MG15 - Talk detail

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In this work we investigate how one can define a quantum field theory with good ultraviolet properties for a perturbative inhomogeneous Dirac field in inflationary hybrid Loop Quantum Cosmology (LQC). Since the aim is to provide a quantum representation for the entire cosmological system, we exploit the possibility of considering different separations between the canonical variables that describe the homogeneous geometry and the fermionic perturbations. Each of such choices leads to a different fermionic contribution to the total Hamiltonian. After applying a kind of Born-Oppenheimer approximation in the Hamiltonian constraint equation, a quantum version of that contribution generates a Schrödinger dynamics (the inflaton being the time) for the fermionic part of the wavefunction. This quantum fermionic Hamiltonian contains, in particular, a backreaction term that measures how much the homogeneous part of the wavefunction departs from being an exact solution of the unperturbed inflationary system in LQC. By solving this Schrödinger equation, we are able to provide the necessary and sufficient conditions on the choice of fermionic variables that lead to an absolutely convergent backreaction.

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