Does our universe conform with the existence of a universal maximum
  energy-density $\rho^{uni}_{max}$ ?
  Recent astronomical observations of high redshift quasars, dark
matter-dominated galaxies, mergers of neutron stars, glitch phenomena in
pulsars, cosmic microwave background and experimental data from hadronic
colliders do not rule out, but they even support the hypothesis that the
energy-density in our universe most likely is upper-limited by
$\rho^{uni}_{max},$ which is predicted to lie between $2$ to $3$ the nuclear
density $\rho_0.$ Quantum fluids in the cores of massive NSs with $\rho \approx
\rho^{uni}_{max}$ reach the maximum compressibility state, where they become
insensitive to further compression by the embedding spacetime and undergo a
phase transition into the purely incompressible gluon-quark superfluid state. A
direct correspondence between the positive energy stored in the embedding
spacetime and the degree of compressibility and superfluidity of the trapped
matter is proposed. In this paper relevant observation signatures that support
the maximum density hypothesis are reviewed, a possible origin of
$\rho^{uni}_{max}$ is proposed and finally the consequences of this scenario on
the spacetime's topology of the universe as well as on the mechanisms
underlying the growth rate and power of the high redshift QSOs are discussed.
