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.

42 pages, 4 figures

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• The Born-Oppenheimer Method, Quantum Gravity and Matter
• Observations in Quantum Cosmology
• Gravitational-wave background in bouncing models from semi-classical, quantum and string gravity
• Quantum Cosmology and the Inflationary Spectra from a Non-Minimally Coupled Inflaton
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity
• Induced Gravity and Quantum Cosmology
• Beyond semiclassical time
• Non-standard hierarchies of the runnings of the spectral index in inflation
• Analyzing the influence of graviton fluctuations on the inflationary spectrum with a Kuchař-Torre clock
• Phenomenological inflationary model in Supersymmetric Quantum Cosmology
• Reflected Waves and Quantum Gravity