Probing evolution of Long GRB properties through their cosmic formation history aided by Machine Learning predicted redshifts

Gamma-ray Bursts (GRBs) are valuable probes of cosmic star formation reaching back into the epoch of reionization, and a large dataset with known redshifts ($z$) is an important ingredient for these studies. Usually, $z$ is measured using spectroscopy or photometry, but $\sim80\%$ of GRBs lack such data. Prompt and afterglow correlations can provide estimates in these cases, though they suffer from systematic uncertainties due to assumed cosmologies and due to detector threshold limits. We use a sample with $z$ estimated via machine learning models, based on prompt and afterglow parameters, without relying on cosmological assumptions. We then use an augmented sample of GRBs with measured and predicted redshifts, forming a larger dataset. We find that the predicted redshifts are a crucial step forward in understanding the evolution of GRB properties. We test three cases: no evolution, an evolution of the beaming factor, and an evolution of all terms captured by an evolution factor $(1+z)^\delta$. We find that these cases can explain the density rate in the redshift range between 1-2, but neither of the cases can explain the derived rate densities at smaller and higher redshifts, which may point towards an evolution term different than a simple power law. Another possibility is that this mismatch is due to the non-homogeneity of the sample, e.g., a non-collapsar origin of some long GRB within the sample.