[Paper Review] Time- and Space-Varying Neutrino Mass Matrix from Soft Topological Defects

Gia Dvali, Lena Funcke+1 more|arXiv (Cornell University)|Dec 3, 2021

Neutrino Physics Research4 citations

TL;DR

This paper proposes that time- and space-varying neutrino mass matrices arise from soft, gravity-induced topological defects—such as skyrmions, monopoles, strings, and domain walls—formed during a late-time phase transition in the post-recombination universe. The defects emerge due to spontaneous breaking of neutrino flavor symmetry via a gravitational vacuum susceptibility, with observable signatures in future neutrino experiments that could distinguish between Dirac and Majorana neutrino nature.

ABSTRACT

We study the formation and evolution of topological defects that arise in the post-recombination phase transition predicted by the gravitational neutrino mass model in [Dvali, Funcke, Phys. Rev. D 93, 113002 (2016)]. In the transition, global skyrmions, monopoles, strings, and domain walls form due to the spontaneous breaking of the neutrino flavor symmetry. These defects are unique in their softness and origin; as they appear at a very low energy scale, they only require Standard Model particle content, and they differ fundamentally depending on the Majorana or Dirac nature of the neutrinos. One of the observational signatures is the time dependence and space dependence of the neutrino mass matrix, which could be observable in future neutrino experiments. Already existing data rule out parts of the parameter space in the Majorana case. The detection of this effect could shed light onto the open question of the Dirac versus Majorana neutrino nature.

Motivation & Objective

• To investigate the formation and evolution of topological defects arising from spontaneous breaking of neutrino flavor symmetry in a low-energy gravitational neutrino mass model.
• To determine how the nature of neutrinos (Dirac vs. Majorana) affects the type and stability of resulting defects such as domain walls and strings.
• To explore observational signatures of time- and space-dependent neutrino mass matrices from these defects in future neutrino and cosmological experiments.
• To assess the viability of the model by analyzing constraints from existing data, particularly on domain wall and monopole densities.
• To examine the role of axionic domain walls and their annihilation in contributing to dark radiation or dark matter, depending on the phase transition dynamics.

Proposed method

• Modeling the phase transition using a gravitational vacuum susceptibility condition, ⟨R̃R,R̃R⟩q→0 ≠ 0, which implies a physical θG-term in gravity and triggers fermion condensation.
• Applying the Kibble mechanism to describe the formation of topological defects (skyrmions, monopoles, strings, domain walls) during spontaneous flavor symmetry breaking.
• Using effective field theory to describe the neutrino condensate ⟨ν̄ν⟩ and its coupling to the Higgs-like composite field Φ, leading to effective neutrino masses mν ∼ ΛG.
• Calculating defect energy densities and tensions: ρSW(t) ∼ σW t⁻¹ ∼ ΛG³ t⁻¹ for domain wall networks, with σW ∼ ΛG³ / NF for domain walls.
• Analyzing the dynamics of axionic domain walls (DWs) that do not interact with ambient matter, leading to efficient annihilation and dark radiation production.
• Evaluating the impact of non-topological DWs with pressure differences δp ∼ mν ≤ 0.8 eV and viscosity η from φk boson scattering, determining annihilation rates.

Experimental results

Research questions

• RQ1 How do soft topological defects form in the late universe due to spontaneous breaking of neutrino flavor symmetry?
• RQ2 What is the dependence of defect types (skyrmions, monopoles, strings, domain walls) on whether neutrinos are Dirac or Majorana fermions?
• RQ3 How do time- and space-varying neutrino mass matrices arise from these defects, and what are their observable signatures?
• RQ4 What constraints do existing data place on the parameter space of the model, especially in the Majorana case?
• RQ5 How do axionic domain walls and their annihilation contribute to dark radiation or dark matter, and how does this depend on the phase transition type (first- vs. second-order)?

Key findings

• Topological defects such as skyrmions, monopoles, strings, and domain walls form via the Kibble mechanism during a late-time phase transition triggered by gravitational vacuum susceptibility.
• The energy density of the domain wall–string network scales as ρSW(t) ∼ ΛG³ t⁻¹, with O(10) domain walls per Hubble volume, consistent with cosmological constraints.
• Axionic domain walls annihilate efficiently due to lack of friction, producing dark radiation from decay of ην bosons into φk bosons.
• The model predicts observable time- and space-dependent neutrino mass matrices, which could distinguish between Dirac and Majorana neutrino nature in future experiments.
• Existing data already rule out parts of the parameter space in the Majorana case, particularly constraining domain wall and monopole abundances.
• Non-topological domain walls with pressure differences δp ≤ 0.8 eV and low viscosity from φk scattering rapidly annihilate, diluting any long-lived network.