The Cosmic Rate, Luminosity Function and Intrinsic Correlations of Long
  GRBs
  We calculate durations and spectral parameters for 207 Swift bursts detected
by the BAT instrument from April 2007 to August 2009, including 67 events with
measured redshifts. This is the first supplement to our catalog of 425 Swift
GRBs (147 with redshifts) starting from GRB041220. This complete and extensive
data set, analyzed with a unified methodology, allows us to conduct an accurate
census of intrinsic GRB energetics, hardnesses, durations, and redshifts. The
GRB world model we derive reproduces well the observables from both Swift and
pre-Swift satellites. Comparing to the cosmic star formation rate, we estimate
that only about 0.1% of massive stars explode as bright GRBs. There is strong
evidence for evolution in the Swift population at intermediate and high-z, and
we can rule out (at the 5-sigma level) that this is due to evolution in the
luminosity function of GRBs. Instead, the Swift sample suggests a modest
propensity for low-metallicity, evidenced by an increase in the rate density
with redshift. Treating the multivariate data and selection effects rigorously,
we find a real, intrinsic correlation between E_iso and E_pk (and possibly also
duration); however, the correlation {\it is not} a narrow log-log relation and
its observed appearance is strongly detector-dependent. We also estimate the
high-z rate (3--9% of GRBs at z beyond 5) and discuss the extent of a large
missing population of low-E_pk XRFs as well as a potentially large missing
population of short-duration GRBs that will be probed by EXIST.
