• cosmic renormalization group flow
• cosmology
• fakeons
• inflation
• microcausality violation
• quantum gravity
• scalar perturbations
• Starobinsky potential
• tensor pertubations
• \phi^2 potential

The aim of the thesis is to compute the predictions of a recently proposed theory of quantum gravity within the framework of inflationary cosmology.

The framework of Quantum Field Theory (QFT) provides a powerful description for most natural phenomena. Nevertheless, the issues related to the quantization of gravity still threaten the understanding of many other. Indeed, the quantization of General Relativity (GR) is plagued by tedious infinities: a non-renormalizable QFT cannot be predictive for all the energy scales. Many higher-derivative extensions of GR have been proposed in the context of the Effective Field Theory (EFT) approach, in order to make testable predictions. Anyway, the quest for a fundamental theory of quantum gravity (QG) still remains open. Recently, a new higher-derivative theory of QG has been proposed. The theory heavily relies on the concept of "purely virtual quantum" (or "fakeon"): a particle that can only propagate inside the Feynman diagrams of the theory but cannot appear as an asymptotic state. A good arena for the discussion (and, hopefully, the detection) of the quantum effects generated by these particles is provided by primordial cosmology. For instance, the present CMB anisotropies are produced by the quantum fluctuations originated during inflation.

In the thesis, we compute the tensor and scalar power spectra of some specific single-field slow-roll models. The results are derived by using a new formalism, whose structure closely resembles the mathematical formalism of the Renormalization Group (RG): the cosmic renormalization group}.
The first result of the thesis consists in deriving the predictions of the Starobinsky potential V(\phi)=\frac{m_{\phi}^2}{2\hat{\kappa}^2}(1-e^{\hat{k}\phi})^2 by using an alternative renormalization scheme (the so called geometric framework). In particular, we compare the results with those already derived in the literature, which were computed in a different scheme (the inflaton framework) and show that the physical results are scheme independent. Furthermore, we enlighten the similarities between the high-energy physics RG flow and the cosmic one.
The second part of the thesis is devoted to the study of the quadratic potential V(\phi)=\frac{m_{\phi}^2\phi^2}{2}. This model contains several non-trivial features due to the appearance of singularities in the de Sitter limit. In particular, we derive the tensor and scalar power spectra in the limit of infinitely heavy fakeon (Weyl squared term suppressed). Then we derive the tensor power spectrum in the presence of the Weyl squared term (fakeon of finite mass) and study the conditions under which it makes sense. We uncover that the fakeon projection prevents a smooth de Sitter limit. This unusual feature makes the fakeon decoupling limit singular: we are unable to retrieve the results of the "fakeon-free" theory by performing the heavy fakeon limit. Moreover, we explain this unusual feature in terms of the causality violation, which is introduced by the purely virtual particles. Finally, we discuss the phenomenological implications provided by this specific slow-roll model by making a comparison with the experimental data.