Bayesian leave-one-out cross-validation for astrophysical model comparison using gravitational-wave background data

TL;DR

This study compares different astrophysical models using Bayesian leave-one-out cross-validation on pulsar-timing-array data to assess their predictive performance regarding gravitational-wave background suppression by ultralight-dark-matter.

Contribution

It extends previous work by evaluating four models with Bayesian cross-validation, providing insights into their relative predictive capabilities with current data.

Findings

The phenomenological model has the highest expected log predictive density.

Current data do not decisively favor any single model.

Simplified ultralight-dark-matter model outperforms the realistic implementation in all frequency bins.

Abstract

Previous work showed that ultralight-dark-matter solitons can provide dynamical friction for supermassive black-hole binaries, suppressing low-frequency power in the pulsar-timing-array gravitational-wave background and constraining the particle mass and effective ultralight-dark-matter fraction. Here we extend that analysis by comparing the predictive performance of four models: simplified and realistic ultralight-dark-matter implementations, a phenomenological environmental-hardening model, and a gravitational-wave-only model. We use Bayesian leave-one-out cross-validation on the five lowest pulsar-timing-array frequency bins. The phenomenological model gives the largest expected log predictive density, but its advantage over the other models is not large compared with the estimated standard errors. The current data therefore do not decisively prefer one model overall. The clearest pairwise result is within the ultralight-dark-matter framework: the simplified model outperforms the realistic implementation in all five frequency bins. Current pulsar-timing-array data are therefore compatible with ultralight-dark-matter-induced low-frequency suppression, but do not yet distinguish ultralight-dark-matter significantly from more generic environmental descriptions of supermassive-black-hole-binary evolution.