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We revisit the vital issue of gauge dependence in the scalar-inducedsecondary gravitational waves (SIGWs), focusing on the radiation domination(RD) and matter domination (MD) eras. The energy density spectrum is the mainphysical observable in such induced gravitational waves. For various gaugechoices, there has been a divergence in the energy density,$\Omega_{\text{GW}}$, of SIGWs. We calculate SIGWs in different gauges toquantify this divergence to address the gauge-dependent problem. In ourprevious studies, we had found that the energy density diverges in thepolynomial power of conformal time (e.g., $\eta^6$ in uniform density gauge).We try to fix this discrepancy by adding a counter-term that removes thefictitious terms in secondary tensor perturbations. We graphically compare thecalculations in various gauges and also comment on the physical origin of theobserved gauge dependence.

On the gauge dependence of scalar induced secondary gravitational waves during radiation and matter domination eras