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

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

New mathematics Calzetti, Giavalisco, Ruffini A&A, 1988, 1989, 1991; Ruffini, Song, Taraglio A&A,1988, 1990; Lattanzi, Ruffini, Vereshchagin AIP, 2003, PRD 2005, AIP a) Statistical mechanics, correlations and discreteness in the fractal Ruffini, Song, Taraglio, A&A,1988  ' 1 degree Correlation length Giavalisco-Ruffini, 1987, adopted by Pietronero Upper cut-off in the fractal structure R cutoff ¼100 Mpc Possible connection to the ‘ino’ mass M cell =(M pl /M ino ) 3 M ino b) Macroscopic gravity: Ruffini, Vereshchagin, Zalaletdinov, et al. 2007

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

New astrophysics

E=10 54 ergs seconds 10 3 counts/s seconds 10 3 counts/s

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

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?

Timescales There are three timescales in the problem: 1.t pp - pair production timescale:t pp ~ t c =(  T nc) -1 ; 2.t br – cooling timescale:t br ~  -1 t c ; 3.t hyd – expansion timescale:t hyd ~ c/R 0.

Interactions

Relativistic Boltzmann equations

Numerical method 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

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, erg/cm 3 flat initial spectra

First example electrons and positrons with tiny fraction of photons

ConcentrationsTemperaturesChemical potentials Starting with pairs (first example) Starting with photons (second example)

Compton scattering Start with the distribution functions: where  kT/(m e c 2 ) is the temperature,  =  /(m e c 2 ) 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:

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,  =0 only in thermal equilibrium, so what we found is called kinetic equilibrium.

Kinetic equilibrium Homogeneous isotropic, spatially homogeneous plasma is characterized by two quantities: total energy density  i and total number density  n i (initial conditions). Therefore, two unknowns  k and  k can be found easily, and energy 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!

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:

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 < 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: ]

The horizon paradox in standard cosmology a)Invariance of the laws of physics with space and time b)Spatial energy density homogeneity (Friedmann) c)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)