Statistical mechanics and the description of the early universe I.: Foundations for a slightly non-extensive cosmology

Abstract

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.

32 pages, to appear in Physica A (2001)

References in corpus (2)

• Solar reaction rates, non-extensivity and quantum uncertainty
• Statistical mechanics and the description of the early universe II. Principle of detailed balance and primordial 4He formation

Cited by in corpus (12)

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• Primordial Nucleosynthesis with varying fundamental constants: A semi-analytical approach
• Non-extensive statistics and its effects on cosmology
• Non-Gaussian thermostatistical considerations upon the Saha equation
• Non-Gaussian Effects of the Saha's Ionization in the Early Universe
• Thermal leptogenesis in nonextensive cosmology
• Statistical mechanics and the description of the early universe II. Principle of detailed balance and primordial 4He formation
• Thermodynamic properties of the solid and metal electrons in the nonextensive quantum statistics with a nonextensive parameter transformation
• Thermodynamical Test of Non Extensive Thermostatistics
• An alternative method for solving the Gaussian integral
• A possible correction of the Saha curve for non-equilibrium states
• WIMP Freeze-out dynamics under Tsallis statistics