https://doi.org/10.1140/epjc/s10052-019-7433-9
Regular Article - Theoretical Physics
Quantum thermodynamics in a static de Sitter space-time and initial state of the universe
1
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata, Argentina
2
Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata, Argentina
* e-mail: mbellini@mdp.edu.ar
Received:
28
August
2019
Accepted:
27
October
2019
Published online:
7
November
2019
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 
. 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 
, and a B–H temperature: 
.
© The Author(s), 2019
