Matter at very high temperatures and densities – such as the one encountered shortly after the Big Bang or when two NSs collide – is governed by the strong interaction and may exist in different phases, often exhibiting strong collective properties. One of these phases is the quark-gluon plasma (QGP), which permeated the early universe, but can also be reproduced in collisions of heavy ions at the highest available collision energies (which probe very small net baryon densities). When neutron stars merge emitting strong GWs (which probe very large net baryon densities), more phases may occur, requiring a systematic scan of the quantum chromodynamics (QCD) phase diagram at different energies.
A variety of numerical and analytical concepts have been instrumental to calculate the properties of the QGP and to model the final state of heavy-ion collisions (HIC), ranging from first-principles approaches to study QCD thermodynamics on the lattice, from transport theory to viscous relativistic hydrodynamics, from merging neutron stars to their gravitational and electromagnetic emission. To make progress in this multidisciplinary field and advance our understanding of the phase diagram, a close collaboration between experiment and theory is essential and scientists in ELEMENTS provide the needed expertise. Together, we construct a renewed picture of the phase diagram, exploring in detail regions not considered before, building a comprehensive picture of matter under extreme conditions.