arXiv 1908.117162019-08gr-qchep-thmath-phmath.MP

静态de Sitter时空中的量子热力学与宇宙初态

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

Juan Ignacio Musmarra, Mauricio Bellini

备注：: Version accepted in EPJC. arXiv admin note: text overlap with arXiv:1904.11599
DOI：: 10.1140/epjc/s10052-019-7433-9

摘要：

本文利用相对论量子几何方法研究了静态de Sitter度规因果视界内时空的反作用效应，以便对时空进行量子力学描述。我们从一个关于$r=0$展开的合流超几何函数的多项式条件中找到了标量场的有限个离散能级。与以前的工作一样，我们得到了不确定原理对时空亚视界尺度上的每一个能级都是成立的。我们发现，温度和熵依赖于每个能级上的子态个数，当给定能级的子态个数趋于无穷大时，每个能级的Bekenstein-Hawking温度恢复.我们提出宇宙的原初状态可以用具有普朗克能量$E_p=m_p\,c^2$和B-H温度$T_{BH}=\left(\frac{\hbar\,c}{2π\,l_p\,K_B}\right)$的德西特度规来描述。

英文摘要：

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: $T_{BH}=\left(\frac{\hbar\,c}{2π\,l_p\,K_B}\right)$.

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英文摘要：

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