Quantum thermodynamics in a static de Sitter space-time and initial state of the universe

Abstract

Using Relativistic Quantum Geometry we study back-reaction effects of space-time inside the causal horizon of a static de Sitter metric, in order to make a quantum thermodynamical description of space-time. We found a finite number of discrete energy levels for a scalar field from a polynomial condition of the confluent hypergeometric functions expanded around $r=0$. As in the previous work, we obtain that the uncertainty principle is valid for each energy level on sub-horizon scales of space-time. We found that temperature and entropy are dependent on the number of sub-states on each energy's level and the Bekenstein-Hawking temperature of each energy level is recovered when the number of sub-states of a given level tends to infinity. We propose that the primordial state of the universe could be described by a de Sitter metric with Planck energy $E_p=m_p{c}^2$, and a B-H temperature: $T_{BH}=\left(\frac{\hslash c}{2\pi l_p{K}_B}\right)$.

Version accepted in EPJC. arXiv admin note: text overlap with arXiv:1904.11599

Cited by in corpus (1)

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