A Finite Universe as a Laboratory for Quantum Gravity

We explore a model in which the observed FLRW cosmology admits a finite global completion and ask how this affects prospects for testing quantum gravity. A finite overdense region embedded in a larger background can collapse gravitationally, providing a prehistory for the observed expansion. If the collapse approaches a finite quantum-supported density ρG, positive spatial curvature permits a nonsingular bounce connecting contraction to expansion. Such a cosmology can act as a laboratory for quantum gravity. We use quadratic gravity and PT-symmetric quantum theory as concrete realizations while emphasizing that the strategy is more general. The CMB amplitude of fluctuations constrains the cuadratic coupling, while large-angle CMB parity statistics and particle–antiparticle asymmetry can be related to an effective PT-breaking amplitude. PT completion also suggests a connection to the arrow of time: information inaccessible within one semiclassical branch may remain encoded in a unitary PT-complete quantum state, potentially reformulating aspects of the Past Hypothesis and apparent information loss. The contracting phase provides a second source of structure. Nonlinear structures formed before the bounce may survive behind the particle horizon, with their abundance and mass function constrained by dark matter, early supermassive black holes, lensing and gravitational waves. Strong-gravity measurements provide complementary tests through black-hole perturbations, horizon absorption and extreme-mass-ratio inspirals. The framework is therefore a network of cross-consistency and falsification tests. Cosmological maps, black holes and gravitational waves can be viewed as experiments in regimes inaccessible to terrestrial laboratories, providing an observational approach to quantum gravity complementary to microscopic theory building.