修正重力（MOG）能解释高速子弹（集束）吗？

Applying MOG to lensing: Einstein rings, Abell 520 and the Bullet Cluster

We investigate gravitational lensing in the context of the MOG modified theory of gravity. Using a formulation of the theory with no adjustable or fitted parameters, we present the MOG equations of motion for slow, nonrelativistic test particles and for ultrarelativistic test particles, such as rays of light. We demonstrate how the MOG prediction for the bending of light can be applied to astronomical observations. Our investigation first focuses on a small set of strong lensing observations where the properties of the lensing objects are found to be consistent with the predictions of the theo…

The Train Wreck Cluster Abell 520 and the Bullet Cluster 1E0657-558 in a Generalized Theory of Gravitation

A major hurdle for modified gravity theories is to explain the dynamics of galaxy clusters. A case is made for a generalized gravitational theory called Scalar-Tensor-Vector-Gravity (STVG) or MOG (modified gravity) to explain merging cluster dynamics. The paper presents the results of a re-analysis of the Bullet Cluster, as well as an analysis of the Train Wreck Cluster in the weak gravitational field limit without dark matter. The King-$β$ model is used to fit the X-ray data of both clusters, and the $κ$-maps are computed using the parameters of this fit. The amount of galaxies in the cluster…

子弹星系团1 E0657 -558的证据显示了在没有暗物质的情况下的修正重力

The Bullet Cluster 1E0657-558 evidence shows Modified Gravity in the absence of Dark Matter

对2006年11月15日发布的数据的详细分析（Clowe等人，2006）计算了子弹星系团1 E0657 -558的X射线面密度σ图和强、弱引力透镜会聚κ图，并将计算结果与修正引力（MOG）和暗物质的预测结果进行了比较。我们的表面密度西格玛模型计算使用国王β模型密度，和质量分布的主集群和等温温度分布由MOG确定。我们发现，主集群的热剖面是近等温的。MOG预测的主团簇等温温度为T = 15.5 ± 3.9 keV，与实验值T = 14.8{+2.0}{-1.7} keV符合得很好。在没有非重子暗物质的情况下，得到了与二维收敛κ图数据的极好拟合，这解释了Clowe等人（2006）报道的σ图和κ图之间的8 σ空间偏移。MOG对卡帕图的预测结果表明，子弹星系团1 E0657 -558中分布着两个重子成分，平均质量分数为83%的团内介质（ICM）气体和17%的星系。相反地，牛顿暗物质kappa模型对于质量分数为0.32的重子与暗物质相比，平均具有76%的暗物质（忽略由于星系的不确定贡献）和24%的ICM气体，当与预测的Lambda-CDM宇宙学重子质量分数0.176{+0.019}{-0.012}相比时，这是统计上显著的结果（Spergel et al.，2006年）。

光的弯曲和修正引力中的透镜效应

The bending of light and lensing in modified gravity

我们的修正引力理论（MOG）在过去被成功地用于解释一系列天文和宇宙学观测，包括星系旋转曲线，CMB声峰和星系质量功率谱。MOG也被成功地用于解释子弹星系团1 E0657 -558的不寻常特征，而没有外来的暗物质。在目前的工作中，我们推导出相对论运动方程的球对称场的点源MOG，特别是，我们推导出光弯曲和透镜方程。我们的结果也有更广泛的应用在扩展的物质分布的情况下，它们可以用来验证子弹集群的结果，并提供了一个可能的解释合并集群在Abell 520。

Acceleration in Modified Gravity (MOG) and the Mass-Discrepancy Baryonic Relation

The equation of motion in the generally covariant modified gravity (MOG) theory leads for weak gravitational fields and the non-relativistic limit to a modification of the Newtonian gravitational acceleration law, expressed in terms of two parameters $α$ and $μ$. The parameter $α$ determines the strength of the gravitational field and $μ$ is the effective mass of the vector field $ϕ_μ$, coupled with gravitational strength to baryonic matter. The MOG acceleration law for weak field gravitation and non-relativistic particles has been demonstrated to fit a wide range of galaxies, galaxy clusters …

修正引力还是暗物质？

Modified Gravity or Dark Matter?

修正引力理论（Modified Gravity，MOG）在不使用暗物质或爱因斯坦宇宙学常数的情况下，已成功地解释了星系的自转曲线、星系团的运动、子弹团和宇宙学观测。我们回顾了该理论的主要理论思想和应用天体物理和宇宙学数据。