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On the gauge dependence of gravitational waves generated at second order from scalar perturbations

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arxiv 1910.01880 v2 pith:H2G3HKC3 submitted 2019-10-04 gr-qc astro-ph.CO

classification gr-qcastro-ph.CO
keywords gaugenewtoniancomovingcurvaturegravitationaluniformwavesdensity
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abstract

We revisit and clarify the gauge dependence of gravitational waves generated at second order from scalar perturbations. In a universe dominated by a perfect fluid with a constant equation-of-state parameter $w$, we compute the energy density of such induced gravitational waves in the Newtonian, comoving, and uniform curvature gauges. Huge differences are found between the Newtonian and comoving gauge results for any $w \,(\ge 0)$. This is always caused by the perturbation of the shift vector. Interestingly, the Newtonian and uniform curvature gauge calculations give the same energy density for $w>0$. In the case of $w=0$, the uniform curvature gauge result differs only by a factor from that of the comoving gauge, but deviates significantly from that of the Newtonian gauge. Our calculation is done analytically for $w=0$ and $w=1/3$, and our result is consistent with the previous numerical one.

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Forward citations

Cited by 6 Pith papers

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

  1. Observable Gravitational Wave Strain at Second Order

    gr-qc 2025-12 conditional novelty 7.0 of 10

    At second order, the gravitational-wave strain measured by geodesic observers exchanging light pulses is the transverse-traceless metric perturbation in the Newton gauge (h_N^(2)).

  2. 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.

  3. Scalar-induced gravitational waves from a box-shaped curvature power spectrum

    gr-qc 2026-07 accept novelty 5.5 of 10

    Analytic SIGW spectra for a log-box curvature power spectrum: narrow-box geometric overlap factor turning IR slope k^{3}ln^{2}k into k^{2}ln^{2}k, plus broad-box product of universal edge functions.

  4. Implications for Pulsar Timing Arrays of Sub-solar Black Hole Detections: From LVK to Einstein Telescope and Cosmic Explorer

    astro-ph.CO 2025-08 conditional novelty 5.0 of 10

    A Bayesian analysis shows that a future sub-solar PBH detection would make the primordial SIGW interpretation of PTA data favored over the SMBH interpretation, but this preference is driven by the detection prior.

  5. 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.

  6. 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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