Positive cosmological constant in loop quantum cosmology

Understand

The k=0 Friedmann Lemaitre Robertson Walker model with a positive cosmological constant and a massless scalar field is analyzed in detail.

• If one uses the scalar field as relational time, new features arise already in the Hamiltonian framework of classical general relativity: In a finite interval of relational time, the universe expands out to infinite proper time and zero matter density.
• In the deparameterized quantum theory, the true Hamiltonian now fails to be essentially self-adjoint both in the Wheeler DeWitt (WDW) approach and in LQC.
• Irrespective of the choice of the self-adjoint extension, the big bang singularity persists in the WDW theory while it is resolved and replaced by a big bounce in loop quantum cosmology (LQC).