In Thiemann-regularized loop quantum cosmology, the mu0 scheme produces pre-bounce emergent matter with equation of state w = -1/3 (string gas), while the bar-mu scheme produces an emergent cosmological constant, and mu0 stays unviable with positive Lambda.
Barbero, A real polynomial formulation of General Relativity in terms of connection
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Some physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology
In Thiemann-regularized loop quantum cosmology, the mu0 scheme produces pre-bounce emergent matter with equation of state w = -1/3 (string gas), while the bar-mu scheme produces an emergent cosmological constant, and mu0 stays unviable with positive Lambda.