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We study relativistic stars in Hordenski theories that evade the gravitational wave constraints and exhibit the Vainshtein mechanism, focusing on a model based on the cubic Galileon Lagrangian. We derive the scalar field profile for static spherically symmetric objects in asymptotically de Sitter space-time with a linear time dependence. The exterior solution matches the black hole solution found in the literature. Due to the Vainshtein mechanism, the stellar structure is indistinguishable from that of General Relativity with the same central density as long as the radius of the star is shorter than the Vainshtein radius. On the other hand, the scalar field is not suppressed beyond the Vainshtein radius. These solutions have an additional integration constant in addition to the mass of the star.
OGAWA et al. (Wed,) studied this question.