Binary Neutron Star Mass Function Cosmology with Redshift Evolving Mass Populations*

Next-generation gravitational wave detectors are expected to detect millions of binary neutron star mergers across their entire redshift range. Observed features in binary neutron star mass distribution, coupled with gravitational wave based distance measurements, will enable precise cosmological inference in the absence of electromagnetic counterparts. However, to achieve bias-free cosmological inferences, it is crucial to accurately model the mass spectrum of binary neutron stars, considering the potential redshift evolution of observable features. In this study we utilize the binary population synthesis simulation code COMPAS to construct catalogs of realistic binary neutron star populations whose mass spectrums are found to evolve with redshift. We illustrate that population models neglecting such evolution introduce biases in cosmological inferences. Additionally, we explore how these biases can be rectified by incorporating the evolution of the mass spectrum into the population model. Furthermore, we investigate how these biases vary with the number of observations analyzed. We predict the number of events after which an evolving mass population model becomes necessary for achieving bias-free cosmological inferences using binary neutron star observations in the era of next-generation gravitational wave detectors, such as the Cosmic Explorer.