  The search for habitable conditions and signs of life on exoplanets is a
major frontier in modern astronomy. Detecting atmospheric signatures of
Earth-like exoplanets is challenging due to their small sizes and relatively
thin atmospheres. Recently, a new class of habitable sub-Neptune exoplanets,
called Hycean worlds, has been theorized. Hycean worlds are planets with
H2-rich atmospheres and planet-wide oceans with thermodynamic conditions
similar to those in the Earth's oceans. Their large sizes and extended
atmospheres, compared to rocky planets of similar mass, make Hycean worlds
significantly more accessible to atmospheric observations. These planets open a
new avenue in the search for planetary habitability and life elsewhere using
spectroscopic observations with the James Webb Space Telescope (JWST). We
observed the transmission spectrum of a candidate Hycean world, K2-18 b,
recently with JWST in its first year of operations. The spectrum reveals
multiple spectral features of carbon bearing molecules in the planetary
atmosphere, leading to the first detections of methane (CH4) and carbon dioxide
(CO2) in a habitable-zone exoplanet. We discuss inferences of the atmospheric
chemical composition and its implications for the atmospheric, interior and
surface conditions on the planet, along with the possibility of a habitable
ocean underneath the atmosphere. We discuss new observational and theoretical
developments in this emerging frontier and their implications for exoplanetary
habitability and search for life elsewhere.
