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 in all three gauges behave closely with minimal discrepancy. As expected, when going in sub-horizon modes, $k\tau \gg 1$, the discrepancy decreases and the behavior matches, pointing to a gauge-invariant observable.

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• Scalar-Induced Gravitational Waves in Modified Gravity
• Implications for Pulsar Timing Arrays of Sub-solar Black Hole Detections: From LVK to Einstein Telescope and Cosmic Explorer
• The transverse-traceless gauge and the gauge problem of second order gravitational waves
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity