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Gauge transformation of scalar induced gravitational waves

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arxiv 2006.03450 v2 pith:VNL7NHGQ submitted 2020-06-05 gr-qc

Yizhou Lu , Arshad Ali , Yungui Gong , Jiong Lin , Fengge Zhang This is my paper · ORCID
classification gr-qc
keywords gaugesigwsdensityenergygaugesgravitationalscalaruniform
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abstract

The gauge dependence of the scalar induced gravitational waves (SIGWs) generated at the second order imposes a challenge to the discussion of the secondary gravitational waves generated by scalar perturbations. We provide a general formula that is valid in any gauge for the calculation of SIGWs and the relationship for SIGWs calculated in various gauges under the coordinate transformation. The formula relating SIGWs in the Newtonian gauge to other gauges is used to calculate SIGWs in six different gauges. We find that the Newtonian gauge, the uniform curvature gauge, the synchronous gauge and the uniform expansion gauge yield the same result for the energy density of SIGWs. We also identify and eliminate the pure gauge modes that exist in the synchronous gauge. In the total matter gauge and the comoving orthogonal gauge, the energy density of SIGWs increases as $\eta^2$. While in the uniform density gauge, the energy density of SIGWs increases as $\eta^6$.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. General SIGW source for reheating dynamics

    gr-qc 2025-12 conditional novelty 7.0 of 10

    A gauge-invariant source term for scalar-induced gravitational waves is derived for smooth reheating with an inflaton field transitioning into fluids.

  2. On the Gauge Invariance of Secondary Gravitational Waves

    astro-ph.CO 2025-01 conditional novelty 5.0 of 10

    The paper argues that discarding non-light-speed modes of the second-order tensor perturbation makes the induced gravitational wave energy density gauge-invariant in both adiabatic and isocurvature scenarios.

  3. Tensor induced gravitational waves

    astro-ph.CO 2025-07 conditional novelty 4.0 of 10

    Second-order tensor-induced gravitational waves can shift the inferred parameters of small-scale primordial gravitational wave models fitted to NANOGrav 15-year data, with one model favored by Bayes factors.

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