[Paper Review] How scalar-field dark matter may conspire to facilitate baryogenesis at the electroweak scale

Tanja Rindler-Daller, Bohua Li+3 more|arXiv (Cornell University)|Oct 28, 2015

Dark Matter and Cosmic Phenomena1 references3 citations

TL;DR

This paper proposes that scalar-field dark matter (SFDM) with a complex, ultralight bosonic field can induce a stiff equation of state in the early Universe, enhancing the expansion rate. This modified cosmology weakens the sphaleron washout condition, enabling a strong first-order electroweak phase transition despite the measured 125 GeV Higgs mass—offering a viable path to baryogenesis at the electroweak scale within a unified dark matter and baryogenesis framework.

ABSTRACT

The cosmic evolution of a dark matter model which behaves relativistically in the early Universe is explored. Dark matter is described as a complex scalar field, whose earliest evolution is characterized by a stiff equation of state ($p \simeq ρ$). In this phase, it is the dominant component in the Universe. We present constraints from Big Bang nucleosynthesis and primordial gravity waves from inflation. Also, we study how the associated enhanced expansion rate due to the stiff phase might facilitate a first-order electroweak symmetry breaking phase transition, in light of the recently measured value of the Higgs boson mass.

Motivation & Objective

• To address the long-standing problem of baryogenesis at the electroweak scale, which is hindered by the measured 125 GeV Higgs boson mass.
• To explore whether scalar-field dark matter (SFDM) with a complex, ultralight bosonic field can simultaneously resolve dark matter and baryon asymmetry problems.
• To investigate how SFDM’s early stiff phase (p ≈ ρ) increases the Hubble expansion rate, thereby weakening the sphaleron freeze-out condition.
• To assess the feasibility of a strong first-order electroweak phase transition in the Standard Model with a φ⁶ operator, under modified expansion histories due to SFDM.
• To constrain SFDM parameters using Big Bang nucleosynthesis and primordial gravitational wave signals from inflation.

Proposed method

• Modeling dark matter as a complex scalar field ψ with a U(1)-symmetric Lagrangian, including kinetic, mass, and repulsive self-interaction terms.
• Using the Lagrangian L = (ħ²/2m)g^{μν}∂_μψ*∂_νψ - (1/2)mc²|ψ|² - (λ/2)|ψ|⁴ to describe SFDM dynamics and equation of state evolution.
• Tracking the cosmic evolution of SFDM from early stiff phase (p ≈ ρ) to radiation-like (p ≈ ρ/3) and finally to cold dark matter (p ≈ 0) dominance.
• Calculating the Hubble expansion rate H(a) during the electroweak phase transition epoch, showing it to be 3–5 orders of magnitude higher than in ΛCDM due to SFDM's stiff phase.
• Evaluating the sphaleron freeze-out condition v/T ≥ 1.0, showing it is weakened to v/T ≥ 0.73 at Tₙ ≈ 70 GeV and v/T ≥ 0.55 at Tₙ ≈ 150 GeV under SFDM-enhanced expansion.
• Using a modified Higgs potential with a φ⁶ term suppressed by a cutoff scale Λ > 500 GeV to enable a first-order phase transition, and studying its viability under SFDM cosmology.

Experimental results

Research questions

• RQ1 Can scalar-field dark matter with a stiff early phase facilitate a strong first-order electroweak phase transition despite the 125 GeV Higgs boson mass?
• RQ2 How does the enhanced expansion rate from SFDM’s stiff phase affect the sphaleron washout condition required for baryogenesis?
• RQ3 What constraints does Big Bang nucleosynthesis and primordial gravitational waves place on the early evolution of SFDM?
• RQ4 To what extent does the inclusion of a φ⁶ term in the Higgs potential, combined with SFDM-induced expansion history, allow for a viable electroweak baryogenesis mechanism?
• RQ5 How do SFDM parameters such as mass m ≈ 10⁻²² eV/c² and coupling λ ≈ 10⁻⁶² eV cm³ affect the feasibility of electroweak phase transition and baryogenesis?

Key findings

• The stiff phase of scalar-field dark matter (SFDM) increases the Hubble expansion rate by 3–5 orders of magnitude during the electroweak phase transition, compared to standard ΛCDM cosmology.
• This enhanced expansion rate weakens the sphaleron freeze-out condition, reducing the required v/T ratio from ≥1.0 to ≥0.73 at Tₙ ≈ 70 GeV and ≥0.55 at Tₙ ≈ 150 GeV.
• The model remains consistent with Big Bang nucleosynthesis and primordial gravitational wave constraints, provided SFDM’s early evolution is properly tuned.
• The inclusion of a φ⁶ term in the Higgs potential with Λ ≳ 500 GeV allows for a first-order phase transition, and this becomes more feasible under SFDM-enhanced expansion.
• SFDM with m ≈ 10⁻²² eV/c² and λ ≈ 10⁻⁶² eV cm³ can reproduce cold dark matter behavior on large scales while suppressing small-scale structure formation via de Broglie wavelength or self-interaction pressure.
• The critical and nucleation temperatures of the electroweak phase transition are largely insensitive to the modified expansion history, but the effective strength of the transition is significantly enhanced due to weakened washout.