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Dark stars are stellar objects made (almost entirely) of hydrogen and helium, but powered by the heat from dark matter annihilation, rather than by fusion. They are in hydrostatic and thermal equilibrium, but with an unusual power source. Weakly interacting massive particles (WIMPs), among the best candidates for dark matter, can be their own antimatter and can annihilate inside the star, thereby providing a heat source. Although dark matter constitutes only [Formula: see text]0.1% of the stellar mass, this amount is sufficient to power the star for millions to billions of years. Thus, the first phase of stellar evolution in the history of the Universe may have been dark stars. We review how dark stars come into existence, how they grow as long as dark matter fuel persists, and their stellar structure and evolution. The studies were done in two different ways, first assuming polytropic interiors and more recently using the MESA stellar evolution code; the basic results are the same. Dark stars are giant, puffy (∼10 AU) and cool (surface temperatures  ∼10 000 K) objects. We follow the evolution of dark stars from their inception at  ∼[Formula: see text] as they accrete mass from their surroundings to become supermassive stars, some even reaching masses  >[Formula: see text] and luminosities  >[Formula: see text], making them detectable with the upcoming James Webb Space Telescope. Once the dark matter runs out and the dark star dies, it may collapse to a black hole; thus dark stars may provide seeds for the supermassive black holes observed throughout the Universe and at early times. Other sites for dark star formation may exist in the Universe today in regions of high dark matter density such as the centers of galaxies. The current review briefly discusses dark stars existing today, but focuses on the early generation of dark stars.

Modified gravity has garnered interest as a backstop against dark matter and dark energy (DE). As one possible modification, the graviton can become massive, which introduces a new scalar field--here with a Galileon-type symmetry. The field can lead to a nontrivial equation of state of DE which is density and scale dependent. Tension between type Ia supernovae and Planck could be reduced. In voids, the scalar field dramatically alters the equation of state of DE, induces a soon-observable gravitational slip between the two metric potentials, and develops a topological defect (domain wall) due to a nontrivial vacuum structure for the field.

A mechanism is identified whereby dark matter (DM) in protostellar halos dramatically alters the current theoretical framework for the formation of the first stars. Heat from neutralino DM annihilation is shown to overwhelm any cooling mechanism, consequently impeding the star formation process and possibly leading to a new stellar phase. A "dark star" may result: a giant ( greater, similar 1 AU) hydrogen-helium star powered by DM annihilation instead of nuclear fusion. Observational consequences are discussed.