Level 2: Forces — \(10^{-35}\text{s}\)
Elementary particles
Size: \(10^{-18} \text{m}\)
Initial state: GUT quantum fields
Production process: Symmetry breaking
Meta-stable equilibrium: First-generation particles
Stable future: Stable particles (photon, neutrino, LSP)
The 4D Universe
Temperature: \(10^{29} \text{K}\)
Initial state: Curved 4D universe
Production process: Cosmic inflation
Meta-stable equilibrium: Locally flat 4D universe (radiation-dominated)
Stable future: Flat 4D universe
This level will witness the emergence of the fundamental forces. At Level 1, we’ve dabbed quite a bit into theoretical physics, to attempt a coherent presentation. But the period when Level 1 structures emerged, up until \(10^{-35}\text{s}\) was really about the emergence of the primordial distinction between the spacetime background (a many dimensional object that gets compactified into our familiar 4D spacetime) and its physical content (which we can “unpack” as a number of quantum fields).
The universe is still an extremely dense, unfathomably hot, curved spacetime, inhabited by the complete bestiary that was inherited from the "true" Grand Unified Theory (whichever one it is): quarks, leptons, gluons, \(B\), \(W\), \(X\), \(Y\) bosons, sfermions and gauginos, higgs and higgsinos, and likely so many more... All are interacting in a massive tohu-bohu that makes the expression "primordial soup" feel appropriate.
The Standard Model epoch: \(10^{-35}\) to \(10^{-12} \text{s}\)
By the \(10^{-35}\text{s}\) mark, the expansion of the universe has cooled it to a "measly" \(10^{29}\text{K}\). It is in that neighborhood that the likely GUT scale is located, which means that symmetry is broken past that threshold, either in one go or in several successive steps, as we’ve seen. The result, down the line, is the separation of the strong force coupling from the electroweak coupling, inaugurating the Standard Model epoch, when an unbroken \(SU(3)\times SU(2) \times U(1)_Y\) still reigned over quantum interactions. \(X\) and \(Y\) leptoquarks, alongside the whole exotic GUT zoo, acquire mass and disappear from the picture, save from more and more infrequent short-distance interactions. The strong interaction displays the familiar features from today’s world, but the electroweak bosons are still all massless.
Around that time, cosmic inflation starts. It is a period of extremely fast expansion of space, which is dilated by a factor of at least \(10^{26}\) within a period of around \(10^{-32}\text{s}\). If we were to dilate a human cell (\(~1\mu \text{m}\)) by that much, we would end up with an object 100 quadrillion kilometers wide! Yet after inflation, the patch of spacetime that is now the whole observable universe woudl have been less that 3 meters long. As a result of inflation, the universe rapidly cools down to \(10^{22} \text{K}\).
Inflation is still a hypothesis, since its cause cannot be explained in terms of known quantum fields nor in the context of general relativity. Yet it is widely accepted as the solution to the overbearing horizon and flatness puzzles. The universe appears to us to be nearly flat, homogeneous and isotropic on a large scale. Without inflation, this would be incompatible with the laws of physics, but the faster-than-light metric expansion from the inflationary epoch would explain how a minuscule causal patch could still end up much larger than our observable universe, resulting in the flatness and homogeneity we’re now perceiving. The coincidental timing around the GUT breaking scale suggests a possible link between the inflation-causing inflaton field and the symmetry breaking, although that is still highly speculative.
Cosmic inflation stopped abruptly. Although the universe was now cooler by many orders of magnitude, the temperature was still too high for any equilibrium to emerge. The next disturbing even was the breaking of supersymmetry. Very little is known about the one, be it about the exact process or the energy scale at which it happened; we only know, almost certainly, it occured before the breakdown of the electroweak symmetry. Post-supersymmetry breaking, all superpartners become massive. As cooling proceeds, they quickly decay, typically into a lighter superpartner and some ordinary particles. At the end of that process, there can be either no superpartner at all or, in R-symmetry-preserving theories, only the LSP (lightest superpartner). For instance, in the MSSM, the LSP is the neutralino, a gaugino fermion that’s a composite of the bino, neutral wino and higgsinos. It has become a sort of beacon for cosmologists in their desperate attempt to decipher the riddle of "dark matter".
There is a glaring mismatch between the observed gravitational dynamic of the universe and the ordinary matter that we can see (galaxies, nebulae, clouds,...). That visible matter only accounts for 15% of the mass that would explain large-scale dynamics! Obviously, "visible" matter either emits, reflects, or somehow interacts with electromagnetic waves, or some other sort of radiation. That means that the missing matter doesn’t; it is therefore called "dark matter". Neutrinos may seem like good candidates: they don’t interact with anything else, and are now thought to have mass. However their tiny mass, and what we know about their total population form other observations, doesn’t gel well with what we would expect of dark matter. Neutralinos, whose all quantum charges are nil, and have significant mass (100 billion times heavier than the neutrino) seem like good candidates! More generally, supersymmetric LSPs are considered very promising.
The quark epoch: \(10^{-12}\text{s}\) to \(10\mu\text{s}\)
At approximately \(10^{-12} \text{s}\), the temperature has cooled down to \(10^{15} \text{K}\) and we reach the electroweak breaking scale. We reach solid ground at last with this amply confirmed and well-known Higgs mechanism.
All fermions become massive, the electroweak bosons recombine into \(W^\pm\) and \(Z_0\), which become massive, and the photon \(\gamma\), which is massless. The unbroken segment of the internal symmetry group reduces to \(SU(3) \times U(1)_{EM}\). The familiar picture of particle physics emerges: matter, represented by fermions, interacting by exchanging bosons which mediate the fundamental forces.
The era right after electroweak symmetry breaking is called the "quark epoch" because it is still hot enough for quarks to be free, unfettered still from the confining forces that would bind them together into hadrons. As a result, since the strong interaction is already much more intense than the others, and color-charged quarks and gluons are still freely roaming the universe, the strong force entirely dominates. The result is a quark-gluon plasma that is radiation-dominant (that is, most of the universe’s energy is from the massless gluons rather than the massive quarks). Gluons are energetic enough to generate quark-antiquark pairs, which in turn disintegrate into gluons. That plasma can end up locally in a thermal equilibrium.
As cooling continues, the heavier fermions from the second and third generations become more and more rare. The ordinary matter content of the universe is then mostly limited to the classic "roster" of particles that make up us humans: up and down quarks, electrons and neutrinos (with some muons and strange quarks the lightest from the second generation joining the party at times).
The stable future
15 billion years later, the universe’s ordinary matter is still made up of the same basic components: up and down quarks, electrons and neutrinos. Indeed, on such a scale they are almost perfectly stable. The half life of quarks has a lower bound of \(10^{34}\) years (ten decillion!). In a cool universe, quarks are bound into nucleons. Since neutrons decay into protons on much shorter scales, quark decay will largely happen in the form of proton decay, for which in most GUTs the principal reaction is \(p \rightarrow e^+ + \pi^0 \rightarrow e^+ + 2 \gamma\).
Crucially, we also know that the universe is electrically neutral (since the electromagnetic force has infinite range, like gravitation, but is much more intense, gravitational effects couldn’t dominate the macroscopic scales as they do, if it wasn’t the case). This means that the positrons will in turn disintegrate with electrons. The ultimate matter content of the universe will then be limited to neutrinos and potentially an LSP (like the neutralino). There will be no mediator bosons since those fermions are chargeless. As today, there will be one freely travelling boson: the photon.
Level 3: Matter — \(10^{-5}\text{s}\)
Atoms
Size: \(10^{-10} \text{m}\)
Initial state: First-generation particles
Production process: Primordial nucleosynthesis, atomic combination
Meta-stable equilibrium: Light atoms and molecules (first period)
Stable future: Dihydrogen and Helium.
The transparent universe
Temperature: \(10^{12} \text{K}\)
Initial state: Locally flat 4D universe (radiation-dominated)
Production process: Photon decoupling
Meta-stable equilibrium: Matter-dominated, transparent universe
Stable future: Dark energy-dominated universe
The hadron epoch : \(10\mu\text{s}\) to \(0.5 \text{ms}\)
The quark epoch ends when the universe’s temperature crosses \(10^{12}\text{K}\) and is not high enough to sustain unconfined quarks. The intensity of the strong interaction is such that its attractiveness grows with distance, which leads to an incredibly powerful pull on every color-charged particle. Quarks can be confined with baryons (3 quarks of distinct colors) or mesons (one quark and one antiquark, with opposite colors), which are color-neutral particles. Those particles are collectively called hadrons, hence this epoch’s name.
The temperature at the start of the hadron epoch is \(175\text{MeV}\), which means that only up, down and strange quarks were in thermal equilibrium with their antiparticles in the plasma. During the phase transition, the quarks and antiquarks quickly assemble into baryons and mesons, but the temperature is already low enough that hadron-antihadron pairs are not spontaneously produced. The story of the hadron epoch is then one of annihilation. Due to matter-antimatter asymmetry, there will be residual hadrons (or ordinary matter would not exist and the universe would have jumped right to the photon-and-neutrino-only era).
The many heavy hadrons or exotic hadrons (tetraquarks, pentaquarks, hexaquarks, glueballs...) that have been either observed or merely predicted, have then never existed in a meta-stable state, although they are constantly being created to this day, either in extreme environments (supernovae, neutron star collapse...), or more prevalently, when high-energy cosmic rays interact with ordinary matter.
From the up, down and strange quarks that were around, the possible baryons are nucleons or lambdas (including strange quarks among their components). The possible mesons are pions (no strangeness) or kaons (strangeness involved).
By the time the energy is down to \(30\text{MeV}\) all the anti-baryons have annihilated, leaving only the residual output of the baryogenesis in the form of nucleons and lambdas (with density \(10^{10}\) lower than before). The mesons were already dominating the mass content of ordinary matter, but at that point they represent almost all of it.
The meson epoch : \(0.5 \text{ms}\) to \(5 \text{ms}\)
That marks the start of the meson epoch, when initially, a mix of pions and kaons dominate matter. However, as pointed out above, energy is too low to support the production of meson-antimeson pairs. The annihilation process is thus on-going, as well as the decay process of the remaining mesons.
By \(20\text{MeV}\), both the remaining Kaons and the lambda baryons (the "strange" content) are at equal density
The electron epoch : \(10 \text{ms}\) to \(10 \text{s}\)
At that energy level, pions then dominate the hadronic mass in the universe, but their density, although still \(10^{10}\) higher than the nucleons’, has decreased enough that it becomes inferior to that of "matter leptons". With that term we are excluding neutrinos, whose low mass makes them ultra-relativistic particles that we classify as radiation. Let’s not forget the hierarchy at the universe’s level: dark matter represents most of its, follow by photon and neutrino radiation, with ordinary matter only representing a few percentage points. The successive "domination" by quarks, hadrons, mesons and now leptons only refer to an advantage within ordinary matter.
Further, we know that by that point, the muon and tau leptons have almost entirely decayed. The only matter particle that keeps being produced in particle-antiparticle pairs is the electron. Despite its lower mass (2000 times lower than a nucleon’s, 200 times lower than a pion’s), it can dominate by virtue of that continued production.
Pion decay continues, with nucleon-pion equality around \(6\text{MeV}\), and the pions’ extinction at \(3\text{MeV}\). The only remaining hadrons are the nucleons, but they’re now entirely drowned in a sea of electrons and positrons where electromagnetic interactions dominate.
The density is still high enough that the short-distance nature of the weak interaction (since electroweak symmetry breaking) is not really consequential yet, and neutrinos still interact freely with all those particles. The reaction that we know as neutron decay is not only hyper-frequent, it is also reversible, with protons and neutrons thus being in perfect parity (because they are constantly turning into each other).
That starts to change as cooling marches on, and the proton-to-neutron ratio keeps increasing, until \(1\text{s}\) (\(1\text{MeV})\), when neutrino entirely decouple from matter and the ratio freezes around 5 protons to 1 neutron. Neutrinos then adopt the behavior we know today, as a form of radiation that’s travelling freely accross the universe, with only the occasional interaction when it gets close enough to another particle.
The nucleon epoch : \(10 \text{s}\) to \(2 \text{min}\)
At the end of the electron epoch, pairs stop being produced and electron-positron density decreases quickly as they annihilate. Since nucleons are heavier, they end up dominating the mass of ordinary matter (as they do today). The neutron-to-proton ratio has been frozen out at 0.21 and due to electromagnetic neutrality there is one electron for each proton. Neutron, protons and electrons now cohabit in a structure-less plasma where they’re constantly interacting electromagnetically via photons.
The nucleosynthesis epoch : \(2\) to \(20 \text{min}\)
2 minutes after the Big Bang, the primordial nucleosynthesis starts. You may have a notion that the elements we know today were created through a nucleosynthesis process happening in stars’ core. That is indeed the case: this primordial nucleosynthesis only yielded Helium nuclei.
When it began, the environment was cool enough that stable structures could form under the "residual nuclear force". That term designates the attraction between nucleons: although they are individually color-neutral, the sheer intensity of the strong interaction is enough to generate attraction between them (similar to the way that atoms, electrically neutral objects, can still form molecules due to residual electrostatic forces).
Protons and neutrons were already strongly attracted enough to form deuterium, the simplest possible nucleus, but temperature was so high that it immediately decomposed right back. Once that bottleneck is passed, two deuterium nuclei are available to react and yield a Helium-3 (two protons, one neutron) and a free neutron. Then Helium-3 can react with yet another deuterium to create Helium-4 (plus a free proton).
Deuterium and Helium-3 are unstable,: left to their own devices, they decay quickly. However at this energy level, Helium-4 is extremely stable. It doesn’t undergo fission (reverting to lighter elements), and it rarely undergoes fusion (yielding heavier elements). Since the universe is cooling at the same time that this is happening, nucleosynthesis ends before all the hydrogen has been transformed.
The expected composition of the universe’s hadronic mass after that phase is 75% hydrogen, 25% Helium-4 and only traces amount of anything else (0.01% in deuterium and Helium-3, and less than a millionth % in Lithium nuclei). Indeed, that is consistent with the evolution of the neutron-to-proton ratio. Remember that after neutrino decoupling, this had been frozen at 0.21. But free neutrons natural decay into protons via the weak interaction. Accounting for the energy levels and the progress of nucleosynthesis, we expect the final neutron-to-proton ratio to be very close to 1:7. And that is exactly what a 75/25 mass split between hydrogen and helium translates into! (Since helium is 4 times as heavy as hydrogen, this split means there are 12 free protons for each Helium nucleus (2 protons and 2 neutrons); then there are 2 neutrons for every 14 protons).
As a matter of fact, this is exactly the ratio we observe to this day! The helium produced via stellar nucleosynthesis is only a small amount most of it originates in the primordial nucleosynthesis. This is then a resounding success for the whole theory...
The plasma epoch : \(20 \text{min}\) to \(47\text{k}\) years
Nucleosynthesis then leaves a universe composed of free protons, Helium nuclei, and electrons, still interacting with photons in a hot electromagnetic plasma. We could say that matter is in an ionic state, since electrons are moving around freely, as the temperature, at \(10^7 \text{K}\) or so, is still too high to allow electrically neutral objects like atoms to emerge. Even though we are focusing a lot on the evolution of ordinary matter, it is always worth repeating that most of the universe’s energy is stored in dark matter’s mass, and that the second store is in radiation, with ordinary matter’s contribution a distant third.
Since dark matter doesn’t interact with anything and thus has no bearing on the evolution of the universe at the scale under consideration, it is common to say the universe is then radiation-dominated.
The atomic epoch : \(47\text{k}\) to \(370\text{k}\) years
The ion epoch lasted much longer than its predecessors, and it is fair to say that beyond continuous cooling, not much happened during the next millenia. But that was always bound to change. It may seem that the forces on the battlefield were now fixed. Unlike in previous epoch, particles were not changing into each other much, nor were they combining, decomposing, or annihilating a lot. Yet the fact that the universe kept expanding was far from neutral.
It is a well-known fact that energy density doesn’t react in the same way to space expansion for all energy sources. For a scaling factor \(a\), the energy density of matter (both ordinary and dark) evolves as \(a^{-3}\): nothing is more natural since expansion increases all distances by a factor \(a\), and thus all volumes by \(a^3\). But for radiation, that density follows an \(a^{-4}\) law. Lastly for what is sometimes called "dark energy" but can be seen as a "cosmological constant" an unchanging curvature term in the equations governing the universe’s large-scale dynamics , the energy density embedded in spacetime geometry is entirely independent of \(a\).
The first consequence is that the energy density from matter is bound to overtake that of radiation. That is precisely what happens, around 47,000 years after the Big Bang. What practical consequences could this possibly have? They are extremely momentous, since matter domination ushers in the era of large-scale structures. More exactly, it makes that era possible: it will take many million years for meaningful structures to emerge. But it is the end of radiation prevalence that makes it all possible.
We’ve seen somewhere above that cosmic inflation was a neat way to explain how structures (concentration of mass in specific sectors of the universe) could arise from a purely homogeneous and isotropic universe. Inflation was so fast (literally, more than lightning fast), that ordinary quantum fluctuations were frozen and instantly blown up many orders of magnitude in size. After the mighty stretch that inflation inflicted upon spacetime, those relics looked like minuscule variations in curvature, completely negligible factors vs the chaotic plasma where more intense quantum fields deployed their exuberance. But dark matter was not subject to any interactions with other sorts of matter or radiation. Since only gravity could affect it, it started to slowly migrate towards specific regions which will be later known as filaments.
At the time immediately following matter domination though, hadronic matter was still much too agitated in its electromagnetic plasma to feel such gravitational effects.
The premices of change were not long to come though. As temperature crossed \(10,000\text{K}\), combination started. To be more precise: the electromagnetic combination of electrons with nuclei. Up to that point, the natural attraction between the electron’s negative and the nuclei’s positive charges was more than counter-balanced by the prevalent agitation in the giant pinball game that was the primordial plasma. If such combinations formed, they were immediately taken down by a super-energetic photon. Most of the time they could not form at all since particles were too "busy" scattering the photons constantly colliding with them.
With cooling, it became possible for a fraction of the electrons to assemble with nuclei for longer and longer periods, resulting a in a growing ratio of matter in ionic or atomic state. It may seem like the simplest possible compound is the hydrogen atom (1 proton and one electron), but in fact, the hydrogen ionization temperature is much lower than for helium.
The first object to be steadily produced to the point it becomes of some abundance is then the helium cation, around the 120,000 years mark: \[\text{He}^{2+} + \text{e}^- \longrightarrow \text{He}^+\]
Later on, the cation is able to consistently absorb another electron and form the first atom: helium.
\[\text{He}^+ + \text{e}^- \longrightarrow \text{He}\]
At lower temperature, helium can form the first covalent bond with a proton to generate a helium hydride molecular ion.
\[\text{He} + \text{p} \longrightarrow \text{HeH}^+\]
It’s only around 370,000 years after the Big Bang that the hydrogen ionization energy is crossed, an the remaining protons form hydrogen atoms.
\[\text{p} + \text{e}^- \longrightarrow \text{H}\]
With more cooling, hydrogen atoms tend to form bonds with the still-free protons to create dihydrogen cations. That object also appears when all the helium hydride reacts with the newly formed hydrogen. Lastly, an electron is absorbed to form dihydrogen, the first neutral molecule in the universe.
\[\text{H} + \text{p} \longrightarrow \text{H\_2\^+}\] \[\text{HeH\^+} + \text{H} \longrightarrow \text{H\_2\^+} + \text{He}\] \[\text{H\_2\^+} + \text{e\^-} \longrightarrow \text{H\_2}\]
The golden epoch : \(370\text{k}\) to \(2\text{M}\) years
The last sequence from the point where hydrogen atoms appear is very fast. That combination process yields a very large energy in the form of energetic photons, first when the atoms assemble in an excited state, then (almost immediately) when they emit an extra photon during their transition to the bound state.
Now that ordinary matter is entirely atomic or molecular (made largely of dihydrogen and helium), photon scattering is not a significant event anymore, thermically speaking, and these photons are free to travel the universe untethered, like neutrinos have been doing for some time already. That is photon decoupling. That specific batch of photons is known as the Cosmic Microwave Background.
The CMB was originally the same frequency as orangey light, hence the name of this epoch, but with the universe’s expansion it naturally redshifted. At the end of this epoch, roughly two million years after the Big Bang, the universe was filled with a hydrogen/helium gas, some free infrared photons (not interacting with matter in a significant way) as well as neutrinos and dark matter. To a human eye, it would then appear entirely dark.
That is the situation we know today: outer space is generally black-looking, but of course it is now sprinkled with the light from trillions of stars. How those came to be is a topic for our next level.
The stable future
The ultimate fate of structures at this particular level is an interesting case. Remember that this section is often a thought experiment rather than an actual prediction of the future. The question we’re asking is: if we’re only considering the forces under which action the objects from Level 3 emerged, at the range of energy under consideration, and all else being equal, what would happen in the far future?
This is often a way of asking what the most stable state of organization at that level is, since in nature, meta-stable structures always decay into more stable ones, and some that may seem stable even over a billion years, may prove unstable in the longer run.
Atoms and molecules are extremely robust structures. Yet, it is clear that in the real world, they won’t be eternal. A Big Rip might happen; in that case the universe would expand so much that the size of the observable universe from a proton’s perspective would be shorter than any atom’s radius, which would automatically entail all of the atoms’ breakdown. But that’s Level 1’s far future, it involves forces, timescales and phenomena that go beyond Level 3. We also know that protons are likely to decay, in which case hydrogen atoms could very briefly turn into positronium (a positron-electron atom), but ultimately would still annihilate into photons. But that’s Level 2.
Hydrogen and Helium atoms, although they are extremely stable nuclei, could still go through cold fusion, since the bound states of heavier nuclei have lower energies. But we haven’t encountered heavier nuclei yet: that’s Level 4.
At Level 3, it then seems that the electrically neutral, stable structures we’ve encountered: the dihydrogen \(\text{H\_2}\) molecule and the Helium atom are, for all accounts and purposes, pretty much eternal, if temperatures stay below their ionization level. If not for universe-bending relativistic effects, for GUT-only quark decay, or for nuclear cold fusion, they would just persist forever, motionless, all the way down to absolute zero.