I am not a physicist, so I would really appreciate using a simple language for the explanation of my question. From what I understood at the early Big Bang the four fundamental forces were unified to one and the spontaneous symmetry breaking (SSB) occured causing the rise of the different four forces. Would that mean that the fundamental laws changed when SSB occurred? Or was the fundamental laws existing only before SSB?
[Physics] Early time in the Big Bang
big-bangsymmetry-breakingunified-theories
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When we say that the forces were unified, we mean that the interaction was described by a single gauge group. For example, in the original grand unified theory, this group was $SU(5)$, which spontaneously broke down to $SU(3) \times SU(2) \times U(1)$ as the universe cooled. These three components yield the strong, weak, and electromagnetic forces respectively.
I'll try to give a math-free explanation of what this means. To do so I'll have to do a decent amount of cheating.
First, consider the usual strong force. Roughly speaking, the "strong charge" of a quark is a set of three numbers, the red, green, and blue color charges. However, we don't consider the strong force three separate forces because these charges are related by the gauge group: a red quark can absorb a blue anti-red gauge boson and become blue. In the case of the strong force, we call those bosons gluons, and there are 8 of them.
At regular temperatures, the strong force is separate from the electromagnetic force, whose charge is a single number, the electric charge, and whose gauge boson is the photon. There is no gauge boson that converts between color charge and electric charge; the two forces are independent, rather than unified.
When we say all the forces were unified, we mean that all of the Standard Model forces were described by a common set of charges, which are intermixed by 24 gauge bosons. These gauge bosons are all identical in the same way that the 8 gluons are identical. In particular, you can't point at some subset of the 24 and say "these are the gluons", or "this one is the photon". They were all completely interchangeable.
As the universe cooled, spontaneous symmetry breaking occurred. To understand this, consider slowly cooling a lump of iron to below the Curie temperature. As this temperature is passed, the iron spontaneously magnetizes; since the magnetization picks out a specific direction, rotational symmetry is broken.
In the early universe, the same process occurred, though the magnetization field is replaced with an analogue of the Higgs field. This split apart the $SU(5)$ gauge group into the composite gauge group we have today.
The process of spontaneous symmetry breaking is closely analogous to phase transitions, like the magnetization of iron or the freezing of water, which is why we talk about 'strongly/weakly unified' matter as separate states of matter. Like the iron, which state we are in is determined by the temperature of the universe. However, a exact theoretical description of this process requires thermal quantum field theory.
The Planck era is defined as the time when the universe was the size of the Planck length, $10^{-33}$ cms, and less, and the universe's age was $10^{-43}$ sec, the Planck time, and less. It is the earliest epoch we identify after the Big Bang. The Planck temperature at the end of the epoch was about $10^{32}$ degrees Kelvin.
This was way before quarks, leptons, Higgs bosons, and inflation. Neither Quantum Theory (QT) nor General Relativity (GR) have anything to say about what is happening at these sizes, times, energy densities and temperatures, except that they are not applicable.
The wiki article summarizes the epochs, or times, when the universe was dominated by different kinds of physics, from the Planck epoch through the GUT epoch, inflation, electroweak and strong force separation, and on till the current epoch. It is at https://en.m.wikipedia.org/wiki/Chronology_of_the_universe
At Planck times and earlier after the Big Bang, GR effects or equivalently strong gravity effects predicted by GR, would be happening at the sizes and energies such that QT also applies. It needs a unification of GR and QT to have anY explanatory power, a theory of quantum gravity. At these times there are no photons, quarks, electrons, neutrinos, gluons or anything associated specifically with the 4 forces. This was before spacetime was defined by geometry and GR, or even before it existed. The two best known theories of quantum gravity, none proven or accepted, are string theory (ST) and its newer versions of superstrings and M theory, and loop quantum gravity. They both have elementary entities which can be about the Planck size, one is strings and the other loops.
I know quantum loop gravity less well, but when the spacetime is larger than the Planck length ST has strings in a 10 or 11 dimensional spacetime, which were all small dimensions unti the inflationary era where for some reason all but 4 dimensions remained small, and so now we see those 4 dimensions. At least that is one version. Others take multidimensional branes in a higher dimensional space. You can see the wiki references on string theory. But either way at the Planck length it becomes a sort of quantum foam, with no spacetime defined. Spacetime emerges as the scale factor increases and multiple Planck lengths enter in.
So, what happens at the Planck epoch (era) is not well understood. As the universe goes into the next era, the GUT era, 3 of the 4 forces, all but gravity which when we enter the GUT epoch decouples, are unified. ST aims to also explain it, i.e., a unification of the 3 forces (and actually gravity in the Planck era as well). The 3 forces then remain unified until the universe expands and cools some more, the strong force decouples, and later there is inflation and the electroweak force separates into the weak and electromagnetic force, and the Higgs boson emerges. There is more after that.
See the wiki and its references for string theory cosmology, but at inflation and later (maybe even before, up to the Planck epoch) there is commonality with the standard cosmology model. https://en.m.wikipedia.org/wiki/String_cosmology
Best Answer
In simple language we do not have a Theory Of Everything (TOE) therefore any answer about the ultimate existence of specific laws is a tentative one. What we do have is a set of nested mathematical theories that fit observations mainly in the study of particle physics. These theories extrapolated to the extremely high energies at the beginning of the Big Bang look reasonable and explain cosmological observations, thus are in this sense also validated up to now.
The search for the holy grail of unification of all forces started when electricity was unified with magnetism in the nineteenth century. Experimental measurements of the coupling constants that characterize each force , as a function of the energy of the interaction led to the following experimental observation
where we see that the strength of the couplings converges for the three forces that can be studied with particle physics.
The concept of spontaneous symmetry breaking has good experimental validation for the three forces, that they separate as the energy falls, and it is a hypothesis for the gravitational force.
In the sense that the theory is known for the three forces, below 10^15GeV, SSB is a law that exists even at the maximum limit, but it is a mathematical statement. When the TOE is found it is only necessary that its mathematical formulation converges and explains the SSB of the three forces.
We do not know if the unification of all forces happens at an energy value lower than the one available at the Big Bang or starts at the singularity. There can be models though. In the forces plot the unification is given below the maximum, at the Planck Energy . It seems a good hypothesis at the moment. The "laws" start appearing as the universe cools, they pertain to the specific energy range studied experimentally and are a mathematical hypothesis for the yet unexplored. Nature might still have surprises for us.