Antimatter gravity and the Universe

The aim of this brief review is twofold. First, we give an overview of the unprecedented experimental efforts to measure the gravitational acceleration of antimatter; with antihydrogen, in three competing experiments at CERN (AEGIS, ALPHA and GBAR), and with muonium and positronium in other laboratories in the world. Second, we present the 21st Century's attempts to develop a new model of the Universe with the assumed gravitational repulsion between matter and antimatter; so far, three radically different and incompatible theoretical paradigms have been proposed. Two of these three models, Dirac-Milne Cosmology (that incorporates CPT violation) and the Lattice Universe (based on CPT symmetry), assume a symmetric Universe composed of equal amounts of matter and antimatter, with antimatter somehow "hidden" in cosmic voids; this hypothesis produced encouraging preliminary results. The heart of the third model is the hypothesis that quantum vacuum fluctuations are virtual gravitational dipoles; for the first time, this hypothesis makes possible and inevitable to include the quantum vacuum as a source of gravity. Standard Model matter is considered as the only content of the Universe, while phenomena usually attributed to dark matter and dark energy are explained as the local and global effects of the gravitational polarization of the quantum vacuum by the immersed baryonic matter. An additional feature is that we might live in a cyclic Universe alternatively dominated by matter and antimatter. In about three years, we will know if there is gravitational repulsion between matter and antimatter; a discovery that can forever change our understanding of the Universe.