The long gamma-ray burst rate and the correlation with host galaxy
  properties
  To answer questions on the start and duration of the epoch of reionisation,
periods of galaxy mergers and properties of other cosmological encounters, the
cosmic star formation history (CSFH), is of fundamental importance. Using the
association of long gamma-ray bursts (LGRBs) with the death of massive stars
and their ultra-luminous nature, the CSFH can be probed to higher redshifts
than current conventional methods. Unfortunately, no consensus has been reached
on the manner in which the LGRB rate (LGRBR) traces the CSFH, leaving many of
the questions mentioned mostly unexplored by this method. Observations by the
GRB NIR detector (GROND) over the past 4 years have, for the first time,
acquired highly complete LGRB samples. Driven by these completeness levels and
new evidence of LGRBs also occurring in more massive and metal rich galaxies
than previously thought, the possible biases of the LGRBR-CSFH connection are
investigated over a large range of galaxy properties. The CSFH is modelled
using empirical fits to the galaxy mass function and galaxy star formation
rates. Biasing the CSFH by metallicity cuts, mass range boundaries, and other
unknown redshift dependencies, a LGRBR is generated and compared to the highly
complete GROND sample. It is found that there is no strong preference for a
metallicity cut or fixed galaxy mass boundaries and that there are no unknown
redshift effects, in contrast to previous work which suggest values of
Z/Z_sun~0.1-0.3. From the best-fit models, we predict that ~1.2% of the LGRB
burst sample exists above z=6. The linear relationship between the LGRBR and
the CSFH suggested by our results implies that redshift biases present in
previous LGRB samples significantly affect the inferred dependencies of LGRBs
on their host galaxy properties. Such biases can lead to, e.g., an
interpretation of metallicity limitations and evolving LGRB luminosity
functions.
