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  • Letter
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Ultra-low-frequency gravitational waves from cosmological and astrophysical processes

Nature Astronomy volume 5, pages 1268–1274 (2021)Cite this article

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Abstract

Gravitational waves at ultra-low frequencies (≲100 nHz) are key to understanding the assembly and evolution of astrophysical black hole binaries with masses ~106–109 M⊙ at low redshifts1,2,3. These gravitational waves also offer a unique window into a wide variety of cosmological processes4,5,6,7,8,9,10,11. Pulsar timing arrays12,13,14 are beginning to measure15 this stochastic signal at ~1–100 nHz and the combination of data from several arrays16,17,18,19 is expected to confirm a detection in the next few years20. The dominant physical processes generating gravitational radiation at nHz frequencies are still uncertain. Pulsar timing array observations alone are currently unable21 to distinguish a binary black hole astrophysical foreground22 from a cosmological background due to, say, a first-order phase transition at a temperature ~1–100 MeV in a weakly interacting dark sector8,9,10,11. This letter explores the extent to which incorporating integrated bounds on the ultra-low-frequency gravitational wave spectrum from any combination of cosmic microwave background23,24, big bang nucleosynethesis25,26 or astrometric27,28 observations can help to break this degeneracy.

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Fig. 1: Combined constraints on GW backgrounds and foregrounds.
Fig. 2: Posteriors on the PT-model parameters.
Fig. 3: Combined constraints on power-law stochastic GW signals.
Fig. 4: Combined measurements of the GW energy densities in the background and foreground.

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Data availability

The data used for the analyses presented is publicly available from: https://data.nanograv.org.

Code availability

The code used for the analyses presented here, including that to make all figures, is available at https://github.com/cjm96/PTA_and_IntegratedConstraints, which uses code from https://github.com/AMitridate/bokeh/tree/master/bokeh-app.

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Acknowledgements

A.V. acknowledges the support of the Royal Society and Wolfson Foundation. We thank W. Ratzinger and K. Schmitz for useful discussions on the analysis.

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Authors and Affiliations

  1. Institute for Gravitational Wave Astronomy & School of Physics and Astronomy, University of Birmingham, Birmingham, UK

    Christopher J. Moore & Alberto Vecchio

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  1. Christopher J. Moore
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Contributions

Both C.J.M. and A.V. jointly conceived this study. C.J.M. performed the numerical calculations. Both C.J.M. and A.V. jointly analysed and interpreted the results and wrote the manuscript.

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Correspondence to Christopher J. Moore.

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Peer review information Nature Astronomy thanks Lijing Shao and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Moore, C.J., Vecchio, A. Ultra-low-frequency gravitational waves from cosmological and astrophysical processes. Nat Astron 5, 1268–1274 (2021). https://doi.org/10.1038/s41550-021-01489-8

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