{
  "abstract": "We compute the stochastic background of gravitational waves (GWs) produced at second order in cosmological perturbation theory by a primordial curvature power spectrum that is flat in $\\ln k$ over a finite band $[k_-,k_+]=[k_*e^{-Δ},k_*e^{+Δ}]$ and vanishes elsewhere. This logarithmic box interpolates between a monochromatic spectrum as $Δ\\to0$ and a locally scale-invariant plateau as $Δ\\to\\infty$, and its sharp boundaries make the geometry of the source convolution unusually transparent. Working in the radiation era, we reduce the convolution to a compact integral over the overlap between the momentum triangle and the box, and evaluate it analytically in two regimes. For a narrow box we show that, to leading order in the width, the spectrum equals the Dirac-spectrum result multiplied by a purely geometric overlap factor $Φ_{\\rm box}(κ,Δ)$; this factor turns the infrared slope from $k^{3}\\ln^{2}k$ into $k^{2}\\ln^{2}k$ at a break $k_b=2k_*\\sinhΔ$. For a broad box we separate the lower edge, the scale-invariant interior, and the upper edge, derive the leading behaviour in each (an infrared $k^{3}\\ln^{2}k$ rise, a scale-invariant plateau, and a quartic cut-off at the hard endpoint $k=2k_+$), and combine them into a single uniform formula cast as a product of two universal, $Δ$-independent edge functions. We also provide an integral-free closed-form surrogate for these edge functions for use in parameter scans.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.10730",
  "author_total": 2,
  "authors": [
    {
      "name": "Zu-Cheng Chen"
    },
    {
      "name": "Lang Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/09fgt3c8fcqzw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.10730",
  "fulltext_url": null,
  "id": "09fgt3c8fcqzw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.10730",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.CO"
    ],
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7168281495",
  "pdf_url": "https://arxiv.org/pdf/2607.10730",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/09fgt3c8fcqzw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2607.10730",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.10730"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Scalar-induced gravitational waves from a box-shaped curvature power spectrum",
  "title_text": "Scalar-induced gravitational waves from a box-shaped curvature power spectrum",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:11Z",
  "url": "https://research.draconitic.com/paper/09fgt3c8fcqzw",
  "venue": "arXiv",
  "versions": []
}