Fermionic Backreaction on Quantum Spacetimes: Cosmological Implications
This article reviews a Hamiltonian framework for describing Dirac fermions propagating on quantum cosmological spacetimes within loop quantum cosmology. Expanding the fermionic field in spinor harmonics on a closed Friedmann--Lema\^itre--Robertson--Walker background reduces the dynamics to a collection of time-dependent Fermi oscillators, providing a Schr\"odinger-picture description of fermionic perturbations on a quantum geometry. We discuss the emergence of dressed metrics in the test-field approximation, showing that massive fermions probe both temporal and spatial quantum-geometry corrections, whereas massless fermions, owing to conformal invariance, are affected only through a reparametrization of time. We further review the incorporation of fermionic backreaction within a Born--Oppenheimer framework, where the finite-dimensional Hilbert space of each fermionic mode gives rise to two distinct backreaction channels that naturally generate mode-dependent dressed (rainbow) metrics. Finally, we discuss the cosmological implications of fermionic backreaction, including state-dependent modifications of the quantum bounce and the emergence of an effective cosmological constant in the semiclassical regime. These results highlight the distinctive role of fermionic matter in loop quantum cosmology and outline open directions for understanding quantum fields on quantum spacetimes.