  Luminous infrared galaxies and submillimeter galaxies contribute
significantly to stellar mass assembly and the frequency of GRBs in these
systems provides an important test of the connection between the gamma-ray
burst rate and that of overall cosmic star-formation. We present sensitive 3
GHz radio observations using the Karl G. Jansky Very Large Array of 32
uniformly-selected GRB host galaxies spanning a redshift range from 0 < z <
2.5, providing the first fully dust- and sample-unbiased measurement of the
fraction of GRBs originating from the Universe's most bolometrically luminous
galaxies. Four galaxies are detected, with inferred radio star-formation rates
ranging between 50-300 Msun/yr. Three of the four detections correspond to
events consistent with being optically-obscured "dark" bursts. Our overall
detection fraction implies that between 9-23% of GRBs between 0.5 < z < 2.5
occur in galaxies with S_3GHz > 10 uJy, corresponding to SFR >50 Msun/yr at z~1
or >250 Msun/yr at z~2. Similar galaxies contribute approximately 10-30% of all
cosmic star-formation, so our results are consistent with a GRB rate which is
not strongly biased with respect to the total star-formation rate of a galaxy.
However, all four radio-detected hosts have modest stellar masses (~few x 10^10
Msun), significantly lower than IR/submillimeter-selected field galaxies of
similar luminosities. We suggest that the GRB rate may be suppressed in
metal-rich environments but independently enhanced in intense starbursts,
producing a strong efficiency dependence on mass but little net dependence on
bulk galaxy star-formation rate.
