We analytically study the gauge dependence of scalar–induced gravitational waves (SIGWs) sourced by primordial isocurvature perturbations during radiation domination, working across nine gauges. Through analytical integrations of the kernels supported by graphical comparison we identify a clear dichotomy. We find that in some gauges viz. the uniform-density, total-matter, uniform-curvature, comoving-orthogonal, and transverse-traceless gauges the energy density grows polynomially in conformal time ${\eta }^n$, where $n$ varies from 2 to 8, while in rest of the gauges viz. the longitudinal, uniform-expansion, Newtonian-motion, and N-body gauges the late-time energy spectrum converges, and SIGWs behave as radiation. For subhorizon modes ($k\eta \gg 1$), the divergence becomes severe, showing that SIGWs are gauge-dependent observables in this regime. We resolve it through a kernel projection that isolates the luminal, freely propagating gravitational wave components [oscillating as $\sin (k\eta )$ and $\cos (k\eta )$], eliminating spurious contributions. The resulting kernel decays as $(k\eta {)}^{-1}$ and yields a finite, gauge-independent late-time spectrum, confirming that only luminal modes represent physical SIGWs.

Close

PrevNext

View figure in article

• Gravitational waves