Primordial Gravitational Waves from a Quantum Bounce with Emergent Time

We investigate the production of primordial gravitational waves in a cosmological framework
where time is not a fundamental variable. At Planckian energy density, the classical notion of time
ceases 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 show
that tensor modes are unavoidably produced at the bounce through non-adiabatic mode mixing.
The resulting stochastic gravitational-wave background is non-inationary, ultraviolet nite, and
localized 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.