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From new physics to a running power law and back again: Minimal refitting techniques for the reconstruction of the gravitational-wave background signal in pulsar timing array data

David Esmyol1,*, Antonio J. Iovino2,1,†, and Kai Schmitz1,3,‡

  • *Contact author: d_esmy01@uni-muenster.de
  • †Contact author: a.iovino@nyu.edu
  • ‡Contact author: kai.schmitz@uni-muenster.de
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Phys. Rev. D 113, 063016 – Published 9 March, 2026

DOI: https://doi.org/10.1103/dty1-gyx1

Abstract

Pulsar timing array (PTA) collaborations recently presented evidence for a gravitational-wave background (GWB) signal at nanohertz frequencies. In this paper, we introduce new refitting techniques for PTA data analysis that elevate related techniques in the literature to a more rigorous level, and thus provide the basis for fast and accurate Bayesian inference and physically intuitive model comparisons. The key idea behind our approach is to construct maps Φ from GWB spectral models to a running-power-law (RPL) reference model, such that the pullback Φ*PRPL of the RPL posterior density PRPL induces a likelihood on the GWB model parameter space; in other words, we refit spectral models to the RPL posterior density. In order to construct Φ, we introduce a matched-filtering approach in which Φ follows from a χ2 minimization that accounts for the frequency dependence of PTA sensitivity curves. We validate and illustrate our techniques by three concrete examples: GWs from stable cosmic strings, GWs from metastable strings, and scalar-induced GWs.

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Phys. Rev. D 113, 063016– Published 9 March, 2026
  • Received 7 July 2025
  • Accepted 18 February 2026
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