arXiv 1208.08012012-08-03astro-ph.CO

具有多方状态方程的宇宙模型：II。宇宙晚期

Models of universe with a polytropic equation of state: II. The late universe

Pierre-Henri Chavanis

发表信息：: Eur. Phys. J. Plus, 129, 222 (2014)

摘要：

我们构造了一个具有线性分量和多变分量的广义状态方程$p=(αρ+kρ^{1+1/n})c^2$的宇宙模型。本文考虑负指数$n<0$。在这种情况下，多变成分在密度较低的晚期宇宙中占主导地位。对于$α=0$、$n=-1$和$k=-ρ_Λ$，我们得到了一个描述从物质时代到暗能量时代转变的晚期宇宙模型。宇宙在未来永远存在，并在时间尺度$t_Λ=1.46 10^{18} s$上经历宇宙密度为$ρ_Λ=7.02 10^{-24} g/m^3$的暴胀膨胀。对于$α=0$、$n=-1$和$k=ρ_Λ$，我们得到了一个周期性出现和消失的循环宇宙模型。如果我们生活在这个宇宙中，它将在大约23.8亿年后消失。我们把早期宇宙和晚期宇宙联系起来，并提出一个简单的方程来描述宇宙的整个演化。这导致了一个模型的宇宙，是永恒的过去和未来没有奇点（aioniotic宇宙）。这个模型在暴胀的早期和晚期阶段之间表现出一种很好的“对称性”，晚期宇宙中的宇宙常数与早期宇宙中的普朗克常数扮演着相同的角色。普朗克密度和宇宙学密度代表了基本的上限和下限，相差122个数量级。宇宙学常数"问题"可能是一个假问题。我们确定了对应于广义状态方程$p=(αρ+kρ^{1+1/n})c^2$的标量场（quintessence，快子场）的势。我们还提出了一个统一的预辐射，辐射和暗能量通过二次状态方程$p/c^2=-4ρ^2/3ρ_P+ρ/3-4ρ_Λ/3$。

英文摘要：

We construct models of universe with a generalized equation of state $p=(αρ+kρ^{1+1/n})c^2$ having a linear component and a polytropic component. In this paper, we consider negative indices $n<0$. In that case, the polytropic component dominates in the late universe where the density is low. For $α=0$, $n=-1$ and $k=-ρ_Λ$, we obtain a model of late universe describing the transition from the matter era to the dark energy era. The universe exists eternally in the future and undergoes an inflationary expansion with the cosmological density $ρ_Λ=7.02 10^{-24} g/m^3$ on a timescale $t_Λ=1.46 10^{18} s$. For $α=0$, $n=-1$ and $k=ρ_Λ$, we obtain a model of cyclic universe appearing and disappearing periodically. If we were living in this universe, it would disappear in about 2.38 billion years. We make the connection between the early and the late universe and propose a simple equation describing the whole evolution of the universe. This leads to a model of universe that is eternal in past and future without singularity (aioniotic universe). This model exhibits a nice "symmetry" between an early and late phase of inflation, the cosmological constant in the late universe playing the same role as the Planck constant in the early universe. The Planck density and the cosmological density represent fundamental upper and lower bounds differing by 122 orders of magnitude. The cosmological constant "problem" may be a false problem. We determine the potential of the scalar field (quintessence, tachyon field) corresponding to the generalized equation of state $p=(αρ+kρ^{1+1/n})c^2$. We also propose a unification of pre-radiation, radiation and dark energy through the quadratic equation of state $p/c^2=-4ρ^2/3ρ_P+ρ/3-4ρ_Λ/3$.

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