A Population of z > 2 Far-Infrared Herschel-Spire-Selected Starbursts

We present spectroscopic observations for a sample of 36 Herschel-Spire 250-500 mu m selected galaxies (HSGs) at 2 < z < 5 from the Herschel Multi-tiered Extragalactic Survey. Redshifts are confirmed as part of a large redshift survey of Herschel-Spire-selected sources covering similar to 0.93 deg(2) in six extragalactic legacy fields. Observations were taken with the Keck I Low Resolution Imaging Spectrometer and the Keck II DEep Imaging Multi-Object Spectrograph. Precise astrometry, needed for spectroscopic follow-up, is determined by identification of counterparts at 24 mu m or 1.4 GHz using a cross-identification likelihood matching method. Individual source luminosities range from log(L-IR/L-circle dot) = 12.5-13.6 (corresponding to star formation rates (SFRs) 500-9000M(circle dot) yr(-1), assuming a Salpeter initial mass function), constituting some of the most intrinsically luminous, distant infrared galaxies discovered thus far. We present both individual and composite rest-frame ultraviolet spectra and infrared spectral energy distributions. The selection of these HSGs is reproducible and well characterized across large areas of the sky in contrast to most z > 2 HyLIRGs in the literature, which are detected serendipitously or via tailored surveys searching only for high-z HyLIRGs; therefore, we can place lower limits on the contribution of HSGs to the cosmic star formation rate density (SFRD) at (7 +/- 2) x 10(-3) M-circle dot yr(-1) h(3) Mpc(-3) at z similar to 2.5, which is > 10% of the estimated total SFRD of the universe from optical surveys. The contribution at z similar to 4 has a lower limit of 3 x 10(-3) M-circle dot yr(-1) h(3) Mpc(-3), greater than or similar to 20% of the estimated total SFRD. This highlights the importance of extremely infrared-luminous galaxies with high SFRs to the buildup of stellar mass, even at the earliest epochs.