[Paper Review] Boson Stars with Self-Interacting Quantum Scalar Fields

Jeongwon Ho, F. C. Khanna+1 more|ArXiv.org|Jul 18, 2002

Astro and Planetary Science1 references3 citations

TL;DR

This paper demonstrates that quantum real scalar fields can form stable, non-oscillating (static) boson stars—similar to those formed from complex scalar fields—via quantum effects that modify self-interaction strengths. Unlike classical real scalar fields, which form oscillating solitons unstable over cosmological timescales, quantum real scalar fields support static mini-boson stars with masses comparable to those from complex fields, especially when self-interactions are included. The key result is that quantum effects enable real scalar fields to be viable dark matter candidates, and phase transitions in the early universe do not destroy these configurations.

ABSTRACT

The Klein-Gordon-Einstein equations of classical real scalar fields have time-dependent solutions (periodic in time). We show that quantum real scalar fields can form non-oscillating (static) solitonic objects, which are quite similar to the solutions describing boson stars formed with classical and quantum complex scalar fields (the latter will be studied in this paper). We numerically analyze the difference between them concerning the mass of boson stars. On the other hand, we suggest an interesting test (a viable process that the boson star may undergo in the early universe) for the formation of boson stars. That is, it is questioned that after a second-order phase transition (a simple toy model will be considered here), what is the fate of the boson star composed of quantum real scalar field.

Motivation & Objective

• To investigate whether quantum real scalar fields can form stable, non-oscillating solitonic objects (boson stars) under gravity.
• To compare the mass and structure of boson stars formed from quantum real scalar fields with those from classical and quantum complex scalar fields.
• To analyze the impact of a second-order phase transition on the stability and properties of quantum real scalar field boson stars.
• To test the viability of quantum real scalar fields as dark matter candidates by examining their formation and survival in early-universe cosmological scenarios.

Proposed method

• Formulate a self-interacting quantum real scalar field Lagrangian coupled to gravity, using the semi-classical and Hartree (mean-field) approximations.
• Derive the Klein-Gordon-Einstein (KGE) equations for the quantum real scalar field and reduce them to time-independent equations by eliminating time-dependent parts.
• Numerically solve the resulting equations to construct static solitonic solutions (boson stars) and compute their mass-radius relations.
• Introduce a toy model for a second-order phase transition that modifies the scalar field mass and self-interaction strength, then re-solve the equations to assess post-transition stability.
• Compare the effective self-interaction coefficients in the KGE equations across classical complex, quantum complex, and quantum real scalar field cases.
• Use numerical simulations to verify the existence and stability of static boson star solutions under varying interaction strengths and phase transition conditions.

Experimental results

Research questions

• RQ1 Can quantum real scalar fields form stable, non-oscillating boson stars under gravity, similar to those formed from complex scalar fields?
• RQ2 How does the self-interaction strength in the effective KGE equations differ between classical complex, quantum complex, and quantum real scalar fields?
• RQ3 What is the maximum mass of boson stars formed from quantum real scalar fields, and how does it compare to those from classical or quantum complex fields?
• RQ4 How does a second-order phase transition in the early universe affect the existence and properties of quantum real scalar field boson stars?
• RQ5 Can quantum real scalar fields serve as a viable dark matter candidate, given their ability to form stable, compact, static objects?

Key findings

• Quantum real scalar fields can form stable, non-oscillating (static) solitonic objects—boson stars—via quantum effects that modify the effective self-interaction strength.
• The maximum mass of boson stars formed from quantum real scalar fields is enhanced compared to non-interacting cases and is comparable to those from quantum complex scalar fields, due to increased effective interaction terms.
• The effective self-interaction coefficient in the KGE equations for quantum real scalar fields is 3Λ/4, which is larger than the classical complex field case (Λ/2), leading to greater stability and higher maximum masses.
• Numerical results confirm that the maximum mass of boson stars increases with the magnitude of the effective self-interaction coefficient, as predicted by the effective interaction energy argument.
• After a second-order phase transition modeled by an effective mass increase (m → √2m) and reduced self-interaction (Λ → Λ/2), stable boson stars still exist, indicating their robustness in early-universe conditions.
• Quantum real scalar fields can form static mini-boson stars even without self-interaction (Λ = 0), making them identical to those formed from classical and quantum complex scalar fields, thus restoring their viability as dark matter candidates.