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<p>In this work we perform a systematic study of the singularity structure of inflationary correlations at 1-loop. We explicitly compute a few diagrams and find a pattern emerging in the singularities produced. Motivated by this, we derive diagrammatic rules to extract the singularities of any two-site 1-loop diagram. Using these rules, the poles and branch cuts produced can be predicted by simply identifying the energies flowing through certain subgraphs, without having to perform complicated integrals. We demonstrate how these rules follow by analyzing the general structure of the time and momentum integrals of the correlators. An interesting feature of de-Sitter correlators at 1-loop is the presence of an <i>off-shell</i> total energy branch point, which is present in dimensional regularization as well as cutoff regularization. We probe the source of this branch cut in detail, while revisiting the cosmological KLN theorem [<CitationRef CitationID="CR1">1</CitationRef>] in this context. Finally, we show that the branch cuts produced in a renormalised correlator always repackage themselves in a dilatation invariant form to produce logarithms of ratios of comoving scales.</p>

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Singularities in cosmological loop correlators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月10日

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  • Supritha Bhowmick,
  • Mang Hei Gordon Lee,
  • Diptimoy Ghosh,
  • Farman Ullah

摘要

In this work we perform a systematic study of the singularity structure of inflationary correlations at 1-loop. We explicitly compute a few diagrams and find a pattern emerging in the singularities produced. Motivated by this, we derive diagrammatic rules to extract the singularities of any two-site 1-loop diagram. Using these rules, the poles and branch cuts produced can be predicted by simply identifying the energies flowing through certain subgraphs, without having to perform complicated integrals. We demonstrate how these rules follow by analyzing the general structure of the time and momentum integrals of the correlators. An interesting feature of de-Sitter correlators at 1-loop is the presence of an off-shell total energy branch point, which is present in dimensional regularization as well as cutoff regularization. We probe the source of this branch cut in detail, while revisiting the cosmological KLN theorem [1] in this context. Finally, we show that the branch cuts produced in a renormalised correlator always repackage themselves in a dilatation invariant form to produce logarithms of ratios of comoving scales.