Tidal deformabilities of neutron stars in scalar-Gauss-Bonnet gravity and their applications to multimessenger tests of gravity

The spacetime surrounding compact objects such as neutron stars and black holes provides an excellent place to study gravity in the strong, nonlinear, dynamical regime. Here, the effects of strong curvature can leave their imprint on observables which we may use to study gravity. Recently, NICER provided a mass and radius measurement of an isolated neutron star using x-rays, while LIGO/Virgo measured the tidal deformability of neutron stars through gravitational waves. These measurements can be used to test the relation between the tidal deformability and compactness of neutron stars that are known to be universal in general relativity. Here, we take (shift-symmetric) scalar-Gauss-Bonnet gravity (motivated by a low-energy effective theory of a string theory) as an example and study whether one can apply the NICER and LIGO/Virgo measurements to the universal relation to test the theory. To do so, this paper is mostly devoted on theoretically constructing tidally deformed neutron star solutions in this theory perturbatively and calculate the tidal deformability for the first time. We find that the relation between the tidal deformability and compactness remains to be mostly universal for a fixed dimensionless coupling constant of the theory though the relation is different from the one in general relativity. We also present a universal relation between the tidal deformability of one neutron star and the compactness for another neutron star that can be directly applied to observations by LIGO/Virgo and NICER. For the equations of state considered in this paper, it is still inconclusive whether one can place a meaningful bounds on scalar Gauss-Bonnet gravity with the new universal relations. However, we found a new bound from the mass measurement of the pulsar $\mathrm{J}0740+6620$ that is comparable to other existing bounds from black hole observations.