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{hbar ,c}{2pi ,l_p,K_B}right) .
Highlights
Introduction and motivationIn the standard relativistic description, matter (which is described by the matter Lagrangian: L, in the Einstein-Hilbert (EH) action), is responsible for the spatial curvature of space-time, which is represented in the Einstein’s equations through Gαβ
Back-reaction effects are very important in general relativity, and in particular, they are essential to make a correct and accurate description of the initial state of the universe, which is believed to be given by a de Sitter metric
In this work we shall make a semiclassical description of such back-reaction effects, without consider non-commutative aspects of space-time, or the origin of quantum spinor fields that originate these quantum effects
Summary
Introduction and motivationIn the standard relativistic description, matter (which is described by the matter Lagrangian: L, in the Einstein-Hilbert (EH) action), is responsible for the spatial curvature of space-time, which is represented in the Einstein’s equations through Gαβ. A de Sitter space-time is the maximally symmetric vacuum solution of Einstein’s field equations with a positive cosmological constant , which corresponds to a positive vacuum energy density and negative pressure.
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