Gauge-dependence of scalar induced gravitational waves

In this review we look into the gauge-dependence of scalar-induced gravitational waves (SIGWs) that are second-order tensors produced by first-order scalar modes. The method includes deriving the background, first- and second-order Einstein field equations without imposing a gauge. We address the gauge-invariant approach and study the source-term of SIGWs in three different gauges: synchronous, Poisson, and uniform curvature gauge. We find that numerically computed kernels evaluated in a radiation epoch in all three gauges behave closely with minimal discrepancy. As expected, when going to sub-horizon modes, , the discrepancy decreases and the behavior converges, suggesting that SIGWs can be treated as gauge-invariant observables in this regime.