Probable approach to Probable approach to solution of the cosmological solution of the cosmological

constant problemconstant problemVladimir BurdyuzhaVladimir Burdyuzha

Miami-2009, December15, 2009Miami-2009, December15, 2009

IntroductionIntroduction

A.Einstein introd. A.Einstein introd. ΛΛ-term as property of space-term as property of space

GGμνμν + + ΛΛ g gμνμν = - 8= - 8ππ G GNN T Tμνμν

If we put If we put ΛΛ-term in the right side-energy form-term in the right side-energy form

GGμνμν = - 8= - 8ππ G GNN T Tμνμν + + ΛΛ g gμνμν

The modern value of this form energy is: The modern value of this form energy is:

ρρDE DE = = ρρΛΛ ~ 10 ~ 10 -47-47 (GeV) (GeV)4 4 ~ 10 ~ 10 -29-29 g/cm g/cm33

In Planck epoch vacuum energy had densityIn Planck epoch vacuum energy had density

ρρDE DE = = ρρΛΛ ~ 2 x 10 ~ 2 x 10 76 76 (GeV)(GeV)4 4 ~ 10~ 1094 94 g/cmg/cm33

Some exercisesSome exercises

In a homogeneous, spherical systemIn a homogeneous, spherical system

ρρ = E/V where V=(4/3) = E/V where V=(4/3) ππ R R33

MMPlPl= (ħc/G= (ħc/GNN))1/2 1/2 ;; LLPlPl= (G= (GNNħ/cħ/c33))1/21/2

LLPlPl= ħ / M= ħ / MPl Pl c c ρρcr cr = (3H= (3H0022)/8)/8ππGGNN

E ~ (V/LE ~ (V/LPlPl33) M) MPl Pl GGμνμν ≡ R≡ Rμνμν - (1/2)R g- (1/2)R gμνμν

ρρ ~ M ~ MPlPl44

It is crisis of physicsIt is crisis of physics

123 orders unexplained 123 orders unexplained

difference in vacuum energy difference in vacuum energy

were interpreted as crisis of physicswere interpreted as crisis of physics

Modern cosmological paradigm Modern cosmological paradigm

A new cosmological paradigm - multiverse. It is A new cosmological paradigm - multiverse. It is eternally increasing fractal which consists of a eternally increasing fractal which consists of a much number of parts (universes) with much number of parts (universes) with different constants of bound, masses of different constants of bound, masses of particles and other constants of nature. Ourparticles and other constants of nature. Our

Universe is one of them age of which is nearUniverse is one of them age of which is near

3.8x10 3.8x10 9 9 years. During this time our Universe years. During this time our Universe came a thorny path ( evolution). came a thorny path ( evolution).

The Universe evolutionThe Universe evolution

Inflation, reheating, radiation epoch, matter epoch,Inflation, reheating, radiation epoch, matter epoch,

vacuum dominated epoch is now. Universe expands vacuum dominated epoch is now. Universe expands accelerated from z ~ 0.7 because of accelerated from z ~ 0.7 because of ρρgr <gr < ρρDE DE

ΩΩtottot = 1; = 1; 44 % % - baryon component (- baryon component (ΩΩ ), ),

23 % - dark matter23 % - dark matter(Ω(ΩDMDM), ),

7373 % % - dark energy - dark energy (Ω(ΩDEDE).).

ΩΩi i = = ρρii / /ρρcr cr ρρcr cr = (3H= (3H0022)/8)/8ππGGN N

What is vacuum?What is vacuum?

In classical physicsIn classical physics: vacuum is the simplest : vacuum is the simplest system-world without particles and this world system-world without particles and this world

is flat;is flat; In quantum physicsIn quantum physics: vacuum is a system of: vacuum is a system of quantum condensates arising in processes of quantum condensates arising in processes of relativistic phase transitions; relativistic phase transitions; In geometrical physicsIn geometrical physics: vacuum is a state in : vacuum is a state in which geometry of space-time is not deformed.which geometry of space-time is not deformed.

More generalMore general

Vacuum is a stable state of quantum fields Vacuum is a stable state of quantum fields without excitation of wave modes (non-wave without excitation of wave modes (non-wave

modes are condensates) w modes are condensates) w ≡ p/≡ p/ρρ; p = - ; p = - ρρ if w if w = -1= -1 vacuum energy vacuum energy if w if w > -1 quintessence (time evolution) > -1 quintessence (time evolution) if w if w << -1 phantom energy -1 phantom energy

DE modelsDE models

DE models proposed to account for the present DE models proposed to account for the present cosmic acceleration include:cosmic acceleration include:

(i) cosmological constant w=-1 is a special (i) cosmological constant w=-1 is a special member of this class;member of this class;

(ii) quintessence models which are inspired by (ii) quintessence models which are inspired by the simplest class of inflation models (a scalar the simplest class of inflation models (a scalar field rolling down); it is dynamical model;field rolling down); it is dynamical model;

(iii) the Chaplygin gas (CG) model (p(iii) the Chaplygin gas (CG) model (p~ - 1/~ - 1/ρρ););

DE modelsDE models

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

Why vacuum energyWhy vacuum energy

Really a vacuum dominated epoch is nowReally a vacuum dominated epoch is now

ΩΩDE DE ~ 0.73~ 0.73

- 0.14 - 0.14 << 1+w 1+w < 0.12 (95% CL)< 0.12 (95% CL)

Astrophys. J. Suppl. Astrophys. J. Suppl. 180180 330 (2009) 330 (2009)

1+w = 0.013 1+w = 0.013 +0.066+0.066 –0.068–0.068 (0.11 syst (0.11 syst))

CERN COURIER, March (2009)CERN COURIER, March (2009)

Vacuum in the Universe is the Vacuum in the Universe is the combination of a large number of combination of a large number of

mutual connected subsystems:mutual connected subsystems:

a gravitational condensate;a gravitational condensate; -------------------------------------------------------- -------------------------------------------------------- a Higgs condensate;a Higgs condensate; a quark-gluon condensate.a quark-gluon condensate. How these subsystems were coordinated?How these subsystems were coordinated? Which influence had compactification?Which influence had compactification?

The total energy of vacuumThe total energy of vacuum

A small positive value of A small positive value of ΛΛ must be in our Universe must be in our Universe

ΛΛ = = ΛΛ QF QF + + ΛΛGVCGVC

Gravitation vacuum condensate (topological Gravitation vacuum condensate (topological microdefects – wormholes; micromembranes; microdefects – wormholes; micromembranes;

microstrings, monopoles). There is some analogy microstrings, monopoles). There is some analogy between the known vacuum structures and a between the known vacuum structures and a hypothetical structures of the gravitation vacuum hypothetical structures of the gravitation vacuum (condensates of the quark-gluon type consist of (condensates of the quark-gluon type consist of topological structures- instantons). topological structures- instantons).

It is necessary a small positive value of It is necessary a small positive value of ΛΛ only! only!

Quintessence period of the vacuum Quintessence period of the vacuum evolution evolution

3-dim. topological defects (wormholes) 3-dim. topological defects (wormholes)

renormalize renormalize ΛΛ-term: -term: ΛΛ==ΛΛo o - (- (κκħħ22cc2233)/(768)/(768ππ22) )

From 10From 101919 GeV to 150 MeV was sharply GeV to 150 MeV was sharply

quintessence period of the Universe evolution,quintessence period of the Universe evolution,

because of in positive density energy of vacuumbecause of in positive density energy of vacuum

negative contributions of quantum fieldnegative contributions of quantum field

condensates were carried during phase transit. condensates were carried during phase transit.

Phase transitionsPhase transitions

Exact chain of phase transitions is unknownExact chain of phase transitions is unknown

PP→[SU(5)]→[SU(5)]SUSYSUSY→[U(1)xSU(2)xSU(3)]→[U(1)xSU(2)xSU(3)]SUSYSUSY→→

101019 19 GeV 10GeV 101616 GeV GeV

... →... → U(1)xSU(2)xSU(3)→U(1)xSU(3)→U(1) U(1)xSU(2)xSU(3)→U(1)xSU(3)→U(1)

100 GeV 150 MeV100 GeV 150 MeV

Vacuum components of the SMVacuum components of the SM

ΛΛQFQF = = ΛΛEWEW + + ΛΛQCDQCD = - = - ρρEW EW - - ρρQCDQCD

Higgs condensateHiggs condensate

ρρEWEW=-m=-mHH2 2 mmww

22/2g/2g22- (1/128- (1/128ππ22)(m)(mHH44+3m+3mZZ

44+6m+6mWW4 4 --

-12m-12mtt44))

If mIf mH H ~ 160 GeV then ~ 160 GeV then ρρEW EW ~ - (120 GeV)~ - (120 GeV)4 4

(G. Vereshkov et al. 2008) (G. Vereshkov et al. 2008)

QCD condensateQCD condensate

ρρQCDQCD = - (b/32) < = - (b/32) < 00│ G│ Gikikaa G Gikik

aa │0 > │0 >

b= 9 + 8Tb= 9 + 8Tgg (m (muu + m + md d + 0.8 m+ 0.8 mss); T); Tg g = (1.5GeV)= (1.5GeV)-1-1

ρρQCD QCD ~ - (265 MeV)~ - (265 MeV)4 4

quark-hadron phase transition quenches10 ordersquark-hadron phase transition quenches10 orders

(120/0.265)(120/0.265)44 ~ 4x10 ~ 4x1010 10

from (1.22x10from (1.22x101919/0.265)/0.265)44 ~ 4.5 x 10 ~ 4.5 x 10 7878

QCD phase QCD phase transitiontransition

The chiral symmetry SU(3)The chiral symmetry SU(3)LL x SU(3) x SU(3)RR was not was not exact. Pseudo-Goldstone bosons are physical exact. Pseudo-Goldstone bosons are physical realization of this symmetry breaking for 150MeV. realization of this symmetry breaking for 150MeV. ππ mesons are the lightest particles of octet of PG mesons are the lightest particles of octet of PG states and they characterize ground state, so theystates and they characterize ground state, so they

characterize QCD vacuum(Shuryak1996)characterize QCD vacuum(Shuryak1996) Ya. Zel’dovich has got the next formula: Ya. Zel’dovich has got the next formula: ΛΛ = 8 = 8 ππ G GNN

2 2 mm6 6 hh-4-4 (D. Kirzhnits) (D. Kirzhnits)

Vacuum condensate of the last phase Vacuum condensate of the last phase transition transition

From which From which we have: we have:

ΩΩΛΛ = = ρρΛΛ/ / ρρcr cr = = ΛΛ c c2 2 / 3 H/ 3 H0022

if mif mππ~138 MeV, H~138 MeV, H00=70.5 (km/sec)/Mpc=70.5 (km/sec)/Mpc

then then ΩΩΛΛ~ 0.73~ 0.73

In this moment vacuum energy has In this moment vacuum energy has hardened in the relative units.hardened in the relative units.

How many orders leave before nowHow many orders leave before now

(0.265/1.8x10(0.265/1.8x10-12 -12 ))4 4 ~ 5 x 10~ 5 x 104444

ifif ρρDE DE ~ (1.8 x 10 ~ (1.8 x 10 -12-12 GeV) GeV)44

It seems to me a new principle is It seems to me a new principle is necessary to introduce. It may be necessary to introduce. It may be a holographic principle.a holographic principle.

Some physical principlesSome physical principles

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

EntropyEntropy

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

Holographic principleHolographic principle

This principle introduced G. Hooft in This principle introduced G. Hooft in 1993 year (gr-qc/9310006). In 1995 L. 1993 year (gr-qc/9310006). In 1995 L. Susskind introduced a holographic limit. Susskind introduced a holographic limit. Holographic principle asserts that physics Holographic principle asserts that physics of a 3- dim system may be described by a of a 3- dim system may be described by a theory acting on it 2-dim boundary. theory acting on it 2-dim boundary.

The holographic limit puts restriction on The holographic limit puts restriction on a number of freedom degrees which can a number of freedom degrees which can exist inside a limited surface. exist inside a limited surface.

Holographic limit Holographic limit

J.Bekenstein has shown that for BH entropy is J.Bekenstein has shown that for BH entropy is proportional to ¼ an area of horizon of events proportional to ¼ an area of horizon of events

expressed in Planckian units. If our Universe to expressed in Planckian units. If our Universe to be limited and to be measured this limitation then be limited and to be measured this limitation then density of vacuum energy is: density of vacuum energy is: ρρ ≤ 3M ≤ 3M44

plpl/ 8 S; / 8 S;

here: M here: M plpl =1; S =1; S ≤ ≤ ππ R R2 2 MMplpl22

S – entropy of the Universe. S – entropy of the Universe.

C. Balazs and I. Szapidi (hep-th/0603133) C. Balazs and I. Szapidi (hep-th/0603133)

The equation of holographyThe equation of holography

And in holographic limit density of energyAnd in holographic limit density of energy

is: is: ρρ ≤ (3/8 ≤ (3/8ππS) MS) MPlPl4 4 if R=10 if R=1028 28 cm, then cm, then ρρ ≤ 10 ≤ 10-57-57. .

It is upper limit on the middle density of It is upper limit on the middle density of vacuum energy in the Universe That is during vacuum energy in the Universe That is during expansion new quantum states are produced expansion new quantum states are produced with increasing Hubble horizon, continuous with increasing Hubble horizon, continuous enrichment of which requests some energy. enrichment of which requests some energy.

LimitationsLimitations

When holographic approach is right ?When holographic approach is right ?

General relativity is a bright example of General relativity is a bright example of

holographic theory. But quantum theory is not holographic theory. But quantum theory is not holographic theory ( R. Bousso, 1999). holographic theory ( R. Bousso, 1999).

Therefore, holographic approach in cosmology Therefore, holographic approach in cosmology

can work only when our Universe took can work only when our Universe took Friedmann, that is after last relativistic phase Friedmann, that is after last relativistic phase transition (E ~ 150 MeV).transition (E ~ 150 MeV).

CalculationsCalculations

For E ~150 MeV, t ~10 For E ~150 MeV, t ~10 -5 -5 sec and R = 3x10sec and R = 3x1055 cm cm was a causal horizon in that instant. Then was a causal horizon in that instant. Then

(10(102828/ 3x10/ 3x1055))2 2 ~ 10~ 1045 45

During 4x10During 4x1017 17 sec (13.8x10sec (13.8x1099 years) the Universe years) the Universe

had been losing 45 orders on organization of had been losing 45 orders on organization of new quantum states. Probably, vacuum energy,new quantum states. Probably, vacuum energy,

cosmological constant, cosmological constant, ΛΛ-term and DE are the-term and DE are the

same notion.same notion.

Some seditious ideasSome seditious ideas

Thermodynamics of BH is to be traced to the Thermodynamics of BH is to be traced to the thermal nature of the Minkowski vacuum. thermal nature of the Minkowski vacuum. Einstein’s equations have thermodynamic Einstein’s equations have thermodynamic nature (T. Jacobson: 1995 and 2006). This nature (T. Jacobson: 1995 and 2006). This equation is the equation of the Universe state. equation is the equation of the Universe state.

Gravitation on a macroscopic scale is Gravitation on a macroscopic scale is manifestation of vacuum thermodynamics. manifestation of vacuum thermodynamics.

ρρ = 3M = 3M44plpl / 8S is the Friedmann equation. / 8S is the Friedmann equation.

Some explanations

The Universe expands be cooled step by step.The Universe expands be cooled step by step. If our Universe expands accelerated then If our Universe expands accelerated then non-equilibrium thermodynamics takes placenon-equilibrium thermodynamics takes place and the Clausius relation dS = and the Clausius relation dS = δδQ/T is right.Q/T is right. Here: dS -entropy through horizon, Here: dS -entropy through horizon, δδQ - energyQ - energy flux through horizon, T- Unruh temperature, flux through horizon, T- Unruh temperature,

seen an accelerated observer inside horizon. seen an accelerated observer inside horizon.

Conclusion Conclusion

1. During period of vacuum evolution from 101. During period of vacuum evolution from 1019 19

GeV to 150 MeV 78 orders of vacuum energy GeV to 150 MeV 78 orders of vacuum energy of 123 were compensated by vacuum of 123 were compensated by vacuum condensates before “hardness” of relation of condensates before “hardness” of relation of the Universe components (0.04; 0.23; 0.73). the Universe components (0.04; 0.23; 0.73).

2. The holographic approach may solve 2. The holographic approach may solve cosmological constant problem. This method cosmological constant problem. This method

can quench more 45 orders since new can quench more 45 orders since new quantum states were produced for expansion.quantum states were produced for expansion.