Quantum Effects in Cosmology: Unveiling the Quantum Nature of the Primordial Fluctuations

It is commonly accepted in cosmology that a period of inflation took place in the Early Universe. This period of accelerated expansion provides the seeds for structure formation through vacuum fluctuations of the inflaton scalar field. These fluctuations get stretched by the quasi-exponential expansion of the Universe and become squeezed. The generation of perturbations out of the vacuum is a purely quantum phenomenon, however the Cosmological Microwave Background (CMB) measurements are analyzed within a classical framework, via ensemble averages of temperature anisotropies. Indeed, the two-point correlation functions of a squeezed Gaussian state can be obtained even with a classical stochastic description. Therefore the question of whether these fluctuations are really quantum mechanical or classical thermal fluctu- ations arises. In this thesis, we explore the quantum effects in cosmology, focusing on the understanding of the quantum nature of the primordial fluctuations. We start with an overview of Big Bang cosmology and inflation. The work then delves into cosmological perturbation theory. Additionally, we interpret the amplification of the fluctuations in terms of cosmological particle creation, em- ploying Bogoliubov transformations and the squeezing parameters to describe the dynamics of the system in an expanding Universe. We show how pairs of particles with opposite momenta are generated. The physical meaning and the geometrical interpretation of the squeezing parameters is provided. The thesis then examines several criteria which can be used to test the “quantumness” of the inflationary perturbations, such as non-separability and quantum discord. After reviewing these criteria, the thesis focuses on the vi- olation of Bell-like inequalities, which have been computed in the context of inflationary perturbations. My work contributes to the investigation of the ori- gin of the cosmological perturbations by addressing the problem of the ob- servability of the quantum features in a Bell type experiment on the Cosmic Microwave Background (CMB). In order to overcome some difficulties linked to the feasibility of such an experiment, the Leggett-Garg inequalities are stud- ied. The Leggett-Garg inequalities give the correlations between the spin of the same system but measured at different times and they are computed for the cosmological perturbations. Going beyond the Gaussian states description and introducing interactions, the quantum nature of the perturbations can be further tested by measuring the bispectrum, i.e. the three-point function. Indeed, the absence of poles in the bispectrum is shown to be an undeniable proof of the quantum mechan- ical mechanism generating the fluctuations. This work specifically takes into account the bispectrum of tensor perturbations generated during a de Sitter phase of inflation. The bispectrum computed considering the fluctuations to be quantum mechanical is compared with the classical three-point correlation function in order to find a difference between the two approaches. The study performed in this thesis then extends to the treatment of axion perturbations, exploring their quantum mechanical description and evolution. Axions (or axion-like particles) are good candidates to test the quantumness of the perturbations, since they are produced via misalignment mechanism, possibly avoiding decoherence effects during the reheating phase after infla- tion. Moreover they naturally encode self-interactions thanks to their cosine potential. The consequences that a non-trivial evolution of the background ax- ion field has on the squeezing of the perturbations are studied in details. This is the first step towards the analysis of the full bispectrum for the axion field, which could potentially provide a way to access the information on the quan- tumness of the perturbations. Therefore, this thesis naturally aligns with the research programme of the quantum effects in cosmology.