Abstract
The Planck scale physics is still unknown and the full quantum theory of gravity might reveal the mysteries of the Universe beyond the Planck scale. We consider that the maximum available temperature of a system could be higher than the Planck temperature or not. We obtain the maximum available temperature of a system with particles that obey deformed boson statistics. We evaluate the density number of particles and use the hoop conjecture to evaluate the density number of two-particles which form a blackhole as a function of temperature and deformation parameter; q. One can argue that at a certain critical value of temperature, the density number of blackholes will be dominant and this critical temperature is the maximum available temperature for the system. We show that the temperature beyond the Planck temperature is available for more deformed boson statistics while for the ordinary bosons, the maximum available temperature is . In fact, we take a look at the beyond Planck temperature in the early universe and deduce that the deformed statistics is consistent with the very high temperature at the early universe.
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