### Abstract

A tensor-type cosmological perturbation, defined as a transverse and traceless spatial fluctuation, is often interpreted as gravitational waves. While decoupled from the scalar-type perturbations in linear order, the tensor perturbations can be sourced from the scalar-type in nonlinear order. The tensor perturbations generated by the quadratic combination of a linear scalar-type cosmological perturbation are widely studied in the literature, but all previous studies are based on a zero-shear gauge without proper justification. Here, we show that, being second order in perturbation, such an induced tensor perturbation is generically gauge dependent. In particular, the gravitational wave power spectrum depends on the hypersurface (temporal gauge) condition taken for the linear scalar perturbation. We further show that, during the matter-dominated era, the induced tensor modes dominate over the linearly evolved primordial gravitational wave amplitude for K ≳ 10^{-2}(h/Mpc)even for the gauge that gives the lowest induced tensor modes with the optimistic choice of primordial gravitational waves (r = 0.1). The induced tensor modes, therefore, must be modeled correctly specific to the observational strategy for the measurement of primordial gravitational waves from large-scale structure via, for example, the parity-odd mode of weak gravitational lensing, or clustering fossils.

Original language | English (US) |
---|---|

Article number | 46 |

Journal | Astrophysical Journal |

Volume | 842 |

Issue number | 1 |

DOIs | |

State | Published - Jun 10 2017 |

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### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*842*(1), [46]. https://doi.org/10.3847/1538-4357/aa74be

}

*Astrophysical Journal*, vol. 842, no. 1, 46. https://doi.org/10.3847/1538-4357/aa74be

**Gauge Dependence of Gravitational Waves Generated from Scalar Perturbations.** / Hwang, Jai Chan; Jeong, Donghui; Noh, Hyerim.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Gauge Dependence of Gravitational Waves Generated from Scalar Perturbations

AU - Hwang, Jai Chan

AU - Jeong, Donghui

AU - Noh, Hyerim

PY - 2017/6/10

Y1 - 2017/6/10

N2 - A tensor-type cosmological perturbation, defined as a transverse and traceless spatial fluctuation, is often interpreted as gravitational waves. While decoupled from the scalar-type perturbations in linear order, the tensor perturbations can be sourced from the scalar-type in nonlinear order. The tensor perturbations generated by the quadratic combination of a linear scalar-type cosmological perturbation are widely studied in the literature, but all previous studies are based on a zero-shear gauge without proper justification. Here, we show that, being second order in perturbation, such an induced tensor perturbation is generically gauge dependent. In particular, the gravitational wave power spectrum depends on the hypersurface (temporal gauge) condition taken for the linear scalar perturbation. We further show that, during the matter-dominated era, the induced tensor modes dominate over the linearly evolved primordial gravitational wave amplitude for K ≳ 10-2(h/Mpc)even for the gauge that gives the lowest induced tensor modes with the optimistic choice of primordial gravitational waves (r = 0.1). The induced tensor modes, therefore, must be modeled correctly specific to the observational strategy for the measurement of primordial gravitational waves from large-scale structure via, for example, the parity-odd mode of weak gravitational lensing, or clustering fossils.

AB - A tensor-type cosmological perturbation, defined as a transverse and traceless spatial fluctuation, is often interpreted as gravitational waves. While decoupled from the scalar-type perturbations in linear order, the tensor perturbations can be sourced from the scalar-type in nonlinear order. The tensor perturbations generated by the quadratic combination of a linear scalar-type cosmological perturbation are widely studied in the literature, but all previous studies are based on a zero-shear gauge without proper justification. Here, we show that, being second order in perturbation, such an induced tensor perturbation is generically gauge dependent. In particular, the gravitational wave power spectrum depends on the hypersurface (temporal gauge) condition taken for the linear scalar perturbation. We further show that, during the matter-dominated era, the induced tensor modes dominate over the linearly evolved primordial gravitational wave amplitude for K ≳ 10-2(h/Mpc)even for the gauge that gives the lowest induced tensor modes with the optimistic choice of primordial gravitational waves (r = 0.1). The induced tensor modes, therefore, must be modeled correctly specific to the observational strategy for the measurement of primordial gravitational waves from large-scale structure via, for example, the parity-odd mode of weak gravitational lensing, or clustering fossils.

UR - http://www.scopus.com/inward/record.url?scp=85021117157&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021117157&partnerID=8YFLogxK

U2 - 10.3847/1538-4357/aa74be

DO - 10.3847/1538-4357/aa74be

M3 - Article

AN - SCOPUS:85021117157

VL - 842

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1

M1 - 46

ER -