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Gravitational waves from compact binary coalescences are valuable for testing theories of gravity in the strong-field regime. They have also led to improved constraints on the nuclear equation of state at extreme densities by measuring the tidal Love numbers of merging neutron stars. Tidal Love numbers in alternate theories are expected to differ from their general relativistic counterpart. Despite this, tests of general relativity use the general relativistic tidal Love numbers.
Here, we calculate the $l\geq 2$ electric and magnetic tidal Love numbers for non-rotating stars in mono-scalar-tensor theories assuming spontaneous scalarization. We then use several viable equations of state to explore how the mass, radius, and tidal deformability relations differ from those of general relativity. The electric tidal deformability can differ by $\sim 350\%$, and the magnetic tidal deformability differs by $\sim 200 \%$. These deviations occur at large compactnesses ($C = M/r > 0.2$) and vary slightly depending on the equation of state. Lastly, we perform Bayesian parameter estimation of GW170817 to explore exactly how these modified tidal relations can effect inference.
We find that tidal Love numbers and tidal deformabilities can differ significantly from those in general relativity. These changes cause the inferred equation of state to differ between general relativity anf scalar tensor theory.
Applying these tidal Love numbers to the study of gravitational waves will allow for more consistent and accurate tests of scalar modes in gravitational waves from neutron star mergers.