Physicists define the boundaries of physics by trying to describe them theoretically and then testing that description against observation. Our observed expanding Universe is very well described by flat space, with critical density supplied mainly by dark matter and a cosmological constant, that should expand forever.
If we follow this model backwards in time to when the Universe was very hot and dense, and dominated by radiation, then we have to understand the particle physics that happens at such high densities of energy. The experimental understanding of particle physics starts to poop out after the energy scale of electroweak unification, and theoretical physicists have to reach for models of particle physics beyond the Standard Model, to Grand Unified Theories, supersymmetry, string theory and quantum cosmology.
This exploration is guided by three outstanding problems with the Big Bang cosmological model:
1. The flatness problem
2. The horizon problem
3. The magnetic monopole problem
Flatness problem
The Universe as observed today seems to enough energy density in the form of matter and cosmological constant to provide critical density and hence zero spatial curvature. The Einstein equation predicts that any deviation from flatness in an expanding Universe filled with matter or radiation only gets bigger as the Universe expands. So any tiny deviation from flatness at a much earlier time would have grown very large by now. If the deviation from flatness is very small now, it must have been immeasurably small at the start of the part of Big Bang we understand.So why did the Big Bang start off with the deviations from flat spatial geometry being immeasurably small? This is called the flatness problem of Big Bang cosmology.
Whatever physics preceded the Big Bang left the Universe in this state. So the physics description of whatever happened before the Big Bang has to address the flatness problem.
Horizon problem
The cosmic microwave background is the cooled remains of the radiation density from the radiation-dominated phase of the Big Bang. Observations of the cosmic microwave background show that it is amazingly smooth in all directions, in other words, it is highly isotropic thermal radiation. The temperature of this thermal radiation is 2.73° Kelvin. The variations observed in this temperature across the night sky are very tiny.Radiation can only be so uniform if the photons have been mixed around a lot, or thermalized, through particle collisions. However, this presents a problem for the Big Bang model. Particle collisions cannot move information faster than the speed of light. But in the expanding Universe that we appear to live in, photons moving at the speed of light cannot get from one side of the Universe to the other in time to account for this observed isotropy in the thermal radiation. The horizon size represents the distance a photon can travel as the Universe expands.
The horizon size of our Universe today is too small for the isotropy in the cosmic microwave background to have evolved naturally by thermalization. So that's the horizon problem.
Magnetic monopole problem
Normally, as we observe on Earth, magnets only come with two poles, North and South. If one cuts a magnet in half, the result will not be one magnet with only a North pole and one magnet with only a South pole. The result will be two magnets, each of which has its own North and South poles.
A magnetic monopole would be a magnet with only one pole. But magnetic monopoles have never been seen? Why not?
This is different from electric charge, where we can separate an arrangement of positive and negative electric charges so that only positive charge is in one collection and only negative charge is in another.
Particle theories like Grand Unified Theories and superstring theory predict magnetic monopoles should exist, and relativity tells us that the Big Bang should have produced a lot of them, enough to make one hundred billion times the observed energy density of our Universe.
But so far, physicists have been unable to find even one.
So that's a third motivation to go beyond the Big Bang model to look for an explanation of what could have happened when the Universe was very hot and very small.