Unitarity, clock dependence and quantum recollapse in quantum cosmology

Understand

We continue our analysis of a quantum cosmology model describing a flat Friedmann--Lema\^itre--Robertson--Walker universe filled with a (free) massless scalar field and an arbitrary perfect fluid.

• For positive energy density in the scalar and fluid, each classical solution has a singularity and expands to infinite volume.
• When quantising we view the cosmological dynamics in relational terms, using one degree of freedom as a clock for the others.
• Three natural candidates for this clock are the volume, a time variable conjugate to the perfect fluid, and the scalar field.