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 analysed 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 quantised. The
differential equation governing the dynamics of the primordial spectra with its
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.
