Most of the universe today is composed of invisible dark matter
(DM) and dark energy. All the instruments constructed by the human
civilization so far can detect only 4.6% of the total content
of the universe. Existence of the dark components are inferred by
their gravitational effects. DM makes up the underlying structure
of the universe and constitutes 23% of the total composition.
It serves as an invisible scaffolding on which everything we can
see lies. Without the additional gravitational pull of DM, the
centrifugal force on stars and galaxies would not be balanced out,
hence galaxies and clusters of galaxies, i.e. large scale
structures, would fly apart. DM keeps falling from all directions
into the gravitational potential wells of large scale structures.
As it sloshes in and out within smooth potential wells, the phase
space distribution of the particles is characterized everywhere by
a set of discrete flows. The particles in the flows spontaneously
pile up at certain locations, forming caustics which are
generically surfaces enveloping the regions with two extra flows.
The density distribution must have sharp increases (bumps) at the
locations of caustics. Minimal caustic structure is classified as
``outer caustics'' and ``inner caustics.'' The outer caustics are
simple fold catastrophes located on topological spheres
surrounding the large scale structures. The inner caustics are
rings. A caustic ring is a closed tube (like a doughnut) whose
transverse cross-section is an elliptic umbilic catastrophe.
Evidences have been found for the existence of DM caustics. I
discuss our interpretation of the recent gravitational lensing
observations of Jee et al. as first evidence for a caustic ring of
DM in a galaxy cluster.