Gauge-dependence of scalar induced gravitational waves

Abstract 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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mi>τ</mml:mi> <mml:mo>≫</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , the discrepancy decreases and the behavior converges, suggesting that SIGWs can be treated as gauge-invariant observables in this regime.