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Abstract Gravitational waves (GWs) from merging compact objects encode direct information about the luminosity distance to the binary. When paired with a redshift measurement, this enables standard-siren cosmology: a Hubble diagram can be constructed to directly probe the Universe’s expansion. This can be done in the absence of electromagnetic measurements, as features in the mass distribution of GW sources provide self-calibrating redshift measurements without the need for a definite or probabilistic host galaxy association. This “spectral siren” technique has thus far only been applied with simple parametric representations of the mass distribution, and theoretical predictions for features in the mass distribution are commonly presumed to be fundamental to the measurement. However, the use of an inaccurate representation leads to biases in the cosmological inference, an acute problem given the current uncertainties in true source population. Furthermore, it is commonly presumed that the form of the mass distribution must be known a priori to obtain unbiased measurements of cosmological parameters in this fashion. Here, we demonstrate that spectral sirens can accurately infer cosmological parameters without such prior assumptions. We apply a flexible, nonparametric model for the mass distribution of compact binaries to a simulated catalog of 1000 GW signals, consistent with expectations for the next LIGO–Virgo–KAGRA observing run. We find that, despite our model’s flexibility, both the source mass model and cosmological parameters are correctly reconstructed. We predict a 11.2%✎measurement ofH0, keeping all other cosmological parameters fixed, and a 6.4%✎measurement ofH(z= 0.9)✎when fitting for multiple cosmological parameters (1σuncertainties). This astrophysically agnostic spectral siren technique will be essential to arrive at precise and unbiased cosmological constraints from GW source populations.
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This content will become publicly available on February 1, 2026
A precise fitting formula for gravitational wave spectra from the sound shell model
Abstract Obtaining a precise form for the predicted gravitational wave (GW) spectrum from a phase transition is a topic of great relevance for beyond Standard Model (BSM) physicists. Currently, the most sophisticated semi-analytic framework for estimating the dominant contribution to the spectrum is the sound shell model; however, full calculations within this framework can be computationally expensive, especially for large-scale scans. The community therefore generally manages with fit functions to the GW spectrum, the most widely used of which is a single broken power law. We provide a more precise fit function based on the sound shell model: our fit function features a double broken power law with two frequency breaks corresponding to the two characteristic length scales of the problem — inter-bubble spacing and thickness of sound shells, the second of which is neglected in the single broken power law fit. Compared to previously proposed fits, we demonstrate that our fit function more faithfully captures the GW spectrum coming from a full calculation of the sound shell model, over most of the space of the thermodynamic parameters governing the phase transition. The physical origins of the fit parameters and their dependence on the thermodynamic parameters are studied in the underlying sound shell model: in particular, we perform a series of detailed scans for these quantities over the plane of thestrength of the phase transition (α) and the bubble wall velocity (vw). Wherever possible, we comment on the physical interpretations of these scans. From a user-end perspective, we provide data files and scripts inPythonandMathematicathat can be directly utilized by a front-end user to generate accurate GW spectra with our fit function, given initial inputs ofα,vw,β/H(nucleation rate parameter) andTn(nucleation temperature) for the relevant BSM scenario.https://github.com/SFH2024/precise-fit-fopt-gw.
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- Award ID(s):
- 2412671
- PAR ID:
- 10655073
- Publisher / Repository:
- JCAP
- Date Published:
- Journal Name:
- Journal of Cosmology and Astroparticle Physics
- Volume:
- 2025
- Issue:
- 02
- ISSN:
- 1475-7516
- Page Range / eLocation ID:
- 056
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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