Constraining the equation of state in modified gravity via universal relations

Modern multimessenger astronomical observations and heavy ion experiments provide new insights into the structure of compact objects. Nevertheless, much ambiguity remains when it comes to superdense matter above the nuclear saturation density such as that found within neutron stars. Recently, equation of state (EOS)-independent universal relations between the physical parameters of static neutron stars at the maximum-mass point have been derived within General Relativity (GR), and they were used to constrain EOS candidates. In the present paper, we generalize these relations to neutron stars in massive scalar-tensor theories. More specifically, we explore 53 different EOS candidates and prove that the resulting relations for scalarized neutron stars are indeed EOS independent up to a large extent and they can be significantly different compared to GR. As a result, multiple constraints on the EOS are derived within scalar-tensor theories, and it turns out that the allowed set of EOS can differ a lot with respect to Einstein's theory. This demonstrates the importance of modified gravity effects when imposing constraints on the EOS. The derived universal relations can be potentially used as well to test the theory of gravity in an EOS-independent way. We examine also the effects coming from nonbaryonic EOS both in GR and in scalar-tensor theories and show that, even though they spoil significantly the EOS universality, as expected, the effects coming from the modification of the theory of gravity can be significantly larger.