Scalar induced gravitational waves in different gauges

Yuan, Chen; Chen, Zu-Cheng; Huang, Qing-Guo

doi:10.1103/physrevd.101.063018

Cited by 119 publications

(100 citation statements)

References 67 publications

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“…These LIGO/Virgo BBHs present a much heavier mass distribution (in particular the sourceframe primary mass of GW170729 event can be as heavy as 50.2 +16.2 −10.2 M [7]) than that inferred from X-ray observations [28][29][30][31], which would challenge the formation and evolution mechanisms of astrophysical black holes. One possible explanation for LIGO/Virgo BBHs is the primordial black holes (PBHs) [8][9][10] formed through the gravitational collapse of the primordial density fluctuations [32,33], which may accompany the induced GWs [34][35][36][37]. On the other hand, PBHs can also be a candidate of cold dark matter (CDM), and the abundance of PBHs in CDM has been constrained by various experiments [34,36,[38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56].…”

Section: Introductionmentioning

confidence: 99%

Merger history of primordial black-hole binaries

Wu¹

2020

Phys. Rev. D

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As a candidate of dark matter, primordial black holes (PBHs) have attracted more and more attentions as they could be possible progenitors of the heavy binary black holes (BBHs) observed by LIGO/Virgo. Accurately estimating the merger rate of PBH binaries will be crucial to reconstruct the mass distribution of PBHs. It was pointed out the merger history of PBHs may shift the merger rate distribution depending on the mass function of PBHs. In this paper, we use 10 BBH events from LIGO/Virgo O1 and O2 observing runs to constrain the merger rate distribution of PBHs by accounting the effect of merger history. It is found that the second merger process makes subdominant contribution to the total merger rate, and hence the merger history effect can be safely neglected.

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Section: Introductionmentioning

confidence: 99%

Merger history of primordial black-hole binaries

Wu¹

2020

Phys. Rev. D

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“…Even if the description of the longitudinal gauge is considered more computable and hence more reliable (see e. g. [19]), there are no reasons why this should be the case so that the scheme of Ref. [18] has been subsequently replicated with different and sometimes contradictory conclusions [20,21,22]. Reference [20] attributes the difference of the results to the evolutionary features of each gauge.…”

Section: Introductionmentioning

confidence: 99%

“…[18] has been subsequently replicated with different and sometimes contradictory conclusions [20,21,22]. Reference [20] attributes the difference of the results to the evolutionary features of each gauge. Reference [21] suggests that the effective anisotropic stress is gauge-independent but the authors also imply, in their conclusions, that the observational sensitivities for the tensor perturbations induced from the effective anisotropic stress will be different from those for conventional gravitational waves.…”

Section: Introductionmentioning

confidence: 99%

Effective anisotropic stresses of the relic gravitons

Giovannini

2020

Int. J. Mod. Phys. D

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The effective anisotropic stresses induced by the scalar modes of the geometry depend on the coordinate system so that the comparison of the competing results is ultimately determined by the evolution of the pivotal variables in each particular gauge. After arguing that the only reasonable physical coordinate systems for this problem are the ones where the gauge freedom is completely fixed (like the longitudinal and the uniform curvature gauges), we propose a novel gauge-invariant strategy for the comparison of gauge-dependent results. Instead of employing the pivotal variables of a given coordinate system, the effective anisotropic stress is solely expressed in terms of the gravitating normal modes of the plasma and in terms of their conformal time derivatives. The new approach is explicitly gauge-invariant and when the wavelengths of the normal modes are either shorter or larger than the sound horizon, the physical limits of the anisotropic stresses are determined without relying on the specific details of the background evolution. The relevance of the proposed strategy is discussed in the general situation where the scalar anisotropic stress and the nonadiabatic pressure fluctuations are simultaneously present. We finally argue that the anisotropic stress can be most efficiently obtained from the second-order effective action of the curvature inhomogeneities.

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“…Similarly curvature inhomogeneities may cause higher-order corrections to the stochastic backgrounds of relic gravitons and this second effect involves an effective anisotropic stress which is customarily assessed within the Landau-Lifshitz prescription [2,6,10,11]. For the same reasons given above the Landau-Lifshitz approach applied to the scalar modes of the geometry is not gauge-invariant: different and sometimes contradictory statements exist in the current literature [12,13,14,15]. Part of the problem is that the gaugedependent derivations follow the dynamical evolutions of the pivotal variables in the particular coordinate system where the results have been derived.…”

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confidence: 99%

“…A relevant property of M (X) (z, w) is that it is generically symmetric for w → z and z → w. In the particular case of the radiation-dominated plasma the exact expressions of 7into Eq. (14). This procedure has been already discussed for an analog situation of waterfall fields in Ref.…”

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confidence: 99%

Spurious gauge-invariance of higher-order contributions to the spectral energy density of the relic gravitons

Giovannini

2020

Int. J. Mod. Phys. A

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In the same way as the energy density associated with the tensor modes of the geometry modifies the evolution of the curvature perturbations, the scalar modes may also indirectly affect the cosmic backgrounds of relic gravitons by inducing higher-order corrections that are only superficially gauge-invariant. This spurious gauge-invariance gets manifest when the effective anisotropic stresses, computed in different coordinate systems, are preliminarily expressed in a form that only depends on the curvature inhomogeneities defined on comoving orthogonal hypersurfaces and on their corresponding time derivatives. Using this observation we demonstrate in general terms that the higher-order contributions derived in diverse coordinate systems coincide when the wavelengths are smaller than the sound horizon defining the evolution of the curvature inhomogeneities but they lead to sharply different results in the opposite limit. A similar drawback arises when the energy density of the relic gravitons is derived from competing energy–momentum pseudotensors and should be consistently taken into account in the related phenomenological discussions.

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Scalar induced gravitational waves in different gauges

Cited by 119 publications

References 67 publications

Merger history of primordial black-hole binaries

Merger history of primordial black-hole binaries

Effective anisotropic stresses of the relic gravitons

Spurious gauge-invariance of higher-order contributions to the spectral energy density of the relic gravitons

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