Theory and Applications of Physical Science Vol. 3

Nakamura, Kouji; Backerra, Anna C. M.; Mansour, Heba F.; Takagi, Osamu; Sakamoto, Masamichi; Yoichi, Hideo; Kawano, Kimiko; Yamamoto, Mikio; Zbiral, Guido

doi:10.9734/bpi/taps/v3

Cited by 11 publications

(14 citation statements)

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“…If that were the case, it would pose serious problems for the theoretical predictions of induced GWs. Proposed solutions so far rely on either finding gauge invariant variables [32,36,48,49,52,54,55] or arguing which would be the most suitable gauge [32,35]. While these studies go certainly in the right direction, they are not a satisfactory solution of the gauge dependence pointed out in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…Since Ref. [21] first pointed out that the induced GW spectrum is strictly speaking gauge dependent (see also Ref [33] for numerical studies in general cosmological backgrounds), there has been a lot of discussion and proposed solutions to the gauge issue [32][33][34][35][36][48][49][50][51][52][53][54][55][56]. Most of the solutions can be classified in either building a gauge invariant formulation of tensor modes at second order [36,48,49,52,54,55] or finding an appropriate gauge choice that best describes the GW detection [32,35].…”

Section: Introductionmentioning

confidence: 99%

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Approximate gauge independence of the induced gravitational wave spectrum

Domènech,

Sasaki

2020

Preprint

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Gravitational waves (GWs) induced by scalar curvature fluctuations are an important source of the cosmological GW background and a crucial counterpart of the primordial black hole scenario. However, doubts have been cast on the theoretically predicted induced GW spectrum due to its seeming gauge dependence. In this paper, we shed light on the gauge dependence issue of the induced GW spectrum in general cosmological backgrounds. First, inspired by the Hamiltonian formalism we provide very simple formulas for the tensor modes at second order in cosmological perturbation theory. We also emphasize the difference between observable and gauge invariant variables. Second, we argue that the Newton (or shear-free) gauge is suitable for both the calculation of induced GWs and the physical interpretation. We then show that, most notably, the induced GW spectrum is invariant under a set of reasonable gauge transformations, i.e. physically well behaved on small scales, once the source term has become inactive. This includes the commonly used flat, constant Hubble and synchronous gauges but excludes the comoving slicing gauge. We also show that a particular solution of the GW equation in a dust dominated universe while the source term is active can be gauged away by a small change of gauge.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximate gauge independence of the induced gravitational wave spectrum

Domènech,

Sasaki

2020

Preprint

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“…( 7)- (10) in Appendix C. These formulae could also be found in Refs. [8,42,43]. Recently, they have been used in cosmology [8,43] and in the post-Newtonian formalism [44].…”

Section: B Gauge Invariant Metric Perturbationsmentioning

confidence: 99%

Note on gauge invariance of second order cosmological perturbations

Chang,

Wang,

Zhu

2020

Preprint

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“…Phenomenologically, the induced scalar perturbations have been studied in the context of the CMB anisotropies [64][65][66][67][68][69][70][71][72][73][74][75][76][77][78] and the large scale structures [79][80][81][82][83]. Also, there are works focusing on the formalisms of the second-order perturbations, including scalar, vector, and tensor perturbations [84][85][86][87][88][89][90][91]. In this paper, we derive the analytic solutions of the induced scalar perturbations in two eras, a radiation-dominated (RD) era and a matterdominated (MD) era.…”

Section: Introductionmentioning

confidence: 99%

Analytic solutions of scalar perturbations induced by scalar perturbations

Inomata

2020

Preprint

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We study scalar perturbations induced by scalar perturbations through the non-linear interaction appearing at second order in perturbations. We derive analytic solutions of the induced scalar perturbations in a perfect fluid. In particular, we consider the perturbations in a radiation-dominated era and a matter-dominated era. With the analytic solutions, we also discuss the power spectra of the induced perturbations.

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Theory and Applications of Physical Science Vol. 3

Cited by 11 publications

References 0 publications

Approximate gauge independence of the induced gravitational wave spectrum

Approximate gauge independence of the induced gravitational wave spectrum

Note on gauge invariance of second order cosmological perturbations

Analytic solutions of scalar perturbations induced by scalar perturbations

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