Built on

R.-G. Cai, S. Pi, S.-J. Wang, and X.-Y. Yang, Resonant multiple peaks in the induced gravitational waves, J. Cosmol. Astropart. Phys. 05 ( 2019
Original
1901
Earlier work this paper cites.
Y.-F. Cai, C. Chen, X. Tong, D.-G. Wang, and S.-F. Yan, When Primordial Black Holes from Sound Speed Resonance Meet a Stochastic Background of Gravitational Waves, Phys. Rev. D 100
Original
1902
Earlier work this paper cites.
K. Inomata, K. Kohri, T. Nakama, and T. Terada, Enhancement of Gravitational Waves Induced by Scalar Perturbations due to a Sudden Transition from an Early Matter Era to the Radiation Era, Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
K. Inomata, K. Kohri, T. Nakama, and T. Terada, Gravitational Waves Induced by Scalar Perturbations during a Gradual Transition from an Early Matter Era to the Radiation Era, J. Cosmol. Astropart. Phys. 10 ( 2019
Original
1904
Earlier work this paper cites.
M. Drees and Y. Xu, Critical Higgs Inflation and Second Order Gravitational Wave Signatures, arXiv:1905.13581
Original
1905
Earlier work this paper cites.
Y. Lu, Y. Gong, Z. Yi, and F. Zhang, Constraints on primordial curvature perturbations from primordial black hole dark matter and secondary gravitational waves, J. Cosmol. Astropart. Phys. 12 ( 2019
Original
1907
Earlier work this paper cites.
R.-G. Cai, S. Pi, S.-J. Wang, and X.-Y. Yang, Pulsar Timing Array Constraints on the Induced Gravitational Waves, J. Cosmol. Astropart. Phys. 10 ( 2019
Original
1907
Earlier work this paper cites.
R.-G. Cai, S. Pi, and M. Sasaki, Universal infrared scaling of gravitational wave background spectra, arXiv:1909.13728
Original
1909
Earlier work this paper cites.
J.-O. Gong, Analytic integral solutions for induced gravitational waves, arXiv:1909.12708
Original
1909
Earlier work this paper cites.
C. Yuan, Z.-C. Chen, and Q.-G. Huang, Log-dependent slope of scalar induced gravitational waves in the infrared regions, Phys. Rev. D 101
Original
1910
Earlier work this paper cites.
F. Hajkarim and J. Schaffner-Bielich, Thermal History of the Early Universe and Primordial Gravitational Waves from Induced Scalar Perturbations, Phys. Rev. D 101
Original
1910
Earlier work this paper cites.
K. Tomikawa and T. Kobayashi, On the gauge dependence of gravitational waves generated at second order from scalar perturbations, Phys. Rev. D 101
Original
1910
Earlier work this paper cites.
V. De Luca, G. Franciolini, A. Kehagias, and A. Riotto, On the Gauge Invariance of Cosmological Gravitational Waves, J. Cosmol. Astropart. Phys. 03 ( 2020
Original
1911
Earlier work this paper cites.
C. Fu, P. Wu, and H. Yu, Scalar induced gravitational waves in inflation with gravitationally enhanced friction, Phys. Rev. D 101
Original
1912
Earlier work this paper cites.
G. Domènech, Induced gravitational waves in a general cosmological background, Int. J. Mod. Phys. D 29
Original
1912
Earlier work this paper cites.
C. Yuan, Z.-C. Chen, and Q.-G. Huang, Scalar induced gravitational waves in different gauges, Phys. Rev. D 101
Original
1912
Earlier work this paper cites.
K. Inomata and T. Terada, Gauge Independence of Induced Gravitational Waves, Phys. Rev. D 101
Original
1912
Earlier work this paper cites.
W. H. Press and E. T. Vishniac, Tenacious myths about cosmological perturbations larger than the horizon size, Astrophys. J. 239
1980
Earlier work this paper cites.

Similar

J. M. Bardeen, Gauge Invariant Cosmological Perturbations, Phys. Rev. D 22
1980
Cited alongside, same era.
B. Bednarz, On Difficulties in Synchronous Gauge Density Fluctuations, Phys. Rev. D 31
1985
Cited alongside, same era.
C.-P. Ma and E. Bertschinger, Cosmological perturbation theory in the synchronous and conformal Newtonian gauges, Astrophys. J. 455
1995
Cited alongside, same era.
K. Danzmann, LISA: An ESA cornerstone mission for a gravitational wave observatory, Class. Quant. Grav. 14
1997
Cited alongside, same era.
M. Bruni, S. Matarrese, S. Mollerach, and S. Sonego, Perturbations of space-time: Gauge transformations and gauge invariance at second order and beyond, Class. Quant. Grav. 14
1997
Cited alongside, same era.

Then

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Original
2013
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C. Pitrou, X. Roy, and O. Umeh, xPand: An algorithm for perturbing homogeneous cosmologies, Class. Quant. Grav. 30
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C. J. Moore, R. H. Cole, and C. P. L. Berry, Gravitational-wave sensitivity curves, Class. Quant. Grav. 32
Original
2015
Later among the works it cites.
J. Luo et al. (TianQin), TianQin: a space-borne gravitational wave detector, Class. Quant. Grav. 33
Original
2016
Later among the works it cites.
K. Inomata, M. Kawasaki, K. Mukaida, Y. Tada, and T. T. Yanagida, Inflationary primordial black holes for the LIGO gravitational wave events and pulsar timing array experiments, Phys. Rev. D 95

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2020

Gauge transformation of scalar induced gravitational waves

Lu, Yizhou, Ali, Arshad, Gong, Yungui et al.

Understand

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.

Built on

R.-G. Cai, S. Pi, S.-J. Wang, and X.-Y. Yang, Resonant multiple peaks in the induced gravitational waves, J. Cosmol. Astropart. Phys. 05 ( 2019
Original
1901
Earlier work this paper cites.
Y.-F. Cai, C. Chen, X. Tong, D.-G. Wang, and S.-F. Yan, When Primordial Black Holes from Sound Speed Resonance Meet a Stochastic Background of Gravitational Waves, Phys. Rev. D 100
Original
1902
Earlier work this paper cites.
K. Inomata, K. Kohri, T. Nakama, and T. Terada, Enhancement of Gravitational Waves Induced by Scalar Perturbations due to a Sudden Transition from an Early Matter Era to the Radiation Era, Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
K. Inomata, K. Kohri, T. Nakama, and T. Terada, Gravitational Waves Induced by Scalar Perturbations during a Gradual Transition from an Early Matter Era to the Radiation Era, J. Cosmol. Astropart. Phys. 10 ( 2019
Original
1904
Earlier work this paper cites.
M. Drees and Y. Xu, Critical Higgs Inflation and Second Order Gravitational Wave Signatures, arXiv:1905.13581
Original
1905
Earlier work this paper cites.
Y. Lu, Y. Gong, Z. Yi, and F. Zhang, Constraints on primordial curvature perturbations from primordial black hole dark matter and secondary gravitational waves, J. Cosmol. Astropart. Phys. 12 ( 2019
Original
1907
Earlier work this paper cites.
R.-G. Cai, S. Pi, S.-J. Wang, and X.-Y. Yang, Pulsar Timing Array Constraints on the Induced Gravitational Waves, J. Cosmol. Astropart. Phys. 10 ( 2019
Original
1907
Earlier work this paper cites.
R.-G. Cai, S. Pi, and M. Sasaki, Universal infrared scaling of gravitational wave background spectra, arXiv:1909.13728
Original
1909
Earlier work this paper cites.
J.-O. Gong, Analytic integral solutions for induced gravitational waves, arXiv:1909.12708
Original
1909
Earlier work this paper cites.
C. Yuan, Z.-C. Chen, and Q.-G. Huang, Log-dependent slope of scalar induced gravitational waves in the infrared regions, Phys. Rev. D 101
Original
1910
Earlier work this paper cites.
F. Hajkarim and J. Schaffner-Bielich, Thermal History of the Early Universe and Primordial Gravitational Waves from Induced Scalar Perturbations, Phys. Rev. D 101
Original
1910
Earlier work this paper cites.
K. Tomikawa and T. Kobayashi, On the gauge dependence of gravitational waves generated at second order from scalar perturbations, Phys. Rev. D 101
Original
1910
Earlier work this paper cites.
V. De Luca, G. Franciolini, A. Kehagias, and A. Riotto, On the Gauge Invariance of Cosmological Gravitational Waves, J. Cosmol. Astropart. Phys. 03 ( 2020
Original
1911
Earlier work this paper cites.
C. Fu, P. Wu, and H. Yu, Scalar induced gravitational waves in inflation with gravitationally enhanced friction, Phys. Rev. D 101
Original
1912
Earlier work this paper cites.
G. Domènech, Induced gravitational waves in a general cosmological background, Int. J. Mod. Phys. D 29
Original
1912
Earlier work this paper cites.
C. Yuan, Z.-C. Chen, and Q.-G. Huang, Scalar induced gravitational waves in different gauges, Phys. Rev. D 101
Original
1912
Earlier work this paper cites.
K. Inomata and T. Terada, Gauge Independence of Induced Gravitational Waves, Phys. Rev. D 101
Original
1912
Earlier work this paper cites.
W. H. Press and E. T. Vishniac, Tenacious myths about cosmological perturbations larger than the horizon size, Astrophys. J. 239
1980
Earlier work this paper cites.

Similar

J. M. Bardeen, Gauge Invariant Cosmological Perturbations, Phys. Rev. D 22
1980
Cited alongside, same era.
B. Bednarz, On Difficulties in Synchronous Gauge Density Fluctuations, Phys. Rev. D 31
1985
Cited alongside, same era.
C.-P. Ma and E. Bertschinger, Cosmological perturbation theory in the synchronous and conformal Newtonian gauges, Astrophys. J. 455
1995
Cited alongside, same era.
K. Danzmann, LISA: An ESA cornerstone mission for a gravitational wave observatory, Class. Quant. Grav. 14
1997
Cited alongside, same era.
M. Bruni, S. Matarrese, S. Mollerach, and S. Sonego, Perturbations of space-time: Gauge transformations and gauge invariance at second order and beyond, Class. Quant. Grav. 14
1997
Cited alongside, same era.