An Alternative Approach to Vacuum Energy, Dark Matter & Gravitational Lensing

Various TeVeS-like and f(R)-like 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. A common thread of various theories is a non-uniform vector field fluid in the vacuum (see an up-to-date summary of relations between various theories by Halle, Zhao & Li, arXiv0711.0958 1). These ”alternative” theories are in fact in the standard GR framework except that the cosmological ”constant” is replaced by a non-trivial nonuniform vacuum energy. Built initially bottom-up rather than top-down as most gravity theories, TeVeS-like 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, solar system constraints, and gravitational lensing. I will also discuss some theoretical aspects of the theories related to the vacuum energy, and point out some analogies with electromagnetism and the Casimir effect.