Me. Pessah et al., Statistical mechanics and the description of the early universe. (I). Foundations for a slightly non-extensive cosmology, PHYSICA A, 297(1-2), 2001, pp. 164-200
We analyze how the thermal history of the universe is influenced by the sta
tistical description, assuming a deviation from the usual Bose-Einstein, Fe
rmi-Dirac and Boltzmann-Gibbs distribution functions. These deviations repr
esent the possible appearance of non-extensive effects related with the exi
stence of long-range forces, memory effects, or evolution in fractal or mul
ti-fractal space, In the early universe, it is usually assumed that the dis
tribution 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 c
hange 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 S
aha law, and provide an estimate on how known cosmological bounds on the ma
sses of neutrinos are modified by a change in the statistics. We particular
ly analyze here the recombination epoch, making explicit use of the chemica
l potentials involved in order to attain the necessary corrections. All the
se results constitute the basic tools needed for placing bounds on the amou
nt of non-extensivity that could be present at different eras and will be l
ater used to study primordial nucleosynthesis. (C) 2001 Elsevier Science B.
V. All rights reserved.