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PreprintCC0arXiv

Cosmological initial data without periodic boundary conditions

  • Károly Csukás
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Abstract

We apply the parabolic-hyperbolic formulation of the Einstein constraint equations to generate cosmological initial data. The freely specifiable geometric data correspond to flat Friedmann--Lemaître--Robertson--Walker background, while the matter sector contains localized anisotropic perturbations of a perfect fluid. Unlike the standard approach, our method evolves the constraints outward from regular data at the origin and therefore requires no boundary conditions. This makes our method well suited as a starting point in investigating systematic biases introduced by commonly adopted boundary conditions, such as periodic boundaries. A second advantage concerns uniqueness: standard elliptic solvers may fail when multiple solutions exist, whereas solving the constraints as a well-posed evolutionary system always yields a unique solution. To demonstrate our method, we implement it numerically and generate cosmological initial data with localized anisotropic perfect fluid perturbations.

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Cite

BibTeXRIS
BibTeX
@misc{csukas2026cosmological,
  title = {{Cosmological initial data without periodic boundary conditions}},
  author = {Károly Csukás},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.21308},
  eprint = {2607.21308},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.21308},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Cosmological initial data without periodic boundary conditions
AU  - Károly Csukás
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2607.21308
UR  - https://arxiv.org/abs/2607.21308
AB  - We apply the parabolic-hyperbolic formulation of the Einstein constraint equations to generate cosmological initial data. The freely specifiable geometric data correspond to flat Friedmann--Lemaître--Robertson--Walker background, while the matter sector contains localized anisotropic perturbations of a perfect fluid. Unlike the standard approach, our method evolves the constraints outward from regular data at the origin and therefore requires no boundary conditions. This makes our method well suited as a starting point in investigating systematic biases introduced by commonly adopted boundary conditions, such as periodic boundaries. A second advantage concerns uniqueness: standard elliptic solvers may fail when multiple solutions exist, whereas solving the constraints as a well-posed evolutionary system always yields a unique solution. To demonstrate our method, we implement it numerically and generate cosmological initial data with localized anisotropic perfect fluid perturbations.
ER  -