  The gravitational instability, responsible for the formation of the structure
of the Universe, occurs below energy thresholds and above spatial scales of a
self-gravitating expanding region, when thermal energy can no longer
counterbalance self-gravity. I argue that at sufficiently-large scales, dark
energy may restore thermal stability. This stability re-entrance of an
isothermal sphere defines a turnaround radius, which dictates the maximum
allowed size of any structure generated by gravitational instability. On the
opposite limit of high energies and small scales, I will show that an ideal,
quantum or classical, self-gravitating gas is subject to a high-energy
relativistic gravothermal instability. It occurs at sufficiently-high energy
and small radii, when thermal energy cannot support its own gravitational
attraction. Applications of the phenomenon include neutron stars and
core-collapse supernovae. I also extend the original Oppenheimer--Volkov
calculation of the maximum mass limit of ideal neutron cores to the non-zero
temperature regime, relevant to the whole cooling stage from a hot
proto-neutron star down to the final cold state.
