  Traditionally, the search for life on exoplanets has been predominantly
focused on rocky exoplanets. Hycean worlds are a class of habitable
sub-Neptunes with planet-wide oceans and H2-rich atmospheres. Their broad range
of possible sizes and temperatures lead to a wide habitable zone and high
potential for discovery and atmospheric characterization using transit
spectroscopy. Over a dozen candidate Hycean planets are already known to be
transiting nearby M dwarfs, making them promising targets for atmospheric
characterization with the James Webb Space Telescope (JWST). In this work, we
investigate possible chemical conditions on a canonical Hycean world, focusing
on (a) the present and primordial molecular composition of the atmosphere, and
(b) the inventory of bioessential elements for the origin and sustenance of
life in the ocean. Based on photochemical and kinetic modeling for a range of
conditions, we discuss the possible chemical evolution and observable
present-day composition of its atmosphere. In particular, for reduced
primordial conditions the early atmospheric evolution passes through a phase
that is rich in organic molecules that could provide important feedstock for
prebiotic chemistry. We investigate avenues for delivering bioessential metals
to the ocean, considering the challenging lack of weathering from a rocky
surface and the ocean separated from the rocky core by a thick icy mantle.
Based on ocean depths from internal structure modelling and elemental estimates
for the early Earth's oceans, we estimate the requirements for bioessential
metals in such a planet. We find that the requirements can be met for plausible
assumptions about impact history and atmospheric sedimentation, and
supplemented by other steady state sources. We discuss the observational
prospects for atmospheric characterisation of Hycean worlds.
