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Gravitational waves (GWs) from merging black holes allow for unprecedentedprobes of strong-field gravity. Testing gravity in this regime requiresaccurate predictions of gravitational waveform templates in viable extensionsof General Relativity. We concentrate on scalar Gauss-Bonnet gravity, one ofthe most compelling classes of theories appearing as low-energy limit ofquantum gravity paradigms, which introduces quadratic curvature corrections togravity coupled to a scalar field and allows for black hole solutions withscalar-charge. Focusing on inspiralling black hole binaries, we compute theleading-order corrections due to curvature nonlinearities in the GW and scalarwaveforms, showing that the new contributions, beyond merely the effect ofscalar field, appear at first post-Newtonian order in GWs. We provideready-to-implement GW polarizations and phasing. Computing the GW phasing inthe Fourier domain, we perform a parameter-space study to quantify thedetectability of deviations from General Relativity. Our results lay importantfoundations for future precision tests of gravity with both parametrized andtheory-specific searches.

Nonlinear curvature effects in gravitational waves from inspiralling black hole binaries