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Above a critical temperature in the Universe, there was probably a phase of unbroken approximate QCD chiral symmetry. Mathematically, the symmetry breaking is triggered when the operators $\bar{\psi}{\psi}$ for the quark fields $\psi$ acquired a nonzero vacuum expectation value (vev). This vev is called a quark condensate. For me this is a very mathematical description and I failed to translate it into a physical picture. Can someone explain what is really going on above and below this transition temperature in physical terms? My feeling is that above the transition temperature quarks where free and below it, the quarks and antiquarks became trapped to form mesons.

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This is a question that entails the ability to manage QCD at low energies and this is an active field of research yet as we are not able to do it, unless for lattice computations. It can be considered as part of the more general problem of the determination of the phase diagram of QCD (see my answer here).

The idea of chiral symmetry breaking in strong interactions originate from Yochiro Nambu and was firstly treated in two classical papers by him and Giovanni Jona-Lasinio where the NJL model (from the initials of the surnames of the authors) was firstly introduced. Presently, this model represents the only analytical approach to treat the question of the phase diagram in QCD. The quark-scalar meson model is also used but this could be in principle derived from the NJL model by a procedure generally called bosonization. The difference between these two models is that the latter is renormalizable while the former is not and this is the main reason why is often preferred. It should be emphasized that these theoretical analyses are aimed to get an idea of what is going on as emerges from lattice computations that represent our most successful approach to treat QCD at low-energies.

Chiral symmetry breaking is seen to happen in lattice QCD since a critical temperature $T_c\approx 170\ MeV$. Beyond this point the symmetry is restored and, when the chemical potential is also considered, there could be a critical end-point (CEP) beyond which a quark-plasma forms and we have a deconfined phase. Please, note that, as for today, we lack any experimental evidence for the existence of the CEP. This is a cross-over point marking the beginning of a first order phase transition. It means that, below $T_c$ there is the regime of chiral symmetry breaking of the existence of hadronic matter as we know. You can check the diagram I posted in my aforementioned answer.

Please, note that this is a very active field of research and a large amount of literature is produced yearly.

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