arXiv 1909.086982019-09-18gr-qc

从AdS $_5$时空演化宇宙的唯一状态方程

A unique equation of state for the universe evolution from AdS$_5$ space-time

M. M. Lapola, P. H. R. S. Moraes, W. de Paula, J. F. Jesus, R. Valentim, M. Malheiro

备注：: 14 pages, 11 figures

摘要：

我们将诱导物质模型应用于五维度量。对于宇宙学常数为零的情况，我们得到了一个能描述宇宙辐射主导时代的解。正的$Λ$情况产生一个反弹宇宙模型。在负五维宇宙学常数的情况下，标度因子为$a(t)\sim\sqrt[]{\sinh t}$，它不仅能连续地描述宇宙膨胀的晚期加速阶段，而且能连续地描述宇宙膨胀的非加速阶段.这个解决方案连同额外的维的比例因子解决方案产生的材料内容的模型是显着相关的状态方程类似于著名的麻省理工学院袋模型状态方程的夸克物质$p=(ρ-4B)/3$。在我们的例子中，$ρ=ρ_m+B$，其中$ρ_m$是相对论性和非相对论性物质的能量密度，$B=\ Λ /16π$代表袋能量常数，它在四维宇宙中扮演暗能量的角色，$Λ$是AdS $_5$时空的宇宙学常数。我们的模型令人满意地拟合观测数据的低红移样品的实验测量的哈勃参数，这导致$H_0=72.2^{+5.3}_{-5.5}$公里的s $^{-1}$ Mpc $^{-1}$。

英文摘要：

We apply the Induced Matter Model to a five-dimensional metric. For the case with null cosmological constant, we obtain a solution able to describe the radiation-dominated era of the universe. The positive $Λ$ case yields a bounce cosmological model. In the negative five-dimensional cosmological constant case, the scale factor is obtained as $a(t)\sim\sqrt[]{\sinh t}$, which is able to describe not only the late-time cosmic acceleration but also the non-accelerated stages of the cosmic expansion in a continuous form. This solution together with the extra-dimensional scale factor solution yields the material content of the model to be remarkably related through an equation of state analogous to the renowned MIT bag model equation of state for quark matter $p=(ρ-4B)/3$. In our case, $ρ=ρ_m+B$, with $ρ_m$ being the energy density of relativistic and non-relativistic matter and $B=\ Λ /16π$ represents the bag energy constant, which plays the role of the dark energy in the four-dimensional universe, with $Λ$ being the cosmological constant of the AdS$_5$ space-time. Our model satisfactorily fits the observational data for the low redshift sample of the experimental measurement of the Hubble parameter, which resulted in $H_0=72.2^{+5.3}_{-5.5}$km s$^{-1}$ Mpc$^{-1}$.

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