[Paper Review] Stability of domain walls with inflationary fluctuations under potential bias, and gravitational wave signatures

Naoya Kitajima, Junseok Lee+2 more|arXiv (Cornell University)|Nov 24, 2023

Astrophysics and Star Formation Studies9 citations

TL;DR

The paper analyzes how domain-wall networks with inflationary fluctuations respond to a potential bias, finding a longer lifetime than thermal cases, and computes the associated gravitational-wave spectra, highlighting a dependence on an area parameter.

ABSTRACT

A recent study has shown that domain walls with inflationary initial fluctuations exhibit remarkable stability against population bias due to long-range correlations, challenging the claims of prior research. In this paper, we study the dynamics of these domain walls in the presence of potential bias and show that they collapse with a lifetime several times longer than that due to thermal fluctuations. This is interpreted as a difference in the average distance between domain walls, leading us to derive a new formula for the domain wall lifetime which depends on the area parameter in a qualitatively different way from previous studies. In addition, we compute the spectrum of gravitational waves generated by such domain walls and find that both the peak frequency and the peak abundance are lowered in a manner that depends on the area parameter. Based on these findings, we also determine the necessary degree of vacuum degeneracy for axion domain walls to explain the isotropic cosmic birefringence.

Motivation & Objective

• Assess how potential bias destabilizes domain-wall networks with inflationary fluctuations.
• Quantify domain-wall lifetimes under bias and compare to thermal/white-noise initial conditions.
• Compute gravitational-wave spectra from collapsing domain-wall networks under different initial fluctuations.
• Identify how the area parameter governs differences between inflationary and thermal initial conditions.
• Constrain axion-like models for cosmic birefringence via domain-wall dynamics.

Proposed method

• Use a real scalar Z2-type potential V(φ) with an explicit symmetry-breaking linear term δV(φ) = -ε λ v^3 φ.
• Numerically solve the 2D domain-wall dynamics from τ_i = 1/m0 on a large lattice (N_grid^2 = 8192^2 or 16384^2).
• Compare two initial-condition ensembles: white-noise (thermal) and scale-invariant (inflationary) fluctuations.
• Characterize wall evolution via the volume fraction of false vacuum r_V and the area parameter A2 = L_DW H^{-1}, noting A3 versus A2 as appropriate for dimensionality.
• Fit r_V(t) to an exponential-like decay form r_V ∝ exp[-((τ−τ′)/τ_decay)^2] to extract lifetimes.
• Analyze how potential bias ε modifies wall dynamics and lifetimes relative to ε=0 ( unbiased case).
• Discuss implications for gravitational-wave spectra and constraints on vacuum degeneracy in axion-domain-wall scenarios.

Experimental results

Research questions

• RQ1 How does a potential bias affect the stability and collapse timescale of domain-wall networks with inflationary fluctuations?
• RQ2 How do lifetimes under potential bias compare between inflationary-fluctuation initial conditions and white-noise initial conditions?
• RQ3 What is the impact of domain-wall dynamics on the gravitational-wave spectrum, and how does it depend on the area parameter?
• RQ4 Can axion-like models with domain walls account for isotropic cosmic birefringence given the bias-induced evolution?
• RQ5 How does the area parameter govern differences between inflationary and thermal initial conditions in the scaling regime?

Key findings

• Domain-wall networks with inflationary fluctuations decay under potential bias with lifetimes several times longer than those driven by thermal fluctuations.
• The longer lifetimes are linked to differences in the average distance between domain walls, captured by an area-parameter–based description.
• The volume fraction of the false vacuum r_V decays monotonically under bias and can be fitted by r_V ∝ exp[-((τ−τ′)/τ_decay)^2].
• The area parameter A2 shows distinct behavior depending on initial conditions: it remains order one under unbiased scaling, but increases with bias for inflationary fluctuations due to outward expansion of true-vacuum regions.
• The gravitational-wave spectrum from domain-wall dynamics shifts: both the peak frequency and the peak abundance decrease, in a manner that depends on the area parameter.
• An upper limit on the energy difference between adjacent vacua is deduced to accommodate isotropic cosmic birefringence within axion-domain-wall scenarios.