We present a dynamical description of (anti)proton number cumulants and correlation functions in central Au-Au collisions at $\sqrt{s_{NN}}=7.7–200$ GeV by utilizing viscous hydrodynamics simulations. We find that the experimental data of the STAR Collaboration are consistent at sNN≳20GeV with simultaneous effects of global baryon number conservation and repulsive interactions in the baryon sector. The data at lower collision energies show possible indications for sizable attractive interactions among baryons.

The conditions for the formation of a Bose-Einstein condensed phase of pions in the early Universe are determined. Utilizing a hadron resonance gas model with pion interactions constrained to first-principle lattice QCD simulations at nonzero isospin density, we evaluate cosmic trajectories at various values of electron, muon, and tau lepton asymmetries that satisfy the available constraints on the total lepton asymmetry. The cosmic trajectory passes through the pion condensed phase if the combined electron and muon asymmetry is sufficiently large: |l_e + l_μ| > 0.1, with little sensitivity to the difference l_e − l_μ between the individual flavor asymmetries. Future constraints on the values of the individual lepton flavor asymmetries will thus be able to either confirm or rule out the condensation of pions during the cosmic QCD epoch. We demonstrate that the pion condensed phase leaves an imprint both on the spectrum of primordial gravitational waves and on the mass distribution of primordial black holes at the QCD scale, for example, the black hole binary of recent LIGO event GW190521 can be formed in that phase.

Saha equation approach is introduced for describing the production of light (anti-)(hyper-)nuclei in late stages of relativistic heavy-ion collisions, making use of an analogy between the evolution of the early universe after the Big Bang and that of ``Little Bangs’’ created in the lab. The framework is consistent with the available experimental data of the ALICE collaboration for a very broad range of temperatures in the hadronic phase, providing a possible explanation for why the thermal model works so well for describing nuclear abundances in heavy-ion collisions.

This paper introduces the Cluster Expansion Model (CEM) – a model for QCD equation of state at finite baryon density, which is based on the lattice QCD data for Fourier coefficients of baryon number density, obtained in simulation at imaginary $\mu_B$. The CEM is surprisingly simple, permits a closed analytic form, and is consistent with all presently available lattice data.

An extension of the ideal hadron resonance gas (HRG) model is constructed which includes the attractive and repulsive van der Waals (VDW) interactions between baryons. This VDW-HRG model yields the nuclear liquid-gas transition and, compared to the ideal HRG model, leads to a qualitatively different behavior of second and higher moments of fluctuations of conserved charges, in particular in the so-called crossover region $T$~$140–190$ MeV. For many observables this behavior resembles closely the results obtained from lattice QCD simulations.

This paper introduces the Quantum van der Waals (QvdW) equation – a generalization of the famous van der Waals equation to include quantum statistical (Fermi-Dirac or Bose-Einstein) effects. The formalism is applied to describe the nuclear liquid-gas transition in nuclear matter.