Probing quantum gravity using precision primordial cosmology

In this talk we present recent advances in computing precise analytical predictions in the context of cosmic inflation. We develop a systematic framework to calculate the primordial power spectrum up to next-to-next-to-next to leading order (N3LO) in Hubble-flow parameters, applicable to a broad class of effective theories of inflation. For the specific case of Starobinsky inflation in the geometric frame, we find the N3LO corrections lead to a significant 7% reduction in the tensor-to-scalar ratio with respect to its standard expression at N_* = 55, along with deviations from the consistency relation and a negative running of the scalar tilt. Using this framework, we also explored primordial features in the power spectrum induced by the squeezing of the quasi-Bunch-Davies vacuum, which may encode information about a quantum gravity phase before inflation, as P_sqz (k) = |α-β e^iδ_k|² P_qBD (k). We found that the relative phase δ_k is fully determined by the background dynamics and computed the explicit expressions in the case of Starobinsky inflation, where δ_k ~ (π/2) (n_s-1). These results provide precise theoretical predictions for upcoming CMB observations that will be crucial to probe the physics of inflation and beyond.