TY - JOUR

T1 - Statistical mechanics and the description of the early universe I.

AU - Pessah, Martin Elias

AU - F. Torres, Diego

AU - Vucetich, H.

PY - 2001/7/3

Y1 - 2001/7/3

N2 - We analyze how the thermal history of the universe is influenced by the
statistical description, assuming a deviation from the usual Bose-Einstein,
Fermi-Dirac and Boltzmann-Gibbs distribution functions. These deviations
represent the possible appearance of non-extensive effects related with the
existence of long range forces, memory effects, or evolution in fractal or
multi-fractal space. In the early universe, it is usually assumed that the
distribution functions are the standard ones. Then, considering the evolution
in a larger theoretical framework will allow to test this assumption and to
place limits to the range of its validity. The corrections obtained will change
with temperature, and consequently, the bounds on the possible amount of
non-extensivity will also change with time. We generalize results which can be
used in other contexts as well, as the Boltzmann equation and the Saha law, and
provide an estimate on how known cosmological bounds on the masses of neutrinos
are modified by a change in the statistics. We particularly analyze here the
recombination epoch, making explicit use of the chemical potentials involved in
order to attain the necessary corrections. All these results constitute the
basic tools needed for placing bounds on the amount of non-extensivity that
could be present at different eras and will be later used to study primordial
nucleosynthesis.

AB - We analyze how the thermal history of the universe is influenced by the
statistical description, assuming a deviation from the usual Bose-Einstein,
Fermi-Dirac and Boltzmann-Gibbs distribution functions. These deviations
represent the possible appearance of non-extensive effects related with the
existence of long range forces, memory effects, or evolution in fractal or
multi-fractal space. In the early universe, it is usually assumed that the
distribution functions are the standard ones. Then, considering the evolution
in a larger theoretical framework will allow to test this assumption and to
place limits to the range of its validity. The corrections obtained will change
with temperature, and consequently, the bounds on the possible amount of
non-extensivity will also change with time. We generalize results which can be
used in other contexts as well, as the Boltzmann equation and the Saha law, and
provide an estimate on how known cosmological bounds on the masses of neutrinos
are modified by a change in the statistics. We particularly analyze here the
recombination epoch, making explicit use of the chemical potentials involved in
order to attain the necessary corrections. All these results constitute the
basic tools needed for placing bounds on the amount of non-extensivity that
could be present at different eras and will be later used to study primordial
nucleosynthesis.

KW - gr-qc

KW - astro-ph

KW - cond-mat.stat-mech

U2 - 10.1016/S0378-4371(01)00235-7

DO - 10.1016/S0378-4371(01)00235-7

M3 - Journal article

VL - 297

SP - 164

EP - 200

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1-2

ER -