Speaker
Description
A tensor-type cosmological perturbation, defined as a transverse and traceless spatial metric fluctuation, is interpreted as gravitational waves. It decouples from scalar perturbations at linear order but is sourced by them at second order. These induced tensor modes are widely studied, yet all previous work adopts the zero-shear gauge without justification. We show that the induced tensor perturbation is generically gauge dependent: the gravitational wave power spectrum depends on the hypersurface condition chosen for the linear scalar perturbation. During matter domination the induced modes dominate over the linearly evolved primordial amplitude for k ≳ 10⁻² h/Mpc, even in the gauge that minimizes them and for r = 0.1. They therefore must be modeled correctly for each observational strategy targeting primordial gravitational waves from large-scale structure, such as the parity-odd mode of weak lensing or clustering fossils. Taking the CMB B-mode polarization from the relative velocity as an example, we show how a gauge-invariant observable is constructed. Finally, we show that the gauge ambiguity disappears once the induced tensor modes are expressed through the local tidal field.
