1. Space Vacuum and its Synthetic Model Vladimir Burdyuzha Vladimir Burdyuzha Astro-Space Center, Lebedev Physical Institute, Russian Academy of Sciences, Moscow Miami 2007, 18 December, Fort Lauderdale, Florida

2. The refusal of the idea that vacuum is emptiness – the conceptual statement of modern physics

3. What is vacuum? In classical physics: vacuum is the simplest system – world without particles and this world is flat (pseudo-euclidean) In quantum physics: vacuum is a system of vacuum condensates arising in processes of relativistic phase transitions during early Universe evolution

4. In geometrical physics: Vacuum is a state in which geometry of space- time is not deformed More general: vacuum is a stable state of quantum fields without excitation of wave modes (non – wave components are condensates)

5. The physical vacuum is a medium having specific properties: It is a carrier of energy and it has pressure; It has a interior microscopic structure; It has excited states of wave and soliton types; It is a medium without resistance; The wave excitements are usual particles, soliton excitements are Higgs bosons.

6. Vacuum has important differences from usual medium: It is impossible to connect a definite reference system; It has a specific equation of state ε=-p It look the same from any reference system.

7. This equation of state provides automatically constancy of energy density and pressure in all processes of heating and cooling The constant density of vacuum energy was first appeared in Einstein’s equations as lambda-term: R µν – (1/2) R g µν = 8π G N T µν + Λ g µν

8. What is vacuum? Other words vacuum is a medium with a very complicated structure which had changed during early Universe evolution and which can be rebuilt by change of matter existence

9. Vacuum in the Universe is the combination of a large number of mutual connected subsystems: a quark-gluon condensate; a Higgs condensate; a gravitational condensate and others. How these subsystems were coordinated? How compensation of huge positive and negative contributions did take place?

10. Probably, Cosmological constant, Vacuum energy, Lambda-term and Dark energy is the same notion Besides, dark energy is the reason of accelerated expansion of the Universe after red shift z ~ 0,5 (before this red shift our Universe had decelerated expansion)

12. Contents of the Universe Baryons: 4% Dark matter: 23% Dark energy: 73% Massive neutrino: 0.1% Spatial curvature: very close to 0 IN GOLDEN ERA OF COSMOLOGY: “We know a lot about our Universe but understand very little”

13. Some years ago we have only three variants of DE: cosmological constant w= -1 quintessence w> -1 phantom energy w< -1 w ≡ p/ε p - pressure; ε -density of energy

14. Today we have: 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); (iii) the Chaplygin gas (CG) model (p~ - 1/ε);

15. CG appears to be the simplest model attempting to unify DE and nonbaryonic cold dark matter (DM) (iv) phantom DE; (v) oscillating DE; (vi) models with interactions between DE and DM; (vii) scalar-tensor DE - models; (viii) modified gravity DE - models; (ix) DE driven by quantum effects; (x) higher dimensional “braneworld” models; (xi) holographic dark energy (V.Sahni and A.Starobinsky astro-ph/0610026)

16. Dark Energy models considered: the ones most commonly used in papers The equation of state of a “cosmic dark fluid”: Negative w < -1/3 gives an accelerating expansion Two levels of difficulty: 1) A constant EOS w. 2) A variable EOS w(z)

17. Vacuum Condensates: A gravitation condensate: E~ 10 19 GeV A quark-gluon condensate: E~ 0.15 GeV

18. Gravitational Vacuum Condensate It produced after first relativistic phase transition P→D 4 x [SU(5)] SUSY → or after Universe birth from ”nothing” or from “something”. It represents the collection of topological structures (defects) in curvatures of space-time. Topological structures have the Planck size: D = 3 →WH; D = 2 →micro-membranes; D = 1→micro-strings; D = 0→gas of point defects (monopoles). After Universe inflation these defects were smoothed, stretched and broken up and now they are perceived as structures of Λ-term.

19. Gravitational Vacuum Condensate Topological structures exist in gravitational vacuum and they are consequences of the parametrizational noninvariance of quantum geometrodynamics (deWitt,1967). The energy density of the system of topological defects contains a constant part corresponding to worm-holes and members of types 1/a 3 ;1/a 2 ; 1/a corresponding a gas of point defects, micro-membranes, and micro-strings

20. A new experimental fact Dark energy was already boosting the expansion of the Universe as long as nine billions years ago. Investigators using NASA’s Hubble Space Telescope announced this result based on an analysis of the 24 most distant supernovae during last two years (press-release STSci- 2006-52)

21. A theoretical fact Probably in the time of the Universe birth the temperature was near 10 32 K(10 19 GeV) and symmetry was very high. During cooling the Universe was losing symmetry by phase transitions. Nobody knows an exact chain of these transitions. The low energy part of this chain must be the next: → D 4 x SU(3) x U(1) → D 4 x U(1) 100 GeV 150 MeV

22. It was a quantum chromodynamical phase transition Chiral QCD symmetry SU(3) L x SU(3) R is not exact and pseudogoldstone bosons are physical realization of this symmetry breaking. It leads to appearance an octet of pseudoscalar Goldstone states in spectrum of particles. π- mesons, as the lightest particles of this octet, carry the main contribution in periodic collective motion of a nonperturbative vacuum condensate In this process π-mesons are excitations of the ground state (QCD vacuum).D.A.Kirzhnits(2000)

23. Zeldovich’s approximation Λ = 8 π G 2 m π 6 h -4 Ω Λ = ρ Λ /ρ cr ≡ Λ c 2 / 3H 0 2 If H 0 = 72.5 (km/sec)/Mpc then Ω Λ ~ 0.7 Therefore very probably that in the present epoch vacuum energy is a vacuum condensate of last relativistic phase trans.

24. Space vacuum is a complex systems of condensates of quantum fields which were produced in the result of relativistic phase transitions during cooling of the Universe. We researched a quark-gluon phase transition after which vacuum energy has hardened and it has become cosmological constant.

25. Before this a vacuum component of the Universe was changing by jumps during phase transitions since vacuum condensates of quantum fields carried a negative contribution in vacuum positive energy density. This quintessence period of the Universe evolution took place during first parts of a second when our Universe was losing the high symmetry.

26. Λ-term (Vacuum Energy) Probably Λ-term must consist of some components: Λ = Λ QF + Λ WH + Λ G

27. Λ-term consists of some components Λ SM = - (m 2 H m 2 w ) /2g 2 - - (1/128π 2 )(m 4 H + 3m 4 z + 6m 4 w - 12 m 4 t ) λ G is formed by a gravitational vacuum condensate λ G = (9π 2 /2 ǽ 2 )λ n

28. Final results 1. 10 19 GeV → 150 MeV - quintessence period of vacuum evolution t«1 sec 2. 150 MeV → 10 -4 eV – vacuum energy is practically constant t » 1 sec 3. gravitational vacuum condensate has also fixed time in our Universe (if we live in multiverse) 4. 3-dimensional topological defects renormalize Λ- term (Astrophys. Space Sci. 305, 235, 2006)