# If free quarks can't exist, how did the universe form?

As I understand, the Big Bang started with a photon gas that then created the other particles. Thus obviously there would be some free quarks in the early Universe unless quarks are always created in pairs for some reason. How does physics resolve this?

• It wasn't exactly a photon gas. We need a working quantum gravity theory to talk about the very earliest phase of the Big Bang. After the Planck epoch, there was (probably) a grand unification epoch where electromagnetism was united with the weak and strong nuclear forces. IOW, the energy density was so high that photons, the Z & W bosons, and gluons didn't exist. Instead, there were X & Y bosons that couple quarks to leptons. – PM 2Ring Mar 10 '17 at 10:38
• Also see Timeline of the formation of the Universe. Bear in mind that these Wikipedia articles are just simplified summaries of current theories, and they may contain minor inaccuracies. – PM 2Ring Mar 10 '17 at 10:41

"Free quarks can't exist" is simply an oversimplification of the actual situation in quantum chromodynamics (QCD). A better statement is "free quarks cannot exist at low energies", where "low energy" means below the deconfinement scale.

Confinement is precisely the phenomenon that says that the force between two quarks rises linearly with distance, meaning you can never separate two quark, since doing so would require infinite energy. Now, we unfortunately do not have a full theoretical understanding of confinement in continuum QCD, but what we do know - both from heuristic arguments and from lattice computations - is that QCD exhibits a phase transition between a confining phase and a deconfining phase as the energy scale increases.

This is not due to the running coupling as such, but to the expectation value of the order parameter of this phase transition, the Polyakov loop, a variant of the Wilson loop, becoming non-zero. As long as the Polyakov loop is zero, the free energy of a two-quark system is infinite, meaning they cannot be separated. Lattice calculations indeed show that the phase transition to a non-zero Polyakov loop happens as the energy scale increases, so in the early hot universe, free quarks could exist without contradiction to our current situation.

The symmetry which is broken by the Polyakov loop is the so-called "center symmetry" of the gauge theory on the lattice, see this question.

• So the fact that we aren't being torn to Swiss cheese by roving free quarks is just luck? – Dapper Lad Mar 11 '17 at 2:17
• @DapperLad Where did I give the impression of it being "just luck", and how does a circumstance of nature that is "just luck" differ from one that is not? – ACuriousMind Mar 11 '17 at 12:37
• Because you didn't say how free quarks became not free. – Dapper Lad Mar 11 '17 at 23:08

In the first stages of the Universe Quarks and Gluons were asymptotically free. This state of matter is called Quark-Gluon Plasma. Then, as the temperature of the Universe kept decreasing, the so-called hadronization (quarks combine to form hadrons) took place.

The coupling constant of the QCD (which, to make it simple, sort of represents the intensity of the strong interaction between quarks) is a $\textit{running coupling}$: it means it's not really a constant, but it varies with the energy scale. As you can see from the picture below, the $\alpha_{QCD}$ decreases at high transferred momentum. This means that quark tends to behave ALMOST as free particles when the energies are really high. You can also view them as a gas of fermions (quarks) and bosons (gluons).

In these conditions ($\alpha \ll 1$), a perturbative approach is possible: we use pQCD (perturbative QCD).

Quark-Gluon Plasma can be obtained nowadays by high energies collisions of heavy-nuclei. This is achieved at CERN, for example, by the ALICE experiment, by means of Pb-Pb collisions at $5.02$ TeV.

• While everything in this answer is correct, it doesn't actually give the correct reason for why quarks can be free that high energies but cannot at low energies. A large coupling constant does not, inherently, forbid the existence of free unbound quarks. The real reason is that QCD shows a phase transition between a confining and a deconfining phase, and confinement is not a simple consequence of large coupling. The linear force law in the confining phase cannot be derived simply from turning up the coupling. – ACuriousMind Mar 10 '17 at 13:10
• What you say is right. In fact, I kept my answer inside the boundaries of pQCD and asymptotic freedom. I didn't go into the realm of confinement. Firstly because, correct me if I'm wrong, there isn't yet a suitable theoretical explanation. Secondly because I have some open issues on non-perturbative QCD. – Luthien Mar 10 '17 at 13:55
• Is there any fundamental reason why free quarks cannot exist at low energy besides "thats the only way to make physics work"? – Dapper Lad Mar 11 '17 at 2:12
• As far as I know there is not a suitable theoretical explanation yet. You know, a lot of times you just see things happening in experiments and then you build your theory. Confinement is an experimental fact, not fully explained by theory. I guess that ACuriousMind answer is a good one to start with if you want to know more about theories on confinement. – Luthien Mar 11 '17 at 2:29

This article in wikipedia clarifies how the universe has evolved as far as our present understanding of particle physics and general relativity goes.

In particular for the strong interactions, the present theory is QCD,which models quarks and their interactions with other particles.

QCD enjoys two peculiar properties:

Confinement, which means that the force between quarks does not diminish as they are separated. Because of this, when you do separate a quark from other quarks, the energy in the gluon field is enough to create another quark pair; they are thus forever bound into hadrons such as the proton and the neutron or the pion and kaon. Although analytically unproven, confinement is widely believed to be true because it explains the consistent failure of free quark searches, and it is easy to demonstrate in lattice QCD.

Asymptotic freedom, which means that in very high-energy reactions, quarks and gluons interact very weakly creating a quark–gluon plasma.

The present model of the universe starts with enormous energies, and as it expands the individual constituents cool down first into a stage where all forces are unified with all particles zero mass into a quark-gluon plasma

As cooling continues bound hadrons appear.

The quark gluon plasma is studied experimentally at the LHC experiments.

So all the models of particle physics are utilized for the Big Bang model of the universe, and the creation of bound quarks is developed within an extended standard model.

If you read the article you will see that a lot of the model is still at the research stage experimentally.

• Dear Anna V, I read the wikipedia article, but it does not talk about how quarks were formed. First if I understand correctly, there was a sea of photons. But how did quarks form? Quarks are point particles, so we do not know what they consist of, so is there any theory on how they were formed, maybe from photons? – Árpád Szendrei Apr 10 '18 at 11:46
• @ÁrpádSzendrei See also this en.wikipedia.org/wiki/Big_Bang#Inflation_and_baryogenesis . The quark gluon plasma is hypothesized to exist at those early stages. All the particles in the standard model table are in the soup, en.wikipedia.org/wiki/Standard_Model and their antiparticles , it is a working hypothesis. They come into existence because the energy is available for them to do so. In the hypothesis they would form from pair creation, quark antiquark, from the available energy. A lot is speculation, about the fields available at that time in the model. – anna v Apr 10 '18 at 13:11
• One accepts the particle table as axiomatic, in the standard model, i.e. given by measurements. – anna v Apr 10 '18 at 13:12
• Thank you, so you say they were formed by pair creation, from the available energy. But is that energy the sea of photons, or is that energy from the Quantum fields? – Árpád Szendrei Apr 11 '18 at 8:43
• photons come later than the primordial energy of the inflation time, they call the hypotheitical particle inflaton, which carries all the energy before the quark-gluon-electron -photon- ... plasma. – anna v Apr 11 '18 at 9:05

## protected by Qmechanic♦Mar 10 '17 at 13:24

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