We revisit and clarify the gauge dependence of gravitational waves generated at second order from scalar perturbations. In a universe dominated by a perfect fluid with a constant equation-of-state parameter w, we compute the energy density of such induced gravitational waves in the Newtonian, comoving, and uniform curvature gauges. Huge differences are found between the Newtonian and comoving gauge results for any w (≥ 0). This is always caused by the perturbation of the shift vector. Interestingly, the Newtonian and uniform curvature gauge calculations give the same energy density for w > 0. In the case of w = 0, the uniform curvature gauge result differs only by a factor from that of the comoving gauge, but deviates significantly from that of the Newtonian gauge. Our calculation is done analytically for w = 0 and w = 1/3, and our result is consistent with the previous numerical one. *

No abstract

The Effective Field Theory (EFT) of perturbations on an arbitrary background geometry with a timelike scalar profile was recently constructed in the context of scalar-tensor theories. In this paper, we use this EFT to study quasinormal frequencies of odd-parity perturbations on a static and spherically symmetric black hole background. Keeping a set of operators that can accommodate shift-symmetric quadratic higher-order scalar-tensor theories, we demonstrate the computation for two examples of hairy black holes, of which one is the stealth Schwarzschild solution and the other is the Hayward metric accompanied by a non-trivial scalar field. We emphasize that this is the first phenomenological application of the EFT, opening a new possibility to test general relativity and modified gravity theories in the strong gravity regime.