The Swift Gamma-Ray Burst redshift distribution: selection biases and optical brightness evolution at high-z?

We employ realistic constraints on astrophysical and instrumental selection effects to model the Gamma-Ray Burst (GRB) redshift distribution using {\it Swift} triggered redshift samples acquired from optical afterglows (OA) and the TOUGH survey. Models for the Malmquist bias, redshift desert, and the fraction of afterglows missing because of host galaxy dust extinction, are used to show how the "true" GRB redshift distribution is distorted to its presently observed biased distribution. We also investigate another selection effect arising from a correlation between $E_{{\rm iso}}$ and $L_{{\rm opt}}$. The analysis, which accounts for the missing fraction of redshifts in the two data subsets, shows that a combination of selection effects (both instrumental and astrophysical) can describe the observed GRB redshift distribution. Furthermore, the observed distribution is compatible with a GRB rate evolution that tracks the global SFR, although the rate at high-$z$ cannot be constrained with confidence. Taking selection effects into account, it is not necessary to invoke high-energy GRB luminosity evolution with redshift to explain the observed GRB rate at high-$z$.