# Primordial color charge fluctuations that failed to die out due to cosmic inflation

We know that ripping the quarks in a hadron apart will not give us free quarks, but rather new (anti-)quarks are generated that neutralize the color charges of the quarks. We also know that the total color charge of the universe should be zero. These two arguments give the well-known assertion that there are no free quarks, or in fact any free particles with non-zero color charge, in the universe.

But this conclusion does not seem sound to me. My counterarguments are:

1. Cosmic inflation ended at about $$10^{-32}\textrm{ s}$$ after the Big Bang.
2. Thus, when the cosmic inflation had just ended, any given quark in the universe only had time to interact causally with particles within about $$10^{-24}\textrm{ m}$$ from itself. This is within the asymptotic freedom length scale of the strong interaction, so up to this time, quarks acted as if they are free particles, and did not display color confinement. In other words, a quark did not have time to know the colors of all the quarks within the confinement radius ($$\sim 10^{-15} \textrm{ m}$$), so it cannot force its neighborhood to have zero color charge, even though the total size of the universe after the inflation epoch might have been much larger than the confinement radius.
3. Even if the whole universe is color-neutral, the local color charges at individual spatial points of the universe must exhibit statistical fluctuations. In particular, just after the end of inflation the quarks were essentially free, so the correlation of the color charges between two spatial locations should be essentially zero. Consequently, the color charges should exhibit square root law fluctuations. That is, if you select a spatial region so that the region contains $$N$$ quarks, and you observe the total color charge within that region, you should find a color charge whose magnitude is about $$\sqrt{N}$$, unless the region is comparable in size to the universe, where the constraint that the whole universe is color-neutral comes into play and reduces the expected color charge. It's equally easy to see that, the probability that the total color charge in the region was zero, is on the order of $$1/\sqrt{N}$$. (Note that this point is not covered in related questions already present on Physics SE, e.g. this, this and this, and it is essential for my argument, so I think the present question is not duplicate.)
4. It's probably true, or at least not yet ruled out, that our observable universe is smaller than the entire universe. If this is true, then if we select the region as the part of the universe (at the time just after the inflation) that was within our past light cone (hereafter called region A), then the region did not contain the whole universe.
5. Region A would have encapsulated an astronomical number of quarks, many orders of magnitudes more (because of the antiquarks that did not survive till now) than the quarks in our observable universe now (on the order of $$10^{80}$$). As a result, the probability that the total color charge within region A was zero is negligible, below $$10^{-40}$$ or so.
6. The world lines of all colored particles in region A eventually cross our past light cone, while those colored particles that were outside region A cannot cross our past light cone. Thus the total color charge in our observable universe is equal to the total color charge of region A, and is thus almost surely not zero!
7. Moreover, most of the color charge probably still remained inside our past light cone even after color confinement went into effect due to the quark-gluon plasma decayed into hadrons. This is because the hadron epoch ended very early (within $$1 \textrm{ s}$$ after the Big Bang), and the universe expanded really fast (at age $$1 \textrm{ s}$$ the universe was already 10 lightyears in radius) so that most of the quarks that were within region A did not have time to be causally connected to the boundary of our past light cone.

In sum, the problem seems to be: the primordial quark-gluon plasma had statistical fluctuations that gave some parts of it a transient non-zero color charge. And cosmic inflation could separate some positive fluctuations from negative ones for a sufficiently long time (all the way till now) that the fluctuations failed to neutralize each other even when hadrons started to form. If this indeed happened, there must be (or at least have been) free particles with non-zero color charge, in our observable universe, despite that they may be extremely rare (less than $$1$$ color charge per $$10^{40}$$ quarks), so we have not found them yet.

Does the above reasoning make sense? If I do miss something, does my reasoning still show that the absence of free color-charged particles at least does not trivially follow from color confinement, since one must first show that the primordial color charge fluctuations did die out completely before the formation of hadrons?

• A follow-up question: does this reasoning apply to electric charges? In other words, is it true that our observable universe is probably not charge-neutral, and has on the order of $1$ net charge per $10^{40}$ charged particles? If it is easier to refute the electric charge version of my question, an answer dealing solely with electric charges is equally welcome. Jul 19, 2021 at 8:10
• My semi-educated intuition would be that the separation of the primordial quark plasma into causally disconnected regions must've been subject to the same fundamental physical constraints as separating quarks in hadrons is today. In other words, at some point between (or during) inflation and hadron formation pair production (and separation) would've ensured large scale color neutrality. Otherwise you'd be left with unconfined colored particles with ~infinite mass. But I don't know enough about either cosmology or particle physics to say anything about the details of this process. Jul 31, 2021 at 6:53
• (As for electric charges, there's no confinement mechanism for those, so yes, one would expect there to be tiny residual fluctuations in net charge density. Observing them is, of course, another matter…) Jul 31, 2021 at 6:56
• @IlmariKaronen Thank you for your comment! The problem is, color charge is not only confined, but is also conserved. So if at the end of hadronic formation, the observable universe from a certain standpoint contains a nonzero net color charge, then the color charges have to remain there, because there is no opposite color charge in sight, and they cannot satisfy confinement by simply zeroing themselves out (thereby violating color charge conservation). Perhaps they turned into black holes on their way of acquiring an infinite mass, so we don't see their color charges? Jul 31, 2021 at 9:10
• Thinking about this a bit more… a region of space in a rapidly expanding universe can gain or lose color charge by having a quark–antiquark pair appear near the cosmological horizon of the region and having one half of the pair fall outside the horizon. Normally this would be strongly suppressed by color confinement, which keeps the pair from separating too far (and forces the formation of new pairs if they do), but if the region already has a net color charge, it should be strongly favored instead. I might actually try making this an answer… Jul 31, 2021 at 10:11