  With the recent discovery of a dozen dusty star-forming galaxies and around
30 quasars at z>5 that are hyper-luminous in the infrared ($\mu$$L_{\rm
IR}>10^{13}$ L$_{\odot}$, where $\mu$ is a lensing magnification factor), the
possibility has opened up for SPICA, the proposed ESA M5 mid-/far-infrared
mission, to extend its spectroscopic studies toward the epoch of reionization
and beyond. In this paper, we examine the feasibility and scientific potential
of such observations with SPICA's far-infrared spectrometer SAFARI, which will
probe a spectral range (35-230 $\mu$m) that will be unexplored by ALMA and
JWST. Our simulations show that SAFARI is capable of delivering good-quality
spectra for hyper-luminous infrared galaxies (HyLIRGs) at z=5-10, allowing us
to sample spectral features in the rest-frame mid-infrared and to investigate a
host of key scientific issues, such as the relative importance of star
formation versus AGN, the hardness of the radiation field, the level of
chemical enrichment, and the properties of the molecular gas. From a broader
perspective, SAFARI offers the potential to open up a new frontier in the study
of the early Universe, providing access to uniquely powerful spectral features
for probing first-generation objects, such as the key cooling lines of
low-metallicity or metal-free forming galaxies (fine-structure and H2 lines)
and emission features of solid compounds freshly synthesized by Population III
supernovae. Ultimately, SAFARI's ability to explore the high-redshift Universe
will be determined by the availability of sufficiently bright targets (whether
intrinsically luminous or gravitationally lensed). With its launch expected
around 2030, SPICA is ideally positioned to take full advantage of upcoming
wide-field surveys such as LSST, SKA, Euclid, and WFIRST, which are likely to
provide extraordinary targets for SAFARI.
