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以太标量张量理论中宇宙演化的动力学系统分析

Dynamical system analysis of cosmological evolution in the Aether scalar tensor theory

Institute of Physics, University of Tartu（塔尔图大学物理研究所）；Institute of Theoretical Physics and Astrophysics, University of Gdańsk（格但斯克大学理论与天体物理研究所）

João Luís Rosa, Tom Zlosnik

备注：
18 pages, 8 figures, published version
发表信息：
Phys. Rev. D 109, 024018 (2024)
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AI总结：

本研究用动力学系统分析AeST理论的两类函数模型，发现其可在宇宙背景层面近似ΛCDM模型，新模型或能同时实现冷暗物质的宇宙学成功性并满足弱场约束。

摘要：

以太标量张量理论（Aether Scalar Tensor, AeST）是广义相对论（General Relativity, GR）的扩展理论，旨在在不引入暗物质的前提下解释星系和宇宙学观测结果。该理论的作用量包含一个函数，目前仅能通过唯象学考量对其进行约束。在先前的研究中，该函数的形式被设定为能使宇宙演化方程中的有效流体贡献在宇宙晚期越来越近似于尘埃的形式。本研究则考虑另一组函数形式，它们在宇宙早期最近似于尘埃，且随时间逐渐偏离类尘埃行为。研究采用动力学系统形式主义分析两组函数的示例模型，引入一套完整的动力学变量，用于描述时空曲率、不同物质组分的能量密度参数以及AeST标量场，并推导了描述宇宙演化的动力学方程。研究发现，宇宙学相空间存在与物质组分缺失相关的不变子流形，以及与物质、辐射、宇宙学常数主导的宇宙学行为等熟知状态相关的平衡态。对模型进行的完整数值积分显示，各模型在宇宙背景层面均可紧密近似ΛCDM模型。研究还考虑了模型的推广形式，表明新模型可能同时复制冷暗物质的宇宙学成功之处，且能满足弱场准静态区域对该理论的约束。

英文摘要：

The Aether Scalar Tensor (AeST) theory is an extension of General Relativity (GR), proposed for addressing galactic and cosmological observations without dark matter.The action for the theory includes a function that can currently only be constrained by phenomenological considerations. In antecedent work, forms of this function were considered that led to an effective fluid contribution to the cosmological evolution equations that approximated that of dust more and more closely at late cosmic times. In this work we consider an alternative set of functions that most closely approximate dust at the earliest cosmic times and where deviations from dust-like behaviour gradually emerge with time. We use the dynamical system formalism to analyze example models from both possible sets of functions, introducing a complete set of dynamical variables describing the spacetime curvature, energy density parameters of different matter components, and AeST scalar field, and obtain the dynamical equations describing cosmological evolution. The cosmological phase space is found to feature invariant submanifolds associated to the absence of the matter components, as well as equilibrium states associated with well-known cosmological behaviors e.g. matter, radiation, and cosmological constant dominated epochs. A full numerical integration of the dynamical system is performed for the models and it is shown that each can closely approximate the $Λ\mathrm{CDM}$ model at the level of the cosmic background. Generalizations of the models are considered and it is shown that the new models likely can simultaneously replicate the cosmological successes of cold dark matter whilst satisfying constraints on the theory from the weak-field quasistatic regime.

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