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At second-order, scalar perturbations can source traceless and transverseperturbations to the metric, called induced gravitational waves (IGW). Theapparent gauge-dependence of the IGW obscures the interpretation of thestochastic gravitational-wave signal. To elucidate the gauge dependence, westudy the IGW from manifestly gauge-invariant scalar perturbations, namely, therelative velocity between the baryon and cold dark matter. From this relativevelocity perturbation, we compute the dimensionless gravitational wave powerspectrum and the corresponding expected angular power spectrum of the B-modepolarization of the cosmic microwave background. Although the effect turns outto be unobservably small, the calculation demonstrates both the importance ofusing observable quantities to remove the gauge ambiguity and the observableconsequences of tensor perturbations which are not propagating gravitationalwaves.

Gauge-Invariant Tensor Perturbations Induced from Baryon-CDM Relative Velocity and the B-mode Polarization of the CMB