Quantum cosmology and the evolution of inflationary spectra

We illustrate how it is possible to calculate the quantum gravitational effects on the spectra of primordial scalar/tensor perturbations starting from the canonical, Wheeler-De Witt, approach to quantum cosmology. The composite matter-gravity system is analyzed through a Born-Oppenheimer approach in which gravitation is associated with the heavy degrees of freedom and matter (here represented by a scalar field) with the light ones. Once the independent degrees of freedom are identified, the system is canonically quantized and a semiclassical approximation is used for the scale factor. The differential equation governing the dynamics of the primordial spectra with their quantum-gravitational corrections is then obtained and is applied to diverse inflationary evolutions. Finally, the analytical results are compared to observations through a Monte Carlo Markov chain technique and an estimate of the free parameters of our approach is finally presented and the results obtained are compared with previous ones.