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In cosmology, the cosmological constant problem or vacuum catastrophe is the substantial disagreement between the observed values of vacuum energy density (the small value of the cosmological constant) and the much larger theoretical value of zero-point energy suggested by quantum field theory.
The basic idea is simply that the vacuum expectation values of Wilson loops in Chern–Simons theory are link invariants because of the diffeomorphism-invariance of the theory. To calculate these expectation values, however, Witten needed to use the relation between Chern–Simons theory and a conformal field theory known as the Wess–Zumino ...
The symmetry group of this pancake world is then SO(2) semidirect product with R 2, meaning that a two-dimensional rotation plus two extra parameters, the x-tilt and the y-tilt. The reason it is a semidirect product is that, when you rotate, the x-tilt and the y-tilt rotate into each other, since they form a vector and not two scalars .
Loop quantum cosmology (LQC) is a symmetry-reduced model of classical general relativity quantized using methods that mimic those of loop quantum gravity (LQG) that predicts a "quantum bridge" between contracting and expanding cosmological branches.
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Given the difficulty of constructing explicit small families of solutions, much less presenting something like a "general" solution to the Einstein field equation, or even a "general" solution to the vacuum field equation, a very reasonable approach is to try to find qualitative properties which hold for all solutions, or at least for all ...
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