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Background: The properties of quantum particles and fundamental fields are the same all across the Universe. Each particle of a certain kind is identical to all other particles of that kind ("a certain kind" integrates every property a particle might have, including left/right-handedness, etc.).

The manifest reason for this is that the properties of quantum particles were determined in the very early Universe, mostly fractions of a second after the beginning of the Big Bang, through a series of very foundational, "mathematical" events, e.g., symmetry breakings (gravitation separating from all other forces at Planck time; strong from electro-weak at about 103 Planck times; electromagnetic from weak at about 10-25 seconds). From that one central event, the Big Bang, emerged the properties of all known quantum particles (as well as those that might exist, but were never observed, say axions or gravitons).

(Of course, there are larger-scaled, lower-energy particles which joined the Universe relatively much later, rather than being created in the early Big Bang, such as heavier atoms; in any case, they are not fundamental particles or hadrons; also, their properties, for example the amount of nuclear binding energy, are determined by those of fundamental, early Big Bang fields.)

So, there is a direct relation between the size and age of the early Universe and the physical processes which took place at that point in time, or the Compton wavelengths of the particles or phenomena being "created". See the examples above, regarding symmetry breakings and the separation of forces.

Therefore, intuitively it seems that the very early Universe "was a quantum particle-like entity" or was something similar to a single-particle system. In other words, such a small space could not have held a large number of particles, when its entire size was the Compton wavelength of a single particle (of course, as the Big Bang progressed, the newest particle was of lower and lower energy). For example, the 1080 electrons which exist today could only have come into existence after their fundamental properties (mass, quantum numbers) were determined in the early Big Bang.

Indeed, most/many fermions were created later, as the result of pair production and similar processes. However, even considering just the "parent" particles, photons, which originally held that (mass-)energy, the above holds true: not all photons could have been created in the very early Big Bang. At some point in time, the Universe had to switch from being the mathematical, symmetry breaking, small-size quantum factory that determined the quantum numbers, masses and other properties of particles and fields - to actually containing large amounts of those particles.

Question: when, then, did this switch occur? When did a large number of particles, which hold the enormous amount of energy in the Universe, come into existence? Since energy is conserved, that most probably happened very early, but when? Is inflation related to this issue and if so, in what manner?

Thanks in advance.

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The funny thing is that the universe didn't need to switch from being mathematical, symmetry breaking, small-sized quantum factory to something containing large numbers of particles. The universe is still governed by quantum mechanics, to the fullest limit of our understanding. It never stopped being that.

What did occur is that we reached a point where the effects of this quantum behavior became well modeled as particles. There was enough separation between things that it became reasonable to treat them as particles or isolated wave packets, or whatever you choose to view them as.

The opposite behavior is perhaps easier to observe: going from discrete particles to flows. Put a ball bearing in a box. If you tip the box far enough, the ball bearing rolls to one side and out of the box. It's path is well modeled with particle physics. Now do the same, but put two ball bearings in the box. Still particle like. Then three, then four. We should be comfortable with treating this as a bunch of particles.

As they say on the playground, "One, two, skip a few. Ninety nine, one hundred!" Let's get a dump truck full of ball bearings. How do you think they will behave? It turns out that it's very effective to think of them as a fluid flow rather than a set of distinct particles. We can start talking about fluid drag terms and the kind of oscillations that occur in fluid systems. We can even measure the total energy of the system using continuous integration techniques. We can talk about the fluid density.

So at what point did it switch from being particles to fluids? The answer is "never." It always was simply what it was. However, it was more convenient to think of it in terms of particles on one scale and more convenient to think in terms of fluids on the other. In the middle is a frustrating region where you see behaviors that are really hard to explain with particles, and really hard to explain with fluids.

So from that perspective, according to current theory, at roughly $10^{-37}$ seconds after the start of the universe we start to see behaviors that we are comfortable with calling particle/anti-particle creation and destruction events. Or at least, that's what we think. During that time, we predict the universe to have a temperature much higher than anything we've ever actually attained, so it's purely speculative. By $10^{-11}$, the universe had cooled down enough that the energies reached a range we can achieve in a particle accelerator, and we're very comfortable with thinking of particles at those energies. During that fuzzy region in between, you have a strange mix which sometimes exhibits particle like properties, and other times does not.

Another real-life example of these phase transitions acting interesting is the superfluid state. We know that if you add heat to a liquid, you can make it evaporate and turn into a gas. We also know that if you pressurize a gas, you can turn it back into a liquid. We can draw a line between these, and draw a phase diagram:

Phase Diagram

Note the "critical point." When you reach a high enough pressure in a gas or a high enough temperature in a liquid, it actually stops acting like either. There's too much energy for it to act like a liquid, but its too dense to have the free-space between collisions associated with a gas. It actually starts acting like "something else" which is neither liquid nor gas. We simply stop drawing the line between liquid and gas at that point because it ceases to be meaningful.

So what defines this critical point? Well, we do. The critical point is defined to be the pressure/temperature at which we simply cannot see the distinction between the phases. It ceases to be meaningful to model the material as a liquid or a gas.

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The universe evolved from the Big Bang at very high temperatures and densities (infinite from current theory but it is understood that we don't know the physics of the early moments, it is called the Planck era and quantum gravity would have dominated, but we still do not have a good, accepted theory. Maybe string theory or quantum loops or tbd).

See the table in the wiki article below about the different eras. It's all quantum. But as things get cooler we can treat things with more classical models. It is said that a phase transition ocurs from one era to the next.

https://en.m.wikipedia.org/wiki/Chronology_of_the_universe

Initially as the temperature gets lower and the universe expands, the Planck era gives rise to the grand unification era, where the 3 forces remain unified, but gravity decouples as its own. Then in the inflation era inflation (a presumed Inflaton field decays and releases lots of energy, and expansion) ocurs, and the electroweak force decouples from the strong nuclear force. As we go next to the quark era Quarks and gluons appear in a quark-gluon plasma. It is still too hot for them to combine to form hadrons. It keeps going, hadrons form, and the table is nice to see, with neutrinos, leptons and photons appearing in the next eras, and finally nucleosynthesis happens where nucleuses get formed. A matter dominated era follows, till things cool to about 4000K, about 380000 years after the Big Bang, and recombination of electrons and nucleons happens, with the universe becoming mostly electrically neutral, and radiation could then propagate throughout the universe. This is the cosmic microwave background we have detected.

The universe expansion and evolution continued, with galaxies and stars and planets forming, and life.

In all those eras, physics at higher or lower energies dominated. Initially an unknown quantum gravity, then finally to our known Standard Model of the 3 forces, and gravitation weak enough that we did not need quantum gravity but can mostly explain it now with General Relativity. As for daily life, mostly electromagnetism and the even weaker Newtonian gravity (a weaker field approximation to General Relativity).

Of course, there are anyways some areas of the universe where our current theories break down. Inside black holes we'd need quantum gravity, though our General Relativity tends to mostly explain what happens outside them, along with the particle physics from our Standard Model. Other cosmological mysteries also require physics beyond the Standard Model, such as what is dark matter and dark energy. And of course experiments in higher energy accelerators like the LHC continue to look for physics beyond the Standard Model.

So, you always have the full theories, with some yet to be discovered, but we keep getting more knowledgeable about where we are and what's missing. And for classical engineering and physics issues mostly we do well enough with classical mechanics and electromagnetism, augmented by what we do in the micro area (which involves quantum theory) with chips and new molecular compounds (and generally most of modern solid state physics and new materials)

When too many particles and we can't treat one at a time we use statistical mechanics and thermodynamics. And we use approximations of higher energy or higher fidelity physics when we can get away with it. But quantum field theory (with the standard model), and general relativity, are our current best theories of physics, from which we can approximate for more classical or lower energy results, and from which we explore for physics beyond them.

Another treatment of cosmological changes at http://cds.cern.ch/record/436209/files/0004403.pdf

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For completeness here is a timeline of the universe using the standard model of particle physics and General Relativity ( and thermodynamics etc etc)

time line universe

when, then, did this switch occur?

Take your choice going backwards in time.

When did a large number of particles, which hold the enormous amount of energy in the Universe, come into existence?

The universe we have now is after the transparency of light. Particles as we study them now, existed after quark confinement

Since energy is conserved, that most probably happened very early, but when?

The energy of the universe appeared at the time of quantum gravity in this timeline. The coalescence into particles as we know them, after quark confinement.

Is inflation related to this issue and if so, in what manner?

In the quantum gravity era is the beginning of the Universe and the Big Bang model has a fast inflationary period (needed to fit the cosmic microwave background radiation data) as seen in the plot . It is not involved in present day particle creation which happened much later.

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During inflation any pre-existing particles are redshifted into insignificant densities and the universe essentially just contains a potential dominated scalar field known as the inflaton. At the end of inflation the inflaton is thought to have decayed into particles during a process known as reheating. After that the Universe's contents can be described by the Boltzmann equations for the different particle species. It is only recently, at around a redshift of one, that a non-particle contribution, known as dark energy, has started to dominate over the particle contribution.

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