The creation pressure, due to constant specific entropy particle production, vanishes for a fluid where the sum of the energy density and the isotropic pressure is zero; for example in an empty space–time with the cosmological constant interpreted as vacuum energy density. Within the framework of relativistic thermodynamics theories, the energy–momentum tensor of a linear barotropic fluid with constant specific entropy particle production and in generalized equilibrium can be written as the effective energy–momentum tensor of a perfect linear barotropic fluid where the adiabatic index is a homographic function of the initial adiabatic index. This function shows that by adding constant specific entropy particle production to a phantom fluid, the effective perfect fluid will be without phantom property, whereas there are some fluids that with specific entropy particle production have phantom property. This transformation is useful for obtaining the behaviour of the scale factor of cosmological models. By solving the equation that comes from the entropy production equation, then the transport equation in the framework of the Muller-Israel-Stewart second-order causal relativistic thermodynamics, assuming constant specific entropy particle production and the generalized equilibrium, we obtain the bulk viscosity coefficient ζ and the relaxation time τ . The relation ζ ∝ $$ \rho^{{\frac{1}{2}}} $$ ρ 1 2 between ζ and the energy density ρ is predicted in spatially flat homogeneous and isotropic (FLRW) cosmological model for any value of the constant state parameter. The gauge–invariant energy density contrast and velocity perturbations of the previous cosmological model in the matter-dominated era with isentropic particle production are studied. The modes of these perturbations are decaying faster than the corresponding modes for the perfect fluid perturbations in the particle number conservation case. Then the isentropic, usually called adiabatic, gauge–invariant energy density contrast and velocity perturbations in case of a perfect linear barotropic fluid with particle number conservation are studied, in particular for negative values of the constant state parameter.

中文翻译：

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创造压力和广义平衡的一些性质和含义：绝热指数的修正，宇宙学扰动

对于能量密度和各向同性压力之和为零的流体，由于恒定的比熵粒子产生，创生压力消失；例如，在一个空的时空中，宇宙常数被解释为真空能量密度。在相对论热力学理论的框架内，具有恒定比熵粒子产生和广义平衡的线性正压流体的能量-动量张量可以写成完美线性正压流体的有效能量-动量张量，其中绝热指数为初始绝热指数的单应函数。该函数表明，通过向幻影流体添加恒定的比熵粒子产生，有效的完美流体将没有幻影属性，而有一些具有特定熵粒子产生的流体具有幻影属性。这种转换对于获得宇宙模型的比例因子的行为很有用。通过求解来自熵产生方程的方程，然后在Muller-Israel-Stewart二阶因果相对论热力学框架下求解输运方程，假设比熵粒子产生常数和广义平衡，我们得到体积粘度系数ζ 和弛豫时间 τ 。ζ ∝ $$ \rho^{{\frac{1}{2}}} $$ ρ 1 2 之间的关系 ζ 和能量密度 ρ 在空间平坦均匀和各向同性 (FLRW) 宇宙学模型中预测为任何值恒定状态参数。研究了在等熵粒子产生的物质主导时代先前宇宙学模型的规范不变能量密度对比和速度扰动。在粒子数守恒情况下，这些扰动的模式比完美流体扰动的相应模式衰减得更快。然后研究了在具有粒子数守恒的完美线性正压流体情况下的等熵，通常称为绝热，规范不变的能量密度对比度和速度扰动，特别是对于恒定状态参数的负值。在粒子数守恒情况下，这些扰动的模式比完美流体扰动的相应模式衰减得更快。然后，在具有粒子数守恒的完美线性正压流体的情况下，研究了等熵（通常称为绝热、规范不变的能量密度对比度和速度扰动），特别是对于恒定状态参数的负值。在粒子数守恒情况下，这些扰动的模式比完美流体扰动的相应模式衰减得更快。然后，在具有粒子数守恒的完美线性正压流体的情况下，研究了等熵（通常称为绝热、规范不变的能量密度对比度和速度扰动），特别是对于恒定状态参数的负值。