A Century of Cosmology

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(From) massive neutrinos and inos and the upper
cutoff to the fractal structure of the Universe
(to recent progress in theoretical cosmology)
M. Lattanzi, R. Ruffini, G.V. Vereshchagin

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

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Introduction
Cosmology is paradoxically simple, complex and
subtle

• Simplicity
• Einstein
• Friedmann
• Gamov vs. Zeldovich

Complexity observations
Help to understand this complexity comes from
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New mathematics
a) Statistical mechanics, correlations and
discreteness in the fractal
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, AA,1988

• Calzetti, Giavalisco, Ruffini AA, 1988, 1989,
  1991 Ruffini, Song, Taraglio AA,1988, 1990
  Lattanzi, Ruffini, Vereshchagin AIP, 2003, PRD
  2005, AIP 2006.

b) Macroscopic gravity Ruffini, Vereshchagin,
Zalaletdinov, et al. 2007
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New physics neutrinos
Absolute mass measure (KATRIN)
Arbolino, Ruffini, AA,1988
Galactic halos with m?9 eV, a specific
counterexample to Gunn and Tremaine limit
Tremaine, Gunn PRL,1979
Oscillations CERN-Gran Sasso Experiment
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New astrophysics
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E1054 ergs
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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
ee- annihilation in the lepton era
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Pair plasma

• Where do ee pairs exist?
• Energy range 0.1 lt E lt 100 MeV
• (below we dont 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 ee pairs take
  place
• How the plasma evolves?

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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.

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Interactions
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Relativistic Boltzmann equations
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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 ODEs
• 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 DFs
• the code allows solution of a 1D problem
  (spherically symmetric)
• Non-degenerate plasma
• degenerate case is technically possible, but
  numerically is much more complex

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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

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First exampleelectrons and positrons with tiny
fraction of photons
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Starting with pairs (first example)
Starting with photons (second example)
Concentrations
Temperatures
Chemical potentials
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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

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

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Kinetic equilibrium

• Homogeneous isotropic, spatially homogeneous
  plasma is
• characterized by two quantities total energy
  density ? ?i and total
• number density ? ni (initial conditions).
  Therefore, two unknowns ?k and
• jk 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!

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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

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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 lt10-12 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
arXiv0707.3250
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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)