The power of binary pulsars in testing Gauss-Bonnet gravity

Binary pulsars are a powerful tool for probing strong gravity that still outperforms direct gravitational wave observations in a number of directions due to the remarkable accuracy of the pulsar timing. They can constrain very precisely the presence of additional charges of the orbiting neutron stars leading to new channels of energy and angular momentum loss, such as the scalar dipole radiation. In the present paper, we explore in detail the possibility of constraining different classes of scalar-Gauss-Bonnet gravity with binary pulsars. Additionally, the existing constraints related to the observed maximum mass of neutron stars are also updated. Interestingly, depending on the equation of state, the resulting limits on the theory coupling parameters can outperform the constraints coming from binary merger observations by up to a factor of 2 even for the so-called Einstein-dilaton-Gauss-Bonnet gravity where neutron stars are often underestimated as relevant theory probes. As an additional merit, precise Bayesian methods are compared with approximate approaches with the latter showing very good performance despite their simplicity.