Quantum cosmology and the evolution of inflationary spectra

Abstract

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. * Alexander.Kamenshchik@bo.infn.it † Alessandro.Tronconi@bo.infn.it ‡ Giovanni.Venturi@bo.infn.it

Construction of quantum Dirac observables and the emergence of WKB time

“…We have also analysed the connection between the relational view adopted in this paper with another popular approach to the "problem of time": the semiclassical emergence of "WKB time" [24,25,39,39,40,40,49]. This approach is relevant because many important phenomenological applications of quantum cosmology have been developed in this "semiclassical" framework [41][42][43][44][45][46][47][48]. Thus, it is worthwhile to understand its relation to the more complete quantum theory based on the physical Hilbert space and associated quantum Dirac observables.…”

“…Moreover, the explicit connection between this relational view and other approaches to the "problem of time" has remained unclear. In particular, a popular "solution" is the "semiclassical emergence of time": time only exists when the wave function(al) of the gravitational field is in a semiclassical regime (see [24,25,39,40] for a review and [41][42][43][44][45][46][47][48] for phenomenological applications). For this reason, this emergent semiclassical time is often referred to as "WKB time" [39,40,49].…”

The Born–Oppenheimer method, quantum gravity and matter

“…Coarse graining, corresponding to averaging over an oscillatory period for the gravitational wave function, leads to the introduction of time and evolution [19]. On then allowing φ a to have a small dependence on a and adding cosmological perturbations one may determine the power spectrum and obtain predictions for large scale structures from such an approach [32].…”

Quantum-Gravitational Effects on Primordial Power Spectra in Slow-Roll Inflationary Models

“…The issue in choosing the most appropriate reference scale is, however, still under debate and was also discussed in [15].…”