The knowledge about the black hole mass function ( BHMF ) and its evolution would help to understand the origin of the BHs and how BH binaries formed at different stages of the history of the Universe .
We demonstrate the ability of future third generation gravitational wave ( GW ) detector – the Einstein Telescope ( ET ) to infer the slope of the BHMF and its evolution with redshift .
We perform the Monte Carlo simulation of the measurements of chirp signals from binary BH systems ( BBH ) that could be detected by ET , including the BH masses and their luminosity distances ( d _ { L } ) .
We use the mass of a primary black hole in each binary system to infer the BHMF as a power-law function with slope parameter as \alpha .
Taking into account the bias that could be introduced by the uncertainty of measurements and by the selection effect , we carried out the numerical tests and find that only one thousand of GW events registered by ET ( \sim 1 \% amount of its yearly detection rate ) could accurately infer the \alpha with a precision of \alpha \sim 0.1 .
Furthermore , we investigate the validity of our method to recover a scenario where \alpha evolves with redshift as \alpha ( z ) = \alpha _ { 0 } + \alpha _ { 1 } \frac { z } { 1 + z } .
Taking a thousand of GW events and using d _ { L } as the redshift estimator , our tests show that one could infer the value of evolving parameter \alpha _ { 1 } accurately with the uncertainty level of \sim 0.5 .
Our numerical tests verify the reliability of our method .
The uncertainty levels of the inferred parameters can be trusted directly for the several sets of the parameter we assumed , yet shouldn ’ t be treated as a universal level for the general case .