Relativistic stars in beyond Horndeski theories

Abstract

This work studies relativistic stars in beyond Horndeski scalar-tensor\ntheories that exhibit a breaking of the Vainshtein mechanism inside matter,\nfocusing on a model based on the quartic beyond Horndeski Lagrangian. We\nself-consistently derive the scalar field profile for static spherically\nsymmetric objects in asymptotically de Sitter space-time and show that the\nVainshtein breaking branch of the solutions is the physical branch thereby\nresolving several ambiguities with non-relativistic frameworks. The geometry\noutside the star is shown to be exactly Schwarzschild-de Sitter and therefore\nthe PPN parameter $\\beta_{\\rm PPN}=1$, confirming that the external screening\nworks at the post-Newtonian level. The Tolman-Oppenheimer-Volkoff (TOV)\nequations are derived and a new lower bound on the Vainshtein breaking\nparameter $\\Upsilon_1>-4/9$ is found by requiring the existence of static\nspherically symmetric stars. Focusing on the unconstrained case where\n$\\Upsilon_1<0$, we numerically solve the TOV equations for polytropic and\nrealistic equations of state and find stars with larger radii at fixed mass.\nFurthermore, the maximum mass can increase dramatically and stars with masses\nin excess of $3M_\\odot$ can be found for relatively small values of the\nVainshtein breaking parameter. We re-examine white dwarf stars and show that\npost-Newtonian corrections are important in beyond Horndeski theories and\ntherefore the bounds coming from previous analyses should be revisited.\n