This paper explores how gravitational waves from merging black holes could measure when the universe formed stars most actively. Right now astronomers estimate the star-formation rate from light seen by telescopes. Those estimates need corrections for dust and rely on assumptions about how bright stars are. The authors show that the redshift distribution of binary black hole mergers — essentially a map of when and where those mergers happened in cosmic time — can give an independent handle on the same peak era of star formation.

The team simulated one year of binary black hole signals under three different models for the cosmic star-formation history. All models use an “inverse” time-delay law, meaning the chance a binary merges falls roughly like one over the delay time since the stars formed. They assumed a local merger rate of 22 Gpc−3 yr−1 and generated the signals that would be seen by two detector networks. The first network is a planned upgrade to current LIGO detectors (called A#) using the Livingston, Hanford and LIGO-India sites and a lower frequency cutoff of 10 Hz. The second network is a proposed next-generation set of detectors (Cosmic Explorer and Einstein Telescope) with a 5 Hz cutoff. The authors estimated measurement errors with a Fisher-matrix method and then ran a population-level inference to recover the redshift distribution.

Their main numerical results are concrete. For a simulated true merger-rate peak at redshift zpeak = 1.5, the LIGO A# network can recover the peak with a precision of about ±0.1 after one year of observations (they report zpeak = 1.53 +0.12 −0.10 for their Madau–Dickinson model). The next-generation network would do much better: the same simulated scenario yields a precision of about ±0.02 (zpeak = 1.49 +0.02 −0.02). The authors also repeated the study for models whose peaks lie near z ≃ 1.2 and z ≃ 2 and examined how different black‑hole mass ranges contribute to the measurement. They note that low-mass systems are more numerous while high-mass systems are louder, and both effects shape the final constraints.