We study the impact of the viscous effects of the primordial plasma on the evolution of the primordial gravitational waves (pGW) spectrum from Inflation until today, considering a self-consistent interaction that incorporates the back-reaction of the GW into the plasma. We use a relativistic causal hydrodynamic framework with a positive entropy production based on a Second-Order Theory (SOT) in which the viscous properties of the fluid are effectively described by a new set of independent variables. We study how the spin-2 modes typical of SOTs capture the simplest GW-fluid viscous interaction to first order. We consider that all non-ideal properties of the primordial plasma are due to an extra effectively massless self-interacting scalar field whose state becomes a many-particles one after Reheating and for which an effective fluid description is suitable. We numerically solve the evolution equations and explicitly compute the current GW spectrum obtaining two contributions. On the one hand we have the viscous evolution of the pGW: for the collision-dominated regime the GW source becomes negligible while in the collisionless limit there exists an absorption of the pGW energy due to the damping effect produced by the free-streaming spin-2 modes of the fluid and driven by the expansion of the Universe. The latter effect is characterized by a relative amplitude decrease of about 1 to 10 % with respect to the GW free evolution spectrum. On the other hand we get the GW production due to the decay of the initial spin-2 fluctuations of the fluid that is negligible compared with the above-mentioned contribution. This SOT framework captures the same qualitative effects on the evolution of GW coupled to matter reported in previous works in which a kinetic theory approach has been used.

我们研究了原始等离子体的粘性效应对从暴胀到今天的原始引力波 (pGW) 光谱演化的影响，考虑到将 GW 的逆反应结合到等离子体中的自洽相互作用。我们使用基于二阶理论 (SOT) 的具有正熵产生的相对论因果流体动力学框架，其中流体的粘性特性由一组新的自变量有效地描述。我们研究了 SOT 的典型自旋 2 模式如何将最简单的 GW-流体粘性相互作用捕获到一阶。我们认为原始等离子体的所有非理想特性都是由于一个额外有效的无质量自相互作用标量场，其状态在再加热后变为多粒子状态，并且有效的流体描述适用于此。我们对演化方程进行数值求解，并明确计算当前的 GW 光谱，获得两个贡献。一方面，我们有 pGW 的粘性演化：对于以碰撞为主的区域，GW 源变得可以忽略不计，而在无碰撞极限中，由于自由流动的自旋产生的阻尼效应，存在 pGW 能量的吸收。两种流体模式，由宇宙膨胀驱动。后一种效应的特征在于相对于 GW 自由演化谱的相对幅度降低约 1% 到 10%。另一方面，由于流体的初始自旋 2 波动的衰减，我们得到了 GW 的产生，与上述贡献相比可以忽略不计。该 SOT 框架捕获了与先前使用动力学理论方法的工作中报道的物质耦合的 GW 演化的相同定性影响。