# On the Quantum-to-Classical Transition of Primordial Perturbations

## TL;DR

This paper explores how quantum fluctuations in the early universe transition to classical inhomogeneities observed today, analyzing various formalisms and focusing on the pilot-wave approach to understand the quantum-to-classical transition.

## Contribution

It provides a detailed analysis of the quantum-to-classical transition of primordial perturbations, emphasizing the pilot-wave theory as a novel perspective.

## Key findings

- Pilot-wave trajectories illustrate the classical limit of quantum fluctuations.
- Squeezing and decoherence formalisms have limitations in explaining the transition.
- The pilot-wave approach offers a consistent framework for the quantum-to-classical transition.

## Abstract

Detailed measurements of the cosmic microwave background indicate the large-scale homogeneity of the universe. On very small scales, we observe however inhomogeneities such as galaxies, stars, planets and ourselves. In the context of hot Big-Bang cosmology, these inhomogeneities are often explained as the remains of quantum fluctuations at very early times, enlarged to observable scales through the process of inflation. In this dissertation, I examine two important questions surrounding this scenario: a) How do inherently quantal fluctuations transition to the observed inhomogeneities, which behave classically? ; and b) If the initial state of the universe was symmetric, how can the currently observed state? This dissertation is organized in three parts. Part one first introduces the slow-roll inflation model and then discusses the behavior of small (scalar) perturbations to this model. The second part investigates various answers provided to the questions above, starting with some general observations on the classical limit of quantum mechanics with special attention given to the inverted harmonic oscillator. The formalisms of `squeezing' and decoherence are discussed and weak points are pointed out. In the final part, I examine in detail the pilot-wave approach to the problem, discussing in detail the classical limit of the theory and how pilot-wave theory addresses both questions above. Numerical results for pilot-wave trajectories are presented, illustrating directly the classical limit.