A stable initial state is identified in mLQC-I that diagonalizes the Hamiltonian and minimizes particle creation, with mode functions approximated analytically by Airy or cylindrical functions whose constants are fixed by that state.
Then, using the asymptotical behavior ofU(b,x)and ¯U(b,x)forx≫1 givne by Eq.(128), we find that νII k (y)≃ 1 (2g)1/4 ˜ake−F1(y) + ˜bk r 2 π Γ 1 2 −b eF1(y) ,(y≫1)
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Stable initial conditions and analytical investigations of cosmological perturbations in a modified loop quantum cosmology
A stable initial state is identified in mLQC-I that diagonalizes the Hamiltonian and minimizes particle creation, with mode functions approximated analytically by Airy or cylindrical functions whose constants are fixed by that state.