标题： RUNNING VACUUM 模型的热力学方面 显示英文标题

标题： Thermodynamical aspects of running vacuum models

摘要： 大类具有运行真空的模型的热历史被详细讨论，其中有效的宇宙项由哈勃率的截断幂级数描述，其主导项为$\Lambda (H) \propto H^{n+2}$。具体来说，通过假设由真空衰变产生的超相对论粒子以某种方式进入时空，其能量密度为$\rho_r \propto T^{4}$，我们解析地计算了温度演化定律和熵增加函数。对于这里研究的整个真空模型类，我们发现共动辐射熵密度（与有效无质量粒子相关）的初始值从零开始，并且进化得非常快，直到接近真空衰变阶段结束时达到最大值，在此饱和。在绝热FRW相期间辐射熵的晚期守恒也保证了整个运行真空模型类独立于初始条件预测相同正确的今日熵值$S_{0} \sim 10^{87-88}$（自然单位）。此外，通过假设Gibbons-Hawking温度作为初始条件，我们发现晚期和早期真空能量密度之比与量子场论的粗略估计一致，即$\rho_{\Lambda 0}/\rho_{\Lambda I} \sim10^{-123}$。这些结果与幂指数$n$无关，表明观测到的宇宙可能在两个极端的、不稳定的、非奇异的de Sitter相之间平滑演化。 显示英文摘要

摘要： The thermal history of a large class of running vacuum models in which the effective cosmological term is described by a truncated power series of the Hubble rate, whose dominant term is $\Lambda (H) \propto H^{n+2}$, is discussed in detail. Specifically, by assuming that the ultra-relativistic particles produced by the vacuum decay emerge into space-time in such a way that its energy density $\rho_r \propto T^{4}$, the temperature evolution law and the increasing entropy function are analytically calculated. For the whole class of vacuum models explored here we findthat the primeval value of the comoving radiation entropy density (associated to effectively massless particles) starts from zero and evolves extremely fast until reaching a maximum near the end of the vacuum decay phase, where it saturates. The late time conservation of the radiation entropy during the adiabatic FRW phase also guarantees that the whole class of running vacuum models predicts thesame correct value of the present day entropy, $S_{0} \sim 10^{87-88}$ (in natural units), independently of the initial conditions. In addition, by assuming Gibbons-Hawking temperature as an initial condition, we find that the ratio between the late time and primordial vacuum energy densities is in agreement with naive estimates from quantum field theory, namely, $\rho_{\Lambda 0}/\rho_{\Lambda I} \sim10^{-123}$. Such results are independent on the power $n$ and suggests that the observed Universe may evolve smoothly between two extreme, unstable, nonsingular de Sitter phases.