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arXiv 1301.4486gr-qcastro-ph.COhep-th
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宇宙暗区引力的非标准方法

Nonstandard approach to gravity for the dark sector of the Universe

P. C. Stichel, W. J. Zakrzewski

摘要:

本文综述了暗子流体作为宇宙暗区模型的研究现状。非相对论性的无质量粒子被引入作为在一个扩大的相空间中的伽利略群的实现。额外的自由度允许一个非标准的,最小的耦合到重力尊重爱因斯坦的等效原理。扩展到自引力流体的泊松方程的引力势包含一个动态生成的有效引力质量密度的任何一个符号。运动方程(EOM)不含自由参数,是相对于时间不变的。米尔恩规范变换固定量规消除了非物理的自由度。由此产生的拉格朗日量没有自由粒子的限制。它所描述的粒子,暗子,只作为自引力流体的流体粒子存在。这种暗子流体实现了由动力学指数z = 5/3的膨胀扩展的零质量伽利略代数。我们将EOM简化为类Friedmann方程,通过实现伸缩对称性,导出守恒量和唯一的哈密顿动力学。利用Poisson-括号(PB)-代数的Casimir方法,将相空间进行分层,构造了约化相空间中的拉格朗日量。以跃迁红移和Casimir值为积分常数求解类Friedmann方程。我们得到了早期宇宙的减速阶段和晚期宇宙的加速阶段,与观测结果一致。球对称情形下的稳态方程可以模拟星系晕。数值解的非线性微分方程的引力势导致预测的暗物质(DM)的星系旋转曲线(RC)的定性协议与观测数据。我们还提出了该模型的一般协变推广。

英文摘要:

We summarize the present state of research on the darkon fuid as a model for the dark sector of the Universe. Nonrelativistic massless particles are introduced as a realization of the Galilei group in an enlarged phase space. The additional degrees of freedom allow for a nonstandard, minimal coupling to gravity respecting Einstein's equivalence principle. Extended to a self-gravitating fluid the Poisson equation for the gravitational potential contains a dynamically generated effective gravitational mass density of either sign. The equations of motion (EOMs) contain no free parameters and are invariant w.r.t. Milne gauge transformations. Fixing the gauge eliminates the unphysical degrees of freedom. The resulting Lagrangian possesses no free particle limit. The particles it describes, darkons, exist only as fluid particles of a self-gravitating fluid. This darkon fluid realizes the zero-mass Galilean algebra extended by dilations with dynamical exponent z = 5/3. We reduce the EOMs to Friedmann-like equations, derive conserved quantities and a unique Hamiltonian dynamics by implementing dilation symmetry. By the Casimir of the Poisson-bracket (PB)-algebra we foliate the phase space and construct a Lagrangian in reduced phase space. We solve the Friedmann-like equations with the transition redshift and the value of the Casimir as integration constants. We obtain a deceleration phase for the early Universe and an acceleration phase for the late Universe in agreement with observations. Steady state equations in the spherically symmetric case may model a galactic halo. Numerical solutions of a nonlinear differential equation for the gravitational potential lead to predictions for the dark matter (DM) part of the rotation curves (RCs) of galaxies in qualitative agreement with observational data. We also present a general covariant generalization of the model.

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