Approximate gauge independence of the induced gravitational wave spectrum

Understand

Gravitational waves (GWs) induced by scalar curvature fluctuations are an important source of the cosmological GW background and a crucial counterpart of the primordial black hole scenario.

• However, doubts have been cast on the theoretically predicted induced GW spectrum due to its seeming gauge dependence.
• In this paper, we shed light on the gauge dependence issue of the induced GW spectrum in general cosmological backgrounds.
• First, inspired by the Hamiltonian formalism we provide very simple formulas for the tensor modes at second order in cosmological perturbation theory.