An Uneven Vacuum Energy Fluid as $\Lambda$, Dark Matter, MOND and Lens

TL;DR

This paper reviews theories replacing the cosmological constant with a non-uniform vacuum energy fluid, unifying dark matter and dark energy effects, and examines their empirical and theoretical implications in astrophysics.

Contribution

It provides a comprehensive review of non-uniform vacuum energy theories inspired by TeVeS and f(R) gravity, highlighting their empirical consistency and theoretical analogies.

Findings

Consistent explanations for galaxy rotation curves and gravitational lensing.

Unified description of dark matter and dark energy effects.

Theoretical insights into vacuum energy analogies with electromagnetism.

Abstract

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 ${\mathbf V\Lambda}$ 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.