Due to some of the basic principles of quantum mechanics, we have the Wolfgang Pauli exclusion principle, where two fermionic bodies cannot occupy the same quantum state simultaneously. If that is true, then how is all matter, energy, space and time of the universe being compressed into an infinitesimally small Singularity 13.8 billion years ago? Wouldn't particles/bodies be occupying the same space simultaneously in an infinitely small place? Does this mean that the Big Bang is wrong or is Pauli's exclusion principle wrong?
Cosmology – Big Bang and the Pauli Exclusion Principle: Understanding Singularities
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Best Answer
The key confusion is the idea that Pauli Exclusion prevents any two particles from occupying the same space. The actual Pauli Exclusion Principle is slightly different: it prevents any two particles occupying the same quantum state.
If the temperature is higher than the Fermi Energy, there is more than enough thermal energy to give each particle its own quantum state (which includes energy). This allows particles to stack atop each other in space, (but have different momentum and energy). Consider electron clouds which partially overlap in your everyday atom!
The Fermi temperature scales as the Fermi Energy, which in the relativistic case, scales as $L^{-1}$. The temperature of a radiation dominated (as it was, early on) universe also scales as $L^{-1}$. So as we go back in time, to smaller and smaller lengths, the Fermi Temperature will never overtake the Temperature, so the Pauli Exclusion Principle will hold true, but not matter physically. The pressure due to photons will be much larger than any degeneracy pressure.
It's important to note that much of the energy density is in Bosonic fields (photons, scalar fields, etc.) rather than Fermionic fields. And important to note that we do not necessarily know what happens when the Universe is younger than a Planck time, as our understanding of physics above this energy scale is incomplete.