arXiv 2007.059882020-07gr-qccond-mat.otherhep-ph

de Sitter宇宙中的双Hawking温度与宇宙学常数问题

Double Hawking temperature in de Sitter Universe and cosmological constant problem

G. E. Volovik

备注：: 7 pages, no figures

摘要：

与黑洞物理不同的是，de Sitter热力学不受宇宙学视界的影响，有效温度与Hawking温度不同。特别是，德西特宇宙中的原子经历了与局部温度相对应的热激活，该局部温度是霍金温度$T_{\rm loc}=2T_{\rm Hawking}$的两倍。同样的双霍金温度描述了德西特宇宙中大质量标量场的衰变。为什么局部温度正好是霍金温度的两倍，其原因可以从德西特时空的几何学中得到。通过考虑霍金辐射，证实了宇宙视界在de Sitter宇宙中作用的弱化。讨论了德西特时空中粒子的辐射与电场中施温格对产生的区别。我们对de Sitter时空使用定态Painleve-Gullstrand度规，其中粒子是由来自宇宙视界的霍金辐射产生的，而对电场使用与时间无关的规范。在这些定态坐标系中，哈密顿量和大质量粒子的能谱看起来相当相似。然而，最终的结果却有本质的不同。在施温格对产生的情况下，所产生的对的数量密度随时间增长，而在德西特真空中，所产生的对的数量密度是有限的。后者表明来自宇宙视界的霍金辐射不会导致德西特真空的不稳定性。不稳定性的其他机制是宇宙学常数问题的动力学解所必需的。我们考虑局部温度$T_{\rm loc}=2T_{\rm H}$在de Sitter时空衰变中的可能作用，这是由于真空能量与具有该温度的相对论性物质之间的能量交换。

英文摘要：

As distinct from the black hole physics, the de Sitter thermodynamics is not determined by the cosmological horizon, the effective temperature differs from the Hawking temperature. In particular, the atom in the de Sitter universe experiences thermal activation corresponding to the local temperature, which is twice larger than the Hawking temperature, $T_{\rm loc}=2T_{\rm Hawking}$. The same double Hawking temperature describes the decay of massive scalar field in the de Sitter universe. The reason, why the local temperature is exactly twice the Hawking temperature, follows from the geometry of the de Sitter spacetime. The weakening of the role of the cosmological horizon in de Sitter universe is confirmed by considering Hawking radiation. We discuss the difference between the radiation of particles in the de Sitter spacetime and the Schwinger pair creation in the electric field. We use the stationary Painleve-Gullstrand metric for the de Sitter spacetime, where the particles are created by Hawking radiation from the cosmological horizon, and time independent gauge for the electric field. In these stationary frames the Hamiltonians and the energy spectra of massive particles look rather similar. However, the final results are essentially different. In case of Schwinger pair production the number density of the created pairs grows with time, while in the de Sitter vacuum the number density of the created pairs is finite. The latter suggests that Hawking radiation from the cosmological horizon does not lead to instability of the de Sitter vacuum. The other mechanisms of instability are required for the dynamical solution of the cosmological constant problem. We consider the possible role of the local temperature $T_{\rm loc}=2T_{\rm H}$ in the decay of the de Sitter space-time due to the energy exchange between the vacuum energy and relativistic matter with this temperature.

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英文摘要：

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