An uneven vacuum energy fluid as Λ, dark matter, mond and lens

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 Non-uniform Dark Energy fluid (a Nu-Lamba fluid or a V Lambda fluid); a common thread of these theories, according of an up-to-date summary to HZL, (1) 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 nontrivial 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 we attempt a review of some sanity checks of these fast-developing theories from galaxy rotation curves, solar system constraints, and gravitational lensing. We will also discuss some theoretical aspects of these theories related to the vacuum energy, and point out some analogies with electromagnetism and the Casimir effect.