A new look at some general puzzles of Universe

1. A new look at some general puzzles of Universe Our Goal: To Open the Padlocks of Nature! PlamenFiziev, DmitriiShirkov BLTF, JINR, Dubna FIFTEENTH   LOMONOSOV   CONFERENCE   ON ELEMENTARY PARTICLE   PHYSICS Moscow, 18 of August 2011

2. Alternatives to/for the Higgs mechanismQuantum GravityWhat was there BEFORE the Big Bang?Physics on manifolds with variable topological dimension and reduction of space dimensions ? ? ?

3. CP, T violation(discovered in 1956-1964)=> Nobel Price in Physics (1980) 1. LEFTand RIGHTare not equivalent 2. the TIME is not reversible Baryon-Antibaryon asymmetry In the visible universe we have only barions: #ANTIBARIONS =10-18#BARIONS Problem: stillNOconvincing theoretical explanation ? ? ? P.F., D.Shirkov 2011 New idea: asymmetric SPACE-TIME

4. The QFT g '4 model in 4D and 2D dimensions D. V. Shirkov, Particles and Nuclei (PEPAN), Lett. No 6 (162), 2010 The coupling running here is defined by the only diagram the 1st one-loop contribution to 4-vertex function. It behaves quite differently in the “low-Q, 4-dim” region and in the “high-Q, 2-dim” one. Explicitly:

5. Grand Unification by Dimensional Reduction New brave Great Unification by Dimensional Reduction instead of Leptoquarks UV fixed point for g and Grand Unification by Dimensional Reduction

6. The basic problemof the standard approach to quantum gravity is caused by the very classical Einstein-Hilbert action in D = 1 + d : The same in the Standard Model without Higgs boson The quantum gravity is not renormalizable for dimension D > 2 since A New Idea: lower topologicaldimension at small distances D. V. Shirkov, Particles and Nuclei (PEPAN), Lett. No 6 (162), 2010

7. Greg Landsberg, Paris, July 2010

10. Jonas Mureika and Dejan Stojkovic Detecting Vanishing Dimensions via Primordial Gravitational Wave Astronomy PRL 106, 101101 (April, 2011) Lower dimensionality at higher energies has manifold theoretical advantages as recently pointed out by Anchordoqui et al. [arXiv:1003.5914]. Moreover, it appears that experimental evidence may already exist for it: A statistically significant planar alignment of events with energies higher than TeV has been observed in some earlier cosmic ray experiments. We propose a robust and independent test for this new paradigm. Since (2 + 1)-dimensional spacetimes have no gravitational degrees of freedom, gravity waves cannot be produced in that epoch. This places a universal maximum frequency at which primordial waves can propagate, marked by the transition between dimensions. We show that this cutoff frequency may be accessible to future gravitational wave detectors such as the Laser Interferometer Space Antenna.

11. Relation of the above (relativistic) examples with the modern solid state physics of two-dimensional crystals graphene, fulerene, carbon nanotubes, carbon nanobuds, etc: Nobel Prize in Physics 2010

12. Examples of 2-dim manifolds with variable geometries (surfaces of buttles) D. V. Shirkov, A new scientific area Good problems: Solve the Klein-Gordon eq., the Dirac eq. the heat eq., e.t.c., on that kind of variable geometries.

13. KGEq forTEST PARTICLES: 1090 baryons - Eddington number In the STATIC case we assume (at least locally) The Klein GordonEquation on Manifolds with variable topologicaldimension We consider the toy models in which the physical space is a continuous merger : andTHE TIME IS GLOBAL ! Then we have local solutions: With common frequency:

14. Wave Equation in (1+2)-dim Static AxU Shape function: Standard anzatz: Simple problems: The only nontrivial problem: Z-equation centrifugal term The basic Theorem:

15. Some Explicit Examples Two Cylinders of Constant Radii R and r < R, Connected Continuously by a Part of Cone:

16. Continuous spectrum of states Exact Solutions In terms of the Bessel Functions In the limit one obtains the S-matrix Continuous spectrum states No signals with m ≠ 0 from 2D into 1D part due to the centrifugal force

17. The resonant states M = 0 - S–matrix poles A nontrivial dependence on the mass M:

19. According to our basic theorem we reduce the problem to Schrodinger-typeODEqwith potential The exact solution can be written in terms of the HYPERGEOMETRIC FUNCTIONS. The spectrum is real for some

20. Expansion: 5% for 109years What was there BEFORE the Big Bang? Is the Big Bang actually a transition from a LOWER DIMENSIONAL world to the FOUR DIMENSIONAL ONE??? HST • New idea • P.F., D.Shirkov: n

21. ??? How to find the physically admissible solutions and their dynamics The answer: SOLVING EINSTEN EQUATIONS A remarkable result: Many of the needed exact solutions for (1+2)-dim static AxU (axial symmetric universes) were pointed out in arXiv 10041510.

22. According to the Hawking & Penrose theorems the GR dynamics in general physical conditions unavoidable leads to singularities of space-time. What happens after we reach such singularity ??? ?“The end of time …?”A new look at the problem: For the simple example - E. Kasner (1921) solution around the singularity the very dimension of the space changes in two different ways: 3d cube 2d 1d

23. (1+2)-dim Time Dependent AxU Consider and with variable compactification radius

24. Einstein eqs for time dependent (1+2) –dim AxU Determinant: Field equations: Axial symmetry Conservation of the momentum:

25. DIMENSIONALREDUCTIONPOINTS and DIMENSIONALTRANSITIONPOINTS Symbolically:

26. Three vacuum solutions of Einstein eqs In 1. 2. 3. - expanding thread to a cylinder Related by Lorentz transformations: - a static cone: - moving cone

28. Solutions of KGEq on (1+2)-dim AxU with positive term can be described in the Legendre functions.

29. Solutions for the (1+2) AxU filled with “dust” Homogeneous Monge(1784)-Ampere(1820) equation: Implicit general solution: Godograph of the velocity v(t,z) General solution of the Cauchy problem:

30. Three classes of special solutions involving one arbitrary function : are arbitrary constants.

31. Dynamics of DRPs in (1+2) AxUwith “dust” 1. Creaton and anihilation ofpairs of DRPs is possible. 2. Dynamics of DRPsfor the three types of functions : for xi = -1/2,1,2,3; for xi = -1/2,1,2,3; are the zeros of

32. The solutions of matter equations where under a new restriction::

33. A signal, related to degree of freedom specific for the higher-dim part does not penetrate into the smaller-dimensional part, • because of the inertial forces at the junction. • Such forces exist inevitably in curved space times and in spaces with variable dimension. CONCLUDING REMARKS

34. 2.The specific spectrum of scalar excitations characterizes the junction geometry. A new idea: To explain the observed particles spectra by geometry of the junction between domains of the space-time with different topological dimension. CONCLUDING REMARKS

35. 3. Instead of fixing the radii of compactificationρ(t, z) ≥ 0 of the compactified dimensions we let them to be space-time functions, obtained solving Einstein equations. Ifρ(t, z) → ∞ , we have a flat space. In the opposite case, when ρ(t, z) → 0 the topological dimension of the space-time reduces. For (1+d)-case see P.P.F. arXiv:1012.3520 [math-ph]. CONCLUDING REMARKS

36. 4. The set of the dimensional reduction point - DPR may have complicated structure and dynamics: 5.Critical behavior of the solutions for test particles around DPR exist and depends both on geometry and motion. CONCLUDING REMARKS

37. 6.The parity violation, due to the asymmetry of space geometry could yield the CP-andT violation. This gives a hope to recover a simple and natural reason on a basic level for explanation of the real situation with C, P, and T properties of the particles relating these properties to the global properties of the Universe. Another recent attempt, based on local properties of the space-time: see paper: arXiv:1107.1575 Mark J Hadley “The asymmetric Kerr metric as a source of CP violation”. CONCLUDING REMARKS

38. 7. Baryon-antibaryon asymmetry versus asymmetry of the space-time ??? Can it be related with asymmetry of the very space-time ??? CONCLUDING REMARKS

39. 8. The Big Bang = ? = time transformation of space dimensions123 ??? CONCLUDING REMARKS MOVIE 3

40. Thank You for your attention