuum evolution 3-dim. topological defects (wormholes) renormalize Λ-term: Λ=Λo - (κħ2c23)/(768π2) From 1019GeV to 150 MeV was sharply quintessence period of the Universe evolution, because of in positive density energy of vacuum negative contributions of quantum field condensates were carried during phase transit.

  15. Phase transitions Exact chain of phase transitions is unknown P→[SU(5)]SUSY→[U(1)xSU(2)xSU(3)]SUSY→ 1019 GeV 1016GeV ... → U(1)xSU(2)xSU(3)→U(1)xSU(3)→U(1) 100 GeV 150 MeV

  16. Vacuum components of the SM ΛQF = ΛEW + ΛQCD = - ρEW - ρQCD Higgs condensate ρEW=-mH2 mw2/2g2- (1/128π2)(mH4+3mZ4+6mW4 - -12mt4) If mH~ 160 GeV then ρEW ~ - (120 GeV)4 (G. Vereshkov et al. 2008)

  17. QCD condensate ρQCD = - (b/32) < 0│ Gika Gika │0 > b= 9 + 8Tg (mu + md+ 0.8 ms); Tg= (1.5GeV)-1 ρQCD ~ - (265 MeV)4 quark-hadron phase transition quenches10 orders (120/0.265)4 ~ 4x1010 from (1.22x1019/0.265)4 ~ 4.5 x 10 78

  18. QCD phase transition The chiral symmetry SU(3)L x SU(3)R was not exact. Pseudo-Goldstone bosons are physical realization of this symmetry breaking for 150MeV. π mesons are the lightest particles of octet of PG states and they characterize ground state, so they characterize QCD vacuum(Shuryak1996) Ya. Zel’dovich has got the next formula: Λ = 8 π GN2 m6 h-4 (D. Kirzhnits)

  19. Vacuum condensate of the last phase transition From which we have: ΩΛ= ρΛ/ ρcr= Λ c2 / 3 H02 if mπ~138 MeV, H0=70.5 (km/sec)/Mpc then ΩΛ~ 0.73 In this moment vacuum energy has hardened in the relative units.

  20. How many orders leave before now (0.265/1.8x10-12 )4 ~ 5 x 1044 ifρDE ~ (1.8 x 10 -12GeV)4 It seems to me a new principle is necessary to introduce. It may be a holographic principle.

  21. Some physical principles 1. Principle of relativity; 2. Principle of equivalence; 3. Principle of entropy increase; 4. Principle of least action; 5. Heisenberg uncertainly principle; 6. Le Chatelier principle; 7. Pauli’s exclusion principle et al. These principles caused progress of physics

  22. Entropy Holographic principle is connected with entropy L. Bol’tzmann: entropy is number of different microscopic states (thermodynamical definition) C. Shannon: entropy is measure of uncertainly.

  23. Holographic principle This principle introduced G. Hooft in 1993 year (gr-qc/9310006). In 1995 L. Susskind introduced a holographic limit. Holographic principle asserts that physics of a 3- dim system may be described by a theory acting on it 2-dim boundary. The holographic limit puts restriction on a number of freedom degrees which can exist inside a limited surface.

  24. Holographic limit J.Bekenstein has shown that for BH entropy is proportional to ¼ an area of horizon of events expressed in Planckian units. If our Universe to be limited and to be measured this limitation then density of vacuum energy is: ρ ≤ 3M4pl/ 8 S; here: M pl =1; S ≤ π R2 Mpl2 S – entropy of the Universe. C. Balazs and I. Szapidi (hep-th/0603133)

  25. The equation of holography And in holographic limit density of energy is: ρ ≤ (3/8πS) MPl4 if R=1028 cm, then ρ ≤ 10-57. It is upper limit on the middle density of vacuum energy in the Universe That is during expansion new quantum states are produced with increasing Hubble horizon, continuous enrichment of which requests some energy.

  26. Limitations When holographic approach is right ? General relativity is a bright example of holographic theory. But quantum theory is not holographic theory ( R. Bousso, 1999). Therefore, holographic approach in cosmology can work only when our Universe took Friedmann, that is after last relativistic phase transition (E ~ 150 MeV).

  27. Calculations For E ~150 MeV, t ~10 -5 sec and R = 3x105 cm was a causal horizon in that instant. Then (1028/ 3x105)2 ~ 1045 During 4x1017 sec (13.8x109 years) the Universe had been losing 45 orders on organization of new quantum states. Probably, vacuum energy, cosmological constant, Λ-term and DE are the same notion.

  28. Some seditious ideas Thermodynamics of BH is to be traced to the thermal nature of the Minkowski vacuum. Einstein’s equations have thermodynamic nature (T. Jacobson: 1995 and 2006). This equation is the equation of the Universe state. Gravitation on a macroscopic scale is manifestation of vacuum thermodynamics. ρ = 3M4pl / 8S is the Friedmann equation.

  29. Some explanations The Universe expands be cooled step by step. If our Universe expands accelerated then non-equilibrium thermodynamics takes place and the Clausius relation dS = δQ/T is right. Here: dS -entropy through horizon, δQ - energy flux through horizon, T- Unruh temperature, seen an accelerated observer inside horizon.

  30. Conclusion 1. During period of vacuum evolution from 1019 GeV to 150 MeV 78 orders of vacuum energy of 123 were compensated by vacuum condensates before “hardness” of relation of the Universe components (0.04; 0.23; 0.73). 2. The holographic approach may solve cosmological constant problem. This method can quench more 45 orders since new quantum states were produced for expansion.

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