早期宇宙热力学和非粘性和粘性强、电弱时期的演化：可能的解析解
Early Universe Thermodynamics and Evolution in Nonviscous and Viscous Strong and Electroweak epochs: Possible Analytical Solutions
摘要：
基于最近的微扰和非微扰晶格计算，几乎夸克的味道和热贡献的光子，中微子，轻子，电弱粒子，和标量希格斯玻色子，各种热力学量，在消失的净重子密度，如压力，能量密度，体粘度，弛豫时间，和温度已经计算到TeV尺度，即覆盖强子，早期宇宙中的QGP和电弱（EW）相。这一显着的进展促使本研究确定早期宇宙中体积粘度的可能影响，并了解这将如何从一个时代到另一个时代变化。我们已经考虑到一阶（Eckart）和二阶（Israel-Stewart）理论的相对论性宇宙流体和集成的状态方程的弗里德曼方程的粘性。得到了非线性非齐次微分方程的解析解。对于Israel-Stewart来说，微分方程是非常复杂的。在此概述了它们，作为今后研究的路线图。对于Eckart理论，唯一可能的解决方案是函数$H(a(t))$，其中$H(t)$是哈勃参数，$a(t)$是比例因子，但迄今为止，它们都不能直接用固有时间或宇宙时间$t$表示。对于Eckart-type粘性背景，特别是在有限宇宙学常数下，得到了非奇异的$H(t)$和$a(t)$，其中对于QCD/EW和渐近EoS，$H(t)$发散.对于非粘性背景，$H(a(t))$的相关性是单调的。同样的结论也适用于理想的地球服务系统。我们还得出结论，随着$a(t)$的增加，$H(a(t))$的减少率在不同的时期，在消失和有限的宇宙学常数。这些结果有助于加深我们对核合成和宇宙学大尺度结构的理解。
英文摘要：
Based on recent perturbative and non-perturbative lattice calculations with almost quark flavors and the thermal contributions from photons, neutrinos, leptons, electroweak particles, and scalar Higgs bosons, various thermodynamic quantities, at vanishing net-baryon densities, such as pressure, energy density, bulk viscosity, relaxation time, and temperature have been calculated up to the TeV-scale, i.e. covering hadron, QGP and electroweak (EW) phases in the early Universe. This remarkable progress motivated the present study to determine the possible influence of the bulk viscosity in the early Universe and to understand how this would vary from epoch to epoch. We have taken into consideration first- (Eckart) and second-order (Israel-Stewart) theories for the relativistic cosmic fluid and integrated viscous equations of state in Friedmann equations. Nonlinear nonhomogeneous differential equations are obtained as analytical solutions. For Israel-Stewart, the differential equations are very sophisticated to be solved. They are outlined here as road-maps for future studies. For Eckart theory, the only possible solution is the functionality, $H(a(t))$, where $H(t)$ is the Hubble parameter and $a(t)$ is the scale factor, but none of them so far could to be directly expressed in terms of either proper or cosmic time $t$. For Eckart-type viscous background, especially at finite cosmological constant, non-singular $H(t)$ and $a(t)$ are obtained, where $H(t)$ diverges for QCD/EW and asymptotic EoS. For non-viscous background, the dependence of $H(a(t))$ is monotonic. The same conclusion can be drawn for an ideal EoS. We also conclude that the rate of decreasing $H(a(t))$ with increasing $a(t)$ varies from epoch to epoch, at vanishing and finite cosmological constant. These results obviously help in improving our understanding of the nucleosynthesis and the cosmological large-scale structure.
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