Abstract
Horndeski's theory of gravity is the most general scalar-tensor theory with a single scalar whose equations of motion contain at most second-order derivatives. A subsector of Horndeski's theory known as ``Fab Four'' gravity allows for dynamical self-tuning of the quantum vacuum energy, and therefore it has received particular attention in cosmology as a possible alternative to the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. Here we study compact stars in Fab Four gravity, which includes as special cases general relativity (``George''), Einstein-dilaton-Gauss-Bonnet gravity (``Ringo''), theories with a nonminimal coupling with the Einstein tensor (``John''), and theories involving the double-dual of the Riemann tensor (``Paul''). We generalize and extend previous results in theories of the John class and were not able to find realistic compact stars in theories involving the Paul class.
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