Primordial Gravitational Waves from a Quantum Bounce with Emergent Time

We investigate the production of primordial gravitational waves in a cosmological frameworkwhere time is not a fundamental variable. At Planckian energy density, the classical notion of timeceases to be operational and the Universe undergoes a quantum bounce rather than a singularity.Using an eective dynamics inspired by loop quantum cosmology and group eld theory, we showthat tensor modes are unavoidably produced at the bounce through non-adiabatic mode mixing.The resulting stochastic gravitational-wave background is non-inationary, ultraviolet nite, andlocalized in frequency, with a characteristic peak and oscillatory structure in the millihertz range.A decisive test of the model is provided by future space-based interferometers such as LISA.