负曲率循环宇宙中的系列加速-减速跃迁
Serial Acceleration-Deceleration Transitions in a Cyclic Universe with Negative Curvature
摘要：
在这项工作中，我们开发了一个通用的循环宇宙的唯象模型。根据a（t）在转折点t_α和t_ω处没有奇异行为的周期性要求，以及从Hubble函数H（t）可以导出唯一的解析形式来拟合H（z）上的数据的要求，我们构造了周期标度因子a（t）。我们得到了a（t）的两个版本，称为模型A和模型C。哈勃数据选择模型A。在已知哈勃函数H（t）和H（z）解析形式的基础上，计算了减速参数q（t）和q（z），研究了膨胀阶段的加速-减速转变。我们发现在t_α=0时的初始加速度在t_{ad1} = 3.313 × 10 ^{-38}s时过渡到减速阶段，在t_{da} =6.713 Gyr时过渡到现在的加速度阶段。当前加速应在过渡到最终减速时结束，此时t_{ad2} =38.140 Gyr。膨胀期为60.586 Gyr。完整的循环周期为T=121.172 Gyr。利用减速参数q（z）和q（t）求解了暗能量Ω_0和暗物质Ω_M的能量密度的Friedmann方程，描述了它们在z和t较大范围内的演化。我们证明了在模型A中，曲率密度Ω_c（z）从早期的平坦宇宙演化到今天的反de-Sitter时空曲线。模型A中没有标准模型充盈。
英文摘要：
In this work we develop a general phenomenological model of the Cyclic Universe. We construct periodic scale factor a(t) from the requirements of the periodicity of a(t) with no singular behavior at the turning points t_αand t_ωand the requirement that a unique analytical form of the Hubble function H(z) can be derived from the Hubble function H(t) to fit the data on H(z). We obtain two versions of a(t) called Model A and Model C. Hubble data select Model A. With the analytical forms of the Hubble functions H(t) and H(z) known we calculate the deceleration parameters q(t) and q(z) to study the acceleration-deceleration transitions during the expansion phase. We find that the initial acceleration at t_α=0 transits at t_{ad1}=3.313x10^{-38}s into deceleration period that transits at t_{da}=6.713 Gyr to the present period of acceleration. The present acceleration shall end in a transition to the final deceleration at t_{ad2}=38.140 Gyr. The expansion period lasts 60.586 Gyr. The complete cycle period is T=121.172 Gyr. We use the deceleration parameters q(z) and q(t) to solve the Friedmann equations for the energy densities of Dark Energy Ω_0 and Dark Matter Ω_M to describe their evolutions over a large range of z and t. We show that in the Model A the curvature density Ω_c(z) evolves from a flat Universe in the early times to a curves anti de-Sitter spacetime today. There is no Standard Model Inflation in the Model A.
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