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Abstract

A major science goal of gravitational-wave (GW) observations is to probe the
nature of gravity and constrain modifications to General Relativity. An
established class of modified gravity theories are scalar-tensor models, which
introduce an extra scalar degree of freedom. This affects the internal
structure of neutron stars (NSs), as well as their dynamics and GWs in binary
systems, where distinct novel features can arise from the appearance of scalar
condensates in parts of the parameter space. To improve the robustness of the
analyses of such GW events requires advances in modeling
internal-structure-dependent phenomena in scalar-tensor theories. We develop an
effective description of potentially scalarized NSs on large scales, where
information about the interior is encoded in characteristic Love numbers or
equivalently tidal deformabilities. We demonstrate that three independent tidal
deformabilities are needed to characterize the configurations: a scalar,
tensor, and a novel 'mixed' parameter, and develop the general methodology to
compute these quantities. We also present case studies for different NS
equations of state and scalar properties and provide the mapping between the
deformabilities in different frames often used for calculations. Our results
have direct applications for future GW tests of gravity and studies of
potential degeneracies with other uncertain physics such as the equation of
state or presence of dark matter in NS binary systems.