[Paper Review] Cosmological model selection from standard siren detections by third-generation gravitational wave obervatories

Josiel Mendonça, Riccardo Sturani|arXiv (Cornell University)|May 9, 2019

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper demonstrates that third-generation gravitational wave detectors like the Einstein Telescope can use standard siren observations to discriminate between cosmological models via Bayesian model selection. With ~1,000 detections and sub-10% luminosity distance uncertainty, the ΛCDM model can be decisively favored over alternatives with varying dark energy, especially when events are concentrated at lower redshifts (z ≲ 1) where measurement errors are minimized.

ABSTRACT

The multi-messenger observation of GW170817 enabled the first historic measurement of the Hubble constant via a standard siren, so-called in analogy to standard candles that enabled the measurement of the luminosity distance versus redshift relationship at small redshift. In the next decades, third-generation observatories are expected to detect hundreds to thousand of gravitational wave events from compact binary coalescences with potentially a joint electromagnetic counterpart. In the present work, we show how future standard siren detections can be used within the framework of Bayesian model selection to discriminate between cosmological models differing by the parameterization of the late-time acceleration. In particular, we found quantitative conditions for the standard LCDM model to be favored with respect to other models with varying dark energy content, by reducing the uncertainty in the gravitational determination of the luminosity distance with respect to current expectations.

Motivation & Objective

• To investigate whether future standard siren detections from third-generation gravitational wave observatories can discriminate between cosmological models with different dark energy parameterizations.
• To assess the role of luminosity distance measurement precision and event redshift distribution in model selection performance.
• To evaluate the effectiveness of Bayesian evidence in favoring ΛCDM over alternative models such as wCDM and massive gravity, under realistic detection scenarios.
• To determine the minimum number of detections and required distance accuracy needed to achieve statistical confidence in model discrimination.
• To explore how the distribution of events across redshift affects the ability to distinguish between models with similar low-redshift dynamics but different high-redshift behavior.

Proposed method

• Uses Bayesian model selection to compare the evidence for ΛCDM versus alternative models (e.g., wCDM, massive gravity) using simulated standard siren data.
• Employs Monte Carlo simulations with 1,000 injections per realization across 50 realizations to estimate the logarithm of the Bayes factor (evidence ratio) between models.
• Models luminosity distance uncertainty using a redshift-dependent error budget, with a focus on reducing uncertainty to <10% for effective discrimination.
• Simulates event distributions with varying redshift distributions—particularly concentrating events at low redshift (z ≲ 1) to minimize measurement error impact.
• Applies a flat prior on the dark energy equation of state parameter w₀ in the range [−2, 0] for wCDM, and compares with ΛCDM using the same prior framework.
• Validates numerical results against analytical estimates of the Bayes factor using the Savage-Dickey density ratio, confirming consistency between simulation and theory.

Experimental results

Research questions

• RQ1 Can future standard siren detections from third-generation gravitational wave detectors distinguish ΛCDM from alternative dark energy models using Bayesian model selection?
• RQ2 What level of luminosity distance uncertainty is required to achieve strong evidence in favor of ΛCDM over models with varying dark energy?
• RQ3 How does the redshift distribution of standard siren events affect the power of model discrimination?
• RQ4 To what extent does concentrating events at low redshift (z ≲ 1) improve the ability to distinguish cosmological models compared to uniform or high-redshift distributions?
• RQ5 How many standard siren detections are needed to achieve decisive model selection with high confidence?

Key findings

• With approximately 1,000 standard siren detections and luminosity distance uncertainties reduced to below 10%, the ΛCDM model can be decisively favored over alternative models such as wCDM and massive gravity.
• The redshift distribution of events plays a critical role: concentrating detections at low redshift (z ≲ 1) significantly enhances model discrimination power due to reduced measurement errors.
• Even with a large number of detections, models with similar low-redshift dynamics but different high-redshift behavior (e.g., z ≳ 2) remain difficult to distinguish unless distance precision is high.
• The study confirms a strong agreement between numerical simulations and analytical predictions of the Bayes factor, validating the use of the Savage-Dickey density ratio for evidence estimation.
• Reducing luminosity distance uncertainty to 20% or less substantially improves the discrimination power between ΛCDM and alternative models, especially in the case of massive gravity.
• The results suggest that future joint electromagnetic and gravitational wave observations—especially with LISA and quasar counterparts at z ≳ 3—could enable model discrimination with as few as a handful of detections, given 10% distance precision.