Cosmological production of dark matter in the Universe and in the laboratory

TL;DR

This work analyzes cosmological particle production within Quantum Field Theory in Curved Spacetimes, highlighting its potential as a dark matter production mechanism and its realizability in laboratory analogs using Bose-Einstein condensates. It develops a comprehensive QFTCS framework for scalar and vector spectator fields in inflationary backgrounds, including vacuum choices, mode dynamics, power spectra, and entanglement, while also exploring de Sitter-like limits and curvature effects. The study demonstrates that analog gravity experiments with BECs can reconstruct cosmological expansion histories from fluctuation spectra and reinterpret production as a one-dimensional scattering problem, enabling controlled exploration of non-adiabatic transitions and vacuum ambiguities. Overall, the results indicate cosmological particle production as a viable dark matter mechanism under certain couplings and mass ranges, and showcase the power of analog simulations to illuminate quantum effects in curved spacetimes and early-Universe physics.

Abstract

This thesis investigates cosmological particle production within Quantum Field Theory in Curved Spacetimes, both as a dark matter mechanism and through analog simulations using Bose-Einstein condensates. While a full theory of Quantum Gravity remains elusive, studying quantum fields on curved backgrounds provides essential insights into the early Universe. We focus on how dynamical spacetimes, particularly during inflation, generate particles from spectator fields influenced solely by geometry. The work is divided into four parts. Part I establishes the theoretical framework, covering cosmology, inflation, and the principles of analog gravity. Part II analyzes particle production in various inflationary models, showing that scalar and vector fields can account for observed dark matter abundance, especially through tachyonic instabilities. Part III explores BEC experiments, mapping phonons to scalar fields in expanding universes. We demonstrate the reconstruction of expansion histories, reinterpret production as a scattering problem, and propose methods to measure entanglement between produced pairs. Finally, Part IV addresses quantum vacuum ambiguities and the impact of non-adiabatic transitions during the "switch-on" and "switch-off" of expansion. Ultimately, this work highlights the viability of cosmological particle production for dark matter and the power of analog experiments to enhance our understanding of quantum effects in curved spacetimes.

Figures (61)

• Figure 1: Inflaton field $\phi(\eta)$ (upper-left panel), curvature scalar $R(\eta)$ (upper-right panel), and components of the traceless Ricci tensor (bottom row), as functions of conformal time. The range of time corresponds to the end of inflation and the beginning of reheating. The parameters used for all figures in this chapter are given in \ref{['sec:param.sf']}. Figure from VectorDM2024.
• Figure 2: Ricci scalar during the transition from inflation to reheating for the quadratic (blue) and the Starobinsky (red) potential, as a function of cosmological time.
• Figure 3: Maximum of the errors squared as a function of the wavenumber $k$ and the field mass $m$, for $\xi=0.2$ (left) and $\xi=0.8$ (right). We take $\eta_*=-500m_{\phi}$ for all values of $k$, $m$ and $\xi$. Figure from ScalarField2023.
• Figure 4: Maximum of the errors squared times $k^2$ as a function of the wavenumber $k$ and the field mass $m$, for $\xi=0.2$ (left) and $\xi=0.8$ (right). We take $\eta_*=-500m_{\phi}$ for all values of $k$, $m$ and $\xi$. Figure from ScalarField2023.
• Figure 5: Relative error in the absolute value (left panel) and the phase (right panel) of the numerical solution to the exact mode equation \ref{['eq:qftcs.ModeEquation']} compared to the analytical approximation \ref{['eq:sf.ApproximateSRSolution']}, for wavenumbers ranging from $k=0.01m_{\phi}$ to $k=100 m_{\phi}$, and $m=m_{\phi}, \xi=0.5$. Here, we take $\eta_{\text{dS}} = -1000/m_{\phi}$ and $\eta_* = -500/m_{\phi}$. Figure from ScalarField2023.