Galaxy Bias Skews Universe Expansion Rate Measurements from Gravitational Waves

A subtle but significant bias hidden within the models used to map galaxies may be skewing measurements of the universe’s expansion rate, a fresh study reveals. The finding complicates efforts to resolve a long-standing debate in astronomy concerning the Hubble constant – the value that describes how quickly the universe is expanding.

For years, astronomers have wrestled with differing measurements of the Hubble constant. Observations of the early universe, made by the Planck satellite, suggest a value around 67.4 kilometers per second per megaparsec. However, measurements based on observations of nearby objects, like supernovae and Cepheid variable stars, consistently point to a higher value, closer to 73.04. This discrepancy has led to speculation about new physics beyond our current understanding of the cosmos.

How Dark Standard Sirens Aim to Resolve the Debate

Gravitational waves, ripples in spacetime caused by the collision of massive objects like black holes and neutron stars, offer a potentially independent way to measure the Hubble constant. When these events occur, they emit a signal that travels across the universe, and the distance to the source can be determined from the strength of the wave. This method, pioneered by physicist Bernard Schutz in 1986 as detailed in a 1986 Nature article, doesn’t rely on the traditional “cosmic distance ladder” – a series of overlapping measurements that can introduce systematic errors.

However, many gravitational wave events don’t have a corresponding light signature, making it difficult to pinpoint their host galaxy. In these cases, astronomers employ what’s known as the “dark standard siren” approach. This involves statistically matching the gravitational wave event to a catalog of potential host galaxies. The more galaxies in the catalog, and the more accurate their distance measurements, the more precise the Hubble constant estimate becomes.

The Problem with Missing Galaxies

The new research, led by Cezary Turski at Ghent University (UGent), highlights a critical issue with this approach: galaxy catalogs are incomplete. As astronomers look farther into the universe, it becomes increasingly difficult to detect faint and distant galaxies. This incompleteness introduces a bias into the calculations.

Turski’s team analyzed 46 dark siren events using data from the latest GWTC-3 catalog. They found that when galaxy catalogs become sparse, the calculations begin to fill in the gaps with a model of galaxy brightness distribution. This model, often a Schechter function, assumes a certain distribution of galaxy luminosities. However, this assumption can be flawed, particularly at large distances, because the mix of young and classic galaxies changes over cosmic time. The study, published in Monthly Notices of the Royal Astronomical Society, demonstrates that this can lead to an overestimation of the Hubble constant.

The Role of Redshift and Catalog Limits

The bias becomes particularly pronounced when the redshift – a measure of how much the light from a galaxy has been stretched due to the expansion of the universe – exceeds around 0.1. At this point, the widely used GLADE+ catalog, which combines data from six different surveys, begins to lose its reliability. Beyond this redshift, the unseen portion of the universe starts to exert a disproportionate influence on the Hubble constant estimate.

Essentially, the model of the unseen galaxies starts acting as a substitute map, and if that model is inaccurate, the resulting expansion rate will be skewed. The bias isn’t a problem with the gravitational wave signal itself, but rather with the assumptions made about the distribution of galaxies in the universe.

A Partial Fix and Remaining Uncertainties

Turski and his team explored a potential fix by allowing both the Hubble constant and the galaxy population to evolve together during the calculations. Using 42 black-hole events, they found that this approach removed the direct bias in the expansion rate. However, they similarly discovered that the estimated Hubble constant still varied depending on the specific luminosity model used, indicating that some uncertainty remained.

This suggests that the problem isn’t simply about getting the right answer, but about understanding where the remaining uncertainties lie. Even with a more sophisticated approach, the results are still sensitive to the assumptions made about the underlying galaxy population.

Implications for Gravitational-Wave Cosmology

The findings have significant implications for the future of gravitational-wave cosmology. As detectors become more sensitive, they will be able to detect mergers from much farther away, increasing the reliance on statistical methods and galaxy catalogs. The latest catalog already includes 141 events used in dark-siren expansion tests, as noted in LIGO documentation, demonstrating the rapid growth of data volume.

To mitigate the bias, astronomers will need to develop deeper and more accurate galaxy catalogs, as well as more sophisticated models of galaxy evolution. Future surveys, like the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), are expected to provide a more complete census of galaxies, but even these will have limitations.

researchers are exploring alternative tracers of cosmic distances, such as brightest cluster galaxies (BCGs) and luminous red galaxies (LRGs), which may be more readily detectable at high redshifts. A recent study, published in arXiv, investigated using only bright galaxies to improve the precision of Hubble constant estimates, finding potential gains of up to 80% in favorable scenarios.

What’s Next for Dark Siren Cosmology

The path forward for dark siren cosmology involves a multi-pronged approach. Deeper sky surveys are crucial for directly observing more host galaxies, reducing the need to rely on statistical models. Simultaneously, refining galaxy evolution models and incorporating alternative tracers will help to minimize the impact of missing galaxies. The work lays the foundation for employing these alternative tracers, particularly at redshifts where conventional galaxy catalogs offer limited coverage.

resolving the Hubble tension will likely require a combination of different observational techniques and a deeper understanding of the underlying physics of the universe. While gravitational waves offer a promising new avenue for measuring the expansion rate, it’s clear that careful attention must be paid to the systematic uncertainties inherent in the analysis.