Probable approach to solution of the cosmological constant problem

1
Probable approach to solution of the cosmological
constant problem

• Vladimir Burdyuzha
• Miami-2009, December15, 2009

2
Introduction

• A.Einstein introd. ?-term as property of space
• Gµ? ? gµ? - 8p GN Tµ?
• If we put ?-term in the right side-energy form
• Gµ? - 8p GN Tµ? ? gµ?
• The modern value of this form energy is
• ?DE ?? 10 -47 (GeV)4 10 -29 g/cm3
• In Planck epoch vacuum energy had density
• ?DE ?? 2 x 10 76 (GeV)4 1094 g/cm3

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Some exercises

• In a homogeneous, spherical system
• ? E/V where V(4/3) p R3
• MPl (hc/GN)1/2 LPl
  (GNh/c3)1/2
• LPl h / MPl c ?cr
  (3H02)/8pGN
• E (V/LPl3) MPl Gµ? Rµ? -
  (1/2)R gµ?
• ? MPl4

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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).

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The Universe evolution

• Inflation, reheating, radiation epoch, matter
  epoch,
• vacuum dominated epoch is now. Universe expands
  accelerated from z 0.7 because of ?gr lt ?DE
• Otot 1 4 - baryon component (O ),
• 23 - dark matter(ODM),
• 73 - dark energy (ODE).
• Oi ?i /?cr ?cr
  (3H02)/8pGN

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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.

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More general

• Vacuum is a stable state of quantum fields
  without excitation of wave modes (non-wave
• modes are condensates) w p/? p - ?
• if w -1 vacuum energy
• if w gt -1 quintessence (time evolution)
  
• if w lt -1 phantom energy

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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/?)

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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 arXiv0812.2768

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Why vacuum energy

• Really a vacuum dominated epoch is now
• ODE 0.73
• - 0.14 lt 1w lt 0.12 (95 CL)
• Astrophys. J. Suppl. 180 330 (2009)
• 1w 0.013 0.066 0.068 (0.11
  syst)
• CERN COURIER, March (2009)

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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?

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The total energy of vacuum

• A small positive value of ? must be in our
  Universe
• ? ? QF ?GVC
• 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 ?
  only!

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Quintessence period of the vacuum evolution

• 3-dim. topological defects (wormholes)
• renormalize ?-term ??o - (?h2c23)/(768p2)
• From 1019 GeV 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.

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Phase transitions

• Exact chain of phase transitions is unknown
• P?SU(5)SUSY?U(1)xSU(2)xSU(3)SUSY?
• 1019 GeV
  1016 GeV
• ... ? U(1)xSU(2)xSU(3)?U(1)xSU(3)?U(1)
• 100 GeV
  150 MeV

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Vacuum components of the SM

• ?QF ?EW ?QCD - ?EW - ?QCD
• Higgs condensate
• ?EW-mH2 mw2/2g2- (1/128p2)(mH43mZ46mW4 -
• 
  -12mt4)
• If mH 160 GeV then ?EW - (120 GeV)4
  
• (G. Vereshkov et al. 2008)

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QCD condensate

• ?QCD - (b/32) lt 0 Gika Gika 0 gt
• b 9 8Tg (mu md 0.8 ms) Tg (1.5GeV)-1
• ?QCD - (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

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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. p mesons are the lightest particles
  of octet of PG states and they characterize
  ground state, so they
• characterize QCD vacuum(Shuryak1996)
• Ya. Zeldovich has got the next formula
  
• ? 8 p GN2 m6 h-4 (D. Kirzhnits)

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Vacuum condensate of the last phase transition

• From which we have
• O? ??/ ?cr ? c2 / 3 H02
• if mp138 MeV, H070.5 (km/sec)/Mpc
• then O? 0.73
• In this moment vacuum energy has
  hardened in the relative units.

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How many orders leave before now

• (0.265/1.8x10-12 )4 5 x 1044
• if ?DE (1.8 x 10 -12 GeV)4
• It seems to me a new principle is necessary
  to introduce. It may be a holographic principle.

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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. Paulis exclusion principle et al.
• These principles caused progress of physics

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Entropy

• Holographic principle is connected with entropy
• L. Boltzmann entropy is number of different
• microscopic states (thermodynamical definition)
• C. Shannon entropy is measure of uncertainly.

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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.

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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 ? 3M4pl/
  8 S here M pl 1 S p R2 Mpl2
  
• S entropy of the Universe.
• C. Balazs and I. Szapidi (hep-th/0603133)
  

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The equation of holography

• And in holographic limit density of energy
• is ? (3/8pS) MPl4 if R1028 cm, then ?
  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.

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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).

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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, ?-term and DE are the
• same notion.

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Some seditious ideas

• Thermodynamics of BH is to be traced to the
  thermal nature of the Minkowski vacuum.
  Einsteins 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.
• ? 3M4pl / 8S is the Friedmann equation.

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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 dQ/T is right.
  
• Here dS -entropy through horizon, dQ - energy
• flux through horizon, T- Unruh temperature,
  seen an accelerated observer inside horizon.

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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.