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

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.

💡 Research Summary

This dissertation investigates the production of particles from the vacuum in curved space‑time, focusing on its relevance as a dark‑matter generation mechanism and on its experimental realization using Bose‑Einstein condensates (BECs) as analog gravity systems. The work is divided into four parts.

Part I builds the theoretical foundation. It reviews quantum field theory on curved backgrounds (QFTCS), emphasizing the role of the time‑dependent scale factor a(t) in the mode equations and the associated Bogoliubov transformation that mixes positive‑ and negative‑frequency components. The author discusses the well‑known vacuum‑choice ambiguity, contrasting the adiabatic (WKB‑based) vacuum with an instantaneous vacuum defined at each moment, and explains how a non‑adiabatic evolution of a(t) inevitably leads to particle creation.

Part II applies this framework to inflationary cosmology. Various inflationary scenarios—slow‑roll, power‑law, hybrid—are examined with spectator scalar and vector fields that couple minimally or non‑minimally to curvature. When the effective mass squared becomes negative (tachyonic instability), mode amplitudes grow exponentially, yielding a particle number density that can match the observed dark‑matter abundance Ω_DM for a broad range of masses (from ultra‑light ≈10⁻²⁰ eV up to ≈10⁻⁶ eV). Vector fields are shown to generate both transverse and longitudinal modes, enlarging the viable parameter space compared with pure scalar candidates. The analysis identifies “sweet spots” in the (mass, coupling, inflation‑duration) space where the produced relic density equals the measured dark‑matter density.

Part III turns to laboratory analogues. The author designs a 1‑D BEC experiment in which the trapping frequency ω(t) is modulated in time to mimic an expanding Friedmann‑Robertson‑Walker universe. The effective scale factor for phonons scales as a_eff(t)∝ω⁻¹/₂(t), allowing direct control over the analogue Hubble rate. By shaping the “switch‑on” and “switch‑off” ramps (characterized by a time δ), the experiment reproduces the non‑adiabatic evolution that drives particle creation. Bogoliubov coefficients α_k and β_k are extracted via Bragg spectroscopy and time‑resolved density‑density correlations. Crucially, the thesis proposes a concrete protocol to measure entanglement between the produced phonon pairs: a combination of second‑order correlation functions g^{(2)}(x₁,x₂) and quantum state tomography provides an entanglement witness that can be quantified experimentally. Numerical simulations show that for realistic BEC parameters (atom number ~10⁵, trap size ~100 µm, modulation frequencies of a few Hz) the analogue particle spectrum reproduces the theoretical predictions, including the characteristic exponential amplification of tachyonic modes.

Part IV addresses subtle issues of vacuum definition and the impact of finite‑time switching. The author demonstrates that when the switch duration δ is much shorter than the inverse Hubble scale, the total particle number is essentially independent of δ, confirming the robustness of the production mechanism. However, if δ becomes comparable to the Hubble time, additional non‑adiabatic transitions populate high‑frequency modes, generating a UV tail in the spectrum. This effect is traced back to the residual ambiguity between adiabatic and instantaneous vacua and is shown to be experimentally observable as a slight modification of the high‑k tail in the phonon distribution.

Overall, the thesis establishes that cosmological particle production is a viable dark‑matter generation scenario and that BEC‑based analog experiments can faithfully reproduce and probe the underlying quantum processes. The work opens several avenues for future research: extending the analysis to multiple interacting spectator fields, exploring three‑dimensional condensates to simulate higher‑dimensional cosmologies, and improving entanglement‑measurement techniques to test quantum‑information aspects of early‑universe particle creation. The combination of rigorous theoretical modeling with concrete experimental proposals makes this study a significant contribution to both cosmology and quantum‑simulation communities.