  PILOT (the Pathfinder for an International Large Optical Telescope) is a
proposed 2.5 m optical/infrared telescope to be located at Dome C on the
Antarctic plateau. The atmospheric conditions at Dome C deliver a high
sensitivity, high photometric precision, wide-field, high spatial resolution,
and high-cadence imaging capability to the PILOT telescope. These capabilities
enable a unique scientific potential for PILOT, which is addressed in this
series of papers. The current paper presents a series of projects dealing with
the distant (redshift >) Universe, that have been identified as key science
drivers for the PILOT facility. The potential for PILOT to detect the first
populations of stars to form in the early Universe, via infrared projects
searching for pair-instability supernovae and gamma-ray burst afterglows, is
investigated. Two projects are proposed to examine the assembly and evolution
of structure in the Universe: an infrared survey searching for the first
evolved galaxies at high redshift, and an optical survey aimed at
characterising moderate-redshift galaxy clusters. Finally, a large-area
weak-lensing survey and a program to obtain supernovae infrared light-curves
are proposed to examine the nature and evolution of dark energy and dark
matter.
