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. We review the derivation of these corrections, starting from a formalism designed to describe the cosmological perturbations in terms of gauge invariants without freezing the gauge degrees of freedom of the system. We show how a Born-Oppenheimer ansatz leads then to the recovery of a Mukhanov-Sasaki equation in which the coefficients are provided by expectation values on the background geometry. We also discuss technical tools and develop a procedure to deal with these quantum corrections beyond the most direct semiclassical approximation. The case of hybrid Loop Quantum Cosmology is commented in detail, but the presented treatment is general, and aims at increasing the ability to discriminate between the predictions of different quantization proposals for cosmological perturbations

Shapes of gravity. -- Nijmegen (Países Bajos). -- March 30- April 1, 2016. -- http://seangryb.wixsite.com/shapesofgravity.-- https://www.youtube.com/channel/UCgBXeTxD9yfBRvO8W-1wygg

Peer Reviewed