We propose a new class of cosmological unified dark sector models called “Generalized Logotropic Models”. They depend on a free parameter n. The original logotropic model is a special case of our generalized model corresponding to $n=1$. The $\Lambda$CDM model is recovered for $n=0$. In our scenario, the Universe is filled with a single fluid, a generalized logotropic dark fluid (GLDF), whose pressure P includes higher order logarithmic terms of the rest-mass density ${\rho }_m$. The total energy density $ϵ$ is the sum of the rest-mass energy density ${\rho }_m{c}^2$ and the internal energy density u which play the roles of dark matter energy density ${ϵ}_m$ and dark energy density ${ϵ}_{de}$, respectively. We investigate the cosmological behavior of the generalized logotropic models by focusing on the evolution of the energy density, scale factor, equation of state parameter, deceleration parameter and squared speed of sound. Low values of $n\le 3$ are favored. We also study the asymptotic behavior of the generalized logotropic models. In particular, we show that the model presents a phantom behavior and has three distinct ways of evolution depending on the value of n. For $0<n\le 2$, it leads to a little rip and for $n>2$ to a big rip. We predict the value of the big rip time as a function of n without any free (undetermined) parameter.

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广义对标模型及其宇宙学约束

我们提出了一类新的宇宙学统一暗扇区模型，称为“广义 Logotropic 模型”。它们依赖于一个自由参数n。原始的 logotropic 模型是我们的广义模型的一个特例，对应于$n=1$. 这$\Lambda$CDM 模型恢复为$n=0$. 在我们的场景中，宇宙充满了一种单一的流体，一种广义的标识向暗流体 (GLDF)，其压力P包括静止质量密度的高阶对数项${\rho }_{米}$. 总能量密度$\epsilon$是静止质量能量密度的总和${\rho }_{米}{C}^2$和扮演暗物质能量密度角色的内部能量密度u${\epsilon }_{米}$和暗能量密度${\epsilon }_{de}$， 分别。我们通过关注能量密度、比例因子、状态方程参数、减速参数和声速平方的演变来研究广义对标模型的宇宙学行为。的低值$n\le 3$受到青睐。我们还研究了广义对标模型的渐近行为。特别是，我们表明该模型呈现出一种幻象行为，并且根据n的值具有三种不同的进化方式。为了$0<n\le 2$, 它会导致一点点撕裂和$n>2$大裂痕。我们在没有任何自由（未确定）参数的情况下将大裂口时间的值预测为n的函数。