A mechanism for formation of Bose-Einstein condensation in cosmology (1908.08784v2)

Abstract: We introduce a toy model of scalar particles with a trilinear scalar coupling in cosmology. The trilinear coupling $\phi^2\chi$ causes production of non-relativistic $\phi$ particles through the process $\chi\chi\,\rightarrow\,\phi\phi$ where, initially, only relativistic $\chi$ particles are present. We consider the initial times of $\chi\chi\,\rightarrow\,\phi\phi$ and observe that the curved space effects promote formation of Bose-Einstein condensate of $\phi$ particles.

• The paper introduces a scalar field model with a trilinear coupling that drives non-relativistic particle production essential for BEC formation in curved spacetime.
• The research quantifies how microscopic interactions, enhanced by cosmological metrics, accelerate the onset of Bose-Einstein condensation.
• The study establishes specific preconditions and dynamic criteria that bridge quantum field theory applications and cosmological observations.

Overview of a Mechanism for Bose-Einstein Condensation Formation in Cosmology

The paper by Erdem and Gültekin presents a novel model for understanding the initial phase of Bose-Einstein condensation (BEC) formation in the context of cosmology, characterized by scalar particle interactions and cosmological metrics. The paper tackles a significant gap in existing literature by concentrating on the microscopic particle physics mechanisms that can lead to BEC in a cosmological setting, especially under influences of curved spacetime.

Model Description

The authors introduce a scalar field model with a trilinear coupling $\phi \chi$, allowing the process $\chi\chi \rightarrow \phi\phi$ to produce non-relativistic $\phi$ particles from initially relativistic $\chi$ particles. This interaction, set against the backdrop of a Robertson-Walker metric, investigates the dynamics of BEC with scalar fields minimally coupled to gravity. The model dismisses additional complexities by assuming a flat universe ($k=0$), aligning with empirical cosmological observations.

Key Contributions and Results

1. Microscopic Framework: The paper emphasizes the microscopic interactions of particles leading to BEC, a perspective often overlooked in favor of macroscopic descriptions. The $\phi \chi$ interaction term in the Lagrangian provides the needed dynamics for $\phi$ particle production under the examined conditions.
2. Curved Space Effects: The research highlights that curved space accelerates BEC formation by affecting the $\chi\chi \rightarrow \phi\phi$ interactions, distinguishing it from studies that focus solely on flat spacetime decay processes. This insight is pivotal, as it reveals how relativistic considerations can facilitate BEC formation.
3. Conditions for Condensation: The paper establishes several preconditions necessary for BEC formation, including coherence and long-range correlation of particles, achieved through the overlap of de Broglie wavelengths in curved space. It scrutinizes the cross-sections and dynamics under cosmological expansion to ensure high enough production rates for $\phi$ particles despite the universe's expansion.
4. Quantitative Analysis: The model employs conditions ensuring that the variations in effective mass and coupling constants are minimal so as to approximate an effective Minkowski spacetime in relevant time intervals, allowing the use of established quantum field theory methods for rate and cross-section calculations.

Implications and Future Research Directions

The implications span both theoretical and pragmatic realms of cosmology:

• Theoretical: The paper provides a new perspective on how non-relativistic quantum field theories can approximate BEC conditions in a relativistic setting, possibly extending its usage to other scalar field theories in cosmology.
• Practical: Insights derived from this model may assist in developing cosmological simulations where dark matter behaves analogously to a BEC, potentially solving existing anomalies within the $\Lambda$CDM framework.

For future research, the authors suggest a more comprehensive investigation into the role of Bose-Einstein statistics in later stages of condensation formation, as well as the potential for induced $\phi\phi \rightarrow \phi\phi$ processes via the same trilinear coupling. Such studies could further elucidate the thermodynamic characteristics of BECs formed under cosmological influences and contribute to resolving outstanding issues in cosmic microwave background observations and galactic mass distributions.

In conclusion, Erdem and Gültekin's research provides a substantive basis for evaluating the formation of BECs in a cosmological context, offering a route to enrich both theoretical and empirical understandings in modern cosmology.