Various TeVeS-inspired and f(R)-inspired theories of gravity have added an interesting twist to the search for dark matter and vacuum energy, modifying the landscape of astrophysics day by day. These theories can be together called a {\bf N}on-{\bf u}niform Dark Energy fluid (a Nu-Lambda fluid or a ${\mathbf VΛ}$ fluid); a common thread of these theories, according of an up-to-date summary by HZL \cite{Halle}, is a non-uniform vector field, describing an uneven vacuum energy fluid. The so-called "alternative" gravity theories are in fact in the standard GR gravity framework except that the cosmological "constant" is replaced by a non-trivial non-uniform vacuum energy, which couples the effects of Dark Matter and Dark Energy together by a single field. Built initially bottom-up rather than top-down as most gravity theories, TeVeS-inspired theories are healthily rooted on empirical facts. Here I attempt a review of some sanity checks of these fast-developing theories from galaxy rotation curves, gravitational lensing and cosmic acceleration. I will also discuss some theoretical aspects of the vacuum energy, and point out some analogies with electromagnetism and the Casimir effect.
The necessity of dark matter in MOND within galactic scales
为了进一步测试银河系尺度上的修正牛顿动力学（MOND）--最初提出来解释没有暗物质的盘星系的旋转曲线--我们研究了CASTLES数据库中六个强引力透镜早型星系的样本。为了确定这些星系中是否存在暗物质，我们将总质量（来自透镜效应）与恒星质量含量（来自测光和恒星星族合成的比较）进行比较。我们发现，星系尺度上的强引力透镜需要大量的暗物质，即使在MOND。在这样的尺度上，2 eV的中微子无法解释这种多余的物质-与最近解释子弹状星系团透镜数据的说法相反。暗物质的存在被检测到的区域具有更高的加速度比$\sim 10^{-10}$ m/s $^2$的特征MONDian规模。这对MOND来说是一个严重的挑战，除非对透镜效应的正确处理有质的不同（可能是在一个一致的理论中发展，如TeVeS）。
利用MOND理论研究了星系团的弱引力透镜效应。计算了A1689、CL0024+1654、CL1358+6245三个星系团的背景星系的剪切和会聚以及42个SDSS（Sloan Digital Sky Survey）星系团的平均轮廓，并与观测数据进行了比较。质量分布被建模为X射线气体，星系和暗晕的总和。对于作为角半径函数的剪切，MOND预测的斜率比数据更小，而与临界加速度参数$g_0$无关。为了解释任何$g_0$和三个插值函数的数据，必须使用暗晕。如果暗晕是由大量中微子组成的，那么它的质量应该大于2 eV。然而，该约束仍然依赖于暗晕模型，并且存在系统的不确定性，因此需要更仔细的研究来施加严格的约束。
