Speaker: Mercedes Martin-Benito (IA Lisbon)
A lot of attention has been devoted lately to the consideration of quantum corrections to the power spectrum of primordial fluctuations, as a possible window to unveil quantum geometry phenomena in the Early Universe. In this talk I will review the derivation of these corrections in the framework of hybrid Loop Quantum Cosmology (LQC). Homogeneous LQC provides a canonical quantization for FLRW models free of singularities: the classical big bang singularity is replaced by a quantum bounce, the quantum dynamics is everywhere well-defined, and physical observables never diverge. On the other hand, hybrid LQC extends the LQC quantization to systems with inhomogeneities. For the particular case of cosmological perturbations in flat FLRW supplemented with inflation, I will analyze the quantum dynamics of states that verify a Born-Oppenheimer ansatz. They describe a regime where the cosmological perturbations can be regarded as a field propagating over a homogeneous quantum geometry. From those states, we will recover a Mukhanov-Sasaki equation for cosmological perturbations that incorporates the mentioned quantum corrections. Such corrections are encoded in the expectation value of operators of the homogeneous geometry. I will discuss how these corrections might lead to observational imprints in the primordial power spectra.