Bright Siren Cosmology Beyond Fisher: DALI Forecasts for Third-Generation Gravitational Wave Observatories
Abstract
In this work we assess non-Gaussian extensions of Fisher forecasting based on the Derivative Approximation for Likelihoods (DALI). We simulate ensembles of bright siren catalogs for third-generation observatories, adopting a Cosmic Explorer (CE) and a triangular Einstein Telescope (ET) network, frequency-domain inspiral waveforms, and selection-motivated priors for counterpart detection. We reconstruct approximate likelihoods using Fisher and the first DALI correction (Doublet), and propagate the inferred distance information to cosmological inference in a w0waCDM model. We find that the Doublet approximation provides tighter cosmological constraints than the Fisher approximation, reducing the inferred uncertainties by approximately a factor of two in agreement with non-approximate likelihood (called Exact) results. For our GW network onfiguration, 300 bright-siren detections up to z=1 yield an H0 precision of ~2.7% with the Doublet approximation, compared with ~2.5% for the exact likelihood. The adopted non-Gaussian GW priors induce a systematic displacement of the inferred luminosity distances from the fiducial values, which is also present in the exact GW reconstruction and propagates into the cosmological parameters. Compared with the exact cosmological likelihood, the Doublet results differ by only ~10% on average in the parameter uncertainties, compared with ~195% for the traditional Fisher approximation. The Doublet approximation also substantially reduces the computational cost, by a factor of ~55 for the GW analysis and by ~12 for cosmological likelihood evaluations, yielding an estimated reduction of ~55 in the total computational cost of the combined analysis. Our results show the potential of DALI-based approximations to provide accurate and computationally efficient tools for forecasting in bright siren cosmology.
Related
- Distinguishing cosmology, astrophysics and systematics: the Bayesian search for a primordial gravitational-wave background in next-generation observatories
- Reconsidering the role of bright and dark gravitational-wave standard sirens for cosmology
- Galaxy morphology dependent (black hole mass)-(velocity dispersion) relations: implications for gravitational wave forecasts and cosmological simulations
- Cosmology beyond standard sirens: cross-correlation of gravitational waves and neutral hydrogen intensity mapping
- Cosmological Inference with Gravitational-Wave Dark Sirens and 21-cm Intensity Mapping: Forecasts for LIGO-Virgo-KAGRA with MeerKAT and SKAO
BibTeX
@misc{pacheco2026bright,
title = {{Bright Siren Cosmology Beyond Fisher: DALI Forecasts for Third-Generation Gravitational Wave Observatories}},
author = {Mayara H. Pacheco and Josiel M. S. de Souza and Odylio D. Aguiar and Márcio E. S. Alves},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05338},
eprint = {2611.05338},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05338},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bright Siren Cosmology Beyond Fisher: DALI Forecasts for Third-Generation Gravitational Wave Observatories
AU - Mayara H. Pacheco
AU - Josiel M. S. de Souza
AU - Odylio D. Aguiar
AU - Márcio E. S. Alves
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05338
UR - https://arxiv.org/abs/2611.05338
AB - In this work we assess non-Gaussian extensions of Fisher forecasting based on the Derivative Approximation for Likelihoods (DALI). We simulate ensembles of bright siren catalogs for third-generation observatories, adopting a Cosmic Explorer (CE) and a triangular Einstein Telescope (ET) network, frequency-domain inspiral waveforms, and selection-motivated priors for counterpart detection. We reconstruct approximate likelihoods using Fisher and the first DALI correction (Doublet), and propagate the inferred distance information to cosmological inference in a w0waCDM model. We find that the Doublet approximation provides tighter cosmological constraints than the Fisher approximation, reducing the inferred uncertainties by approximately a factor of two in agreement with non-approximate likelihood (called Exact) results. For our GW network onfiguration, 300 bright-siren detections up to z=1 yield an H0 precision of ~2.7% with the Doublet approximation, compared with ~2.5% for the exact likelihood. The adopted non-Gaussian GW priors induce a systematic displacement of the inferred luminosity distances from the fiducial values, which is also present in the exact GW reconstruction and propagates into the cosmological parameters. Compared with the exact cosmological likelihood, the Doublet results differ by only ~10% on average in the parameter uncertainties, compared with ~195% for the traditional Fisher approximation. The Doublet approximation also substantially reduces the computational cost, by a factor of ~55 for the GW analysis and by ~12 for cosmological likelihood evaluations, yielding an estimated reduction of ~55 in the total computational cost of the combined analysis. Our results show the potential of DALI-based approximations to provide accurate and computationally efficient tools for forecasting in bright siren cosmology.
ER -