A Century of Cosmology August 27-31, 2007, Venice

1. (From) massive neutrinos and inos and the upper cutoff to the fractal structure of the Universe (to recent progress in theoretical cosmology) A Century of Cosmology August 27-31, 2007, Venice M. Lattanzi, R. Ruffini, G.V. Vereshchagin

2. Introduction “Cosmology is paradoxically simple, complex and subtle…” Simplicity: Einstein Friedmann Gamov vs. Zeldovich Complexity: observations Help to understand this complexity comes from:

3.  ' 1 degree New mathematics a) Statistical mechanics, correlations and discreteness in the fractal Calzetti, Giavalisco, Ruffini A&A, 1988, 1989, 1991; Ruffini, Song, Taraglio A&A,1988, 1990; Lattanzi, Ruffini, Vereshchagin AIP, 2003, PRD 2005, AIP 2006. Correlation length Giavalisco-Ruffini, 1987, adopted by Pietronero Upper cut-off in the fractal structure Rcutoff¼100 Mpc Possible connection to the ‘ino’ mass Mcell=(Mpl/Mino)3Mino Ruffini, Song, Taraglio, A&A,1988 b) Macroscopic gravity: Ruffini, Vereshchagin, Zalaletdinov, et al. 2007

4. New physics: neutrinos Absolute mass measure (KATRIN) Arbolino, Ruffini, A&A,1988 Galactic halos with m=9 eV, a specific counterexample to Gunn and Tremaine limit Tremaine, Gunn PRL,1979 Oscillations: CERN-Gran Sasso Experiment

5. New astrophysics

6. E=1054 ergs 103 counts/s 103 counts/s 103 counts/s seconds seconds seconds 103 counts/s 103 counts/s 103 counts/s seconds seconds seconds 103 counts/s 103 counts/s 103 counts/s seconds seconds seconds 103 counts/s 103 counts/s 103 counts/s seconds seconds seconds

7. The Standard Cosmology • Invariance of the laws of physics with space and time • Spatial energy density homogeneity (Friedmann) • The horizon paradox: equal CMB temperature in causally unrelated regions (R.B. Partridge, 1975) Attempts of solution: Misner Mixmaster, inflation, etc. last scattering surface e+e- annihilation in the lepton era

8. Pair plasma Where do e+e–pairs exist? Energy range: 0.1 < E <100 MeV (below we don’t have pairs, above there are muons and other particles) We have this in cosmology as well as in GRB sources (in both cases we can assume the plasma to be homogeneous and isotropic) Pair plasma is optically thick, and intense interactions between photons and e+e– pairs take place How the plasma evolves?

9. Timescales There are three timescales in the problem: • tpp - pair production timescale: tpp~ tc=(Tnc)-1; • tbr – cooling timescale: tbr ~  -1 tc; • thyd – expansion timescale: thyd ~ c/R0.

10. Interactions

11. Relativistic Boltzmann equations

12. Numerical method Aksenov, Milgrom, Usov (2004) • Finite grid in the phase space to get ODE instead of PDE basic variables are energies, velocities and angles • Gear method to integrate ODE’s several essentially different timescales: stiff system • Control conservations of energy and particle number “spreading” in the phase space to account for finiteness of the grid • Isotropic DF’s the code allows solution of a 1D problem (spherically symmetric) • Non-degenerate plasma degenerate case is technically possible, but numerically is much more complex

13. Our initial conditions We are interested in time evolution of the plasma, with initially: a) electrons and positrons with tiny fraction of photons b) photons with tiny fraction of electrons and positrons the smallest energy density, 1024 erg/cm3 flat initial spectra

14. First exampleelectrons and positrons with tiny fraction of photons

20. Starting with pairs (first example) Starting with photons (second example) Concentrations Temperatures Chemical potentials

21. Compton scattering Start with the distribution functions: where =kT/(mec2) is the temperature, j =m/(mec2) is the chemical potential, ± denotes positrons and electrons,  stands for photons. Suppose that detailed balance is established with respect to the Compton scattering This means reaction rate for this process vanishes: This leads to:

22. Pair production and annihilation Suppose now that detailed balance with respect to the pair production and annihilation via the process is established as well. From the condition that the corresponding reaction rate vanishes we find that the chemical potentials of electrons, positrons and photons must be the same: However, there is no restriction that the latter is zero! In fact, j =0only in thermal equilibrium, so what we found is called kinetic equilibrium.

23. Kinetic equilibrium Homogeneous isotropic, spatially homogeneous plasma is characterized by two quantities: total energy density i and total numberdensity ni (initialconditions).Therefore, two unknowns k and jk can be found easily, andenergy densities and concentrations for each component can be determined. Compton scattering, pair production and annihilation as well as Coulomb scatterings cannot change the total number of particles. To depart from kinetic equilibrium three-particle reactions are needed!

24. Thermal equilibrium When we consider in addition to above two-particle reactions also relativistic bremsstrahlung, double Compton scattering, three-photon annihilation: and require that the reaction rates vanish for any of them, we arrive to true thermal equilibrium condition:

25. Conclusions • Thermal equilibrium is obtained for electron-positron-photon plasma by using kinetic equations and accounting for binary and triple interactions • The timescale of thermalization is always shorter than the dynamical one both in cosmology and in GRBs: there is enough time to get thermal spectrum of photons even just with electron-positron pairs • If inverse triple interactions are neglected then thermal equilibrium never reached and pairs disappear on timescales <10-12 sec. (as in Cavallo, Rees 1978 scenario) Aksenov, Ruffini, Vereshchagin, “Thermalization of a non-equilibrium electron-positron-photon plasma”, Phys. Rev. Lett. (2007), in press [arXiv:0707.3250]

26. The horizon paradox in standard cosmology • Invariance of the laws of physics with space and time • Spatial energy density homogeneity (Friedmann) • equal CMB temperature in causally unrelated regions follows necessarily from the previous two assumptions, in view of the above treatment It follows from these considerations, in particular, that also the initially cold Universe of Zeldovich would not be viable and would also lead to a hot Big Bang (as predicted by Gamow)