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Bouncing models are alternatives to inflationary cosmology that replace theinitial Big-Bang singularity by a `bouncing' phase. A deeper understanding ofthe initial conditions of the universe, in these scenarios, requires knowledgeof quantum aspects of bouncing models. In this work, we propose two classes ofbouncing models that can be studied with great analytical ease and hence,provide test-bed for investigating more profound problems in quantum cosmologyof bouncing universes. Our model's two key ingredients enable us to dostraightforward analytical calculations: (i) a convenient parametrization ofthe minisuperspace of FRLW spacetimes and (ii) two distinct choices of theeffective perfect fluids that source the background geometry of the bouncinguniverse. We study the quantum cosmology of these models using both theWheeler-de Witt equations and the path integral approach. In particular, wefound a bouncing model analogue of the no-boundary wavefunction and presented aLorentzian path integral representation for the same. We also discuss theintroduction of real scalar perturbations.

No-boundary Wave Function, Wheeler-DeWitt Equation and Path Integral Analysis of the Bouncing `Quantum' Cosmology