[Paper Review] Towards a Solution of the Cosmological Domain Walls Problem

Zygmunt Lalak|ArXiv.org|Feb 23, 1997

Advanced Mathematical Theories and Applications3 citations

TL;DR

This paper proposes that biased cosmological phase transitions generate compact, finite domain wall networks that decay exponentially fast due to intrinsic instability, offering a solution to the cosmological domain wall problem. The authors show that even symmetric initial conditions become unstable due to background fluctuations, and wall lifetimes depend on potential parameters—challenging the standard assumption of robustness.

ABSTRACT

We show that all kinds of biasing of cosmological phase transitions produce qualitatively new type of domain wall networks. The biased networks consist of compact, finite size, bag-like wall structures and exhibit a generic instability. The surface of biased networks disappears exponentially fast after a limited period of scaling. We argue that fluctuations of the background make the network unstable even in the case of the ``symmetric on the average'' initial distribution. We observe that the variation in parameters of the potential, like its hight, can influence the lifetime of the wall network, contrary to the standard beliefs.

Motivation & Objective

• Address the cosmological domain wall problem, where stable domain walls overclose the universe.
• Investigate how biasing phase transitions alters domain wall network dynamics.
• Explore whether compact, finite-sized wall structures can avoid long-term cosmological consequences.
• Examine the role of background fluctuations in destabilizing otherwise symmetric wall networks.
• Challenge the conventional belief that wall lifetimes are independent of potential parameters.

Proposed method

• Model cosmological phase transitions with explicit biasing in the scalar potential.
• Simulate the formation of domain wall networks under biased conditions using field theory techniques.
• Analyze the network's evolution through scaling dynamics and surface energy loss.
• Identify exponential decay of the wall surface area as the key instability mechanism.
• Use fluctuation analysis to assess stability under symmetric initial distributions.
• Vary potential parameters such as height to study their influence on wall network lifetime.

Experimental results

Research questions

• RQ1 Can biased phase transitions produce compact, finite-sized domain wall structures instead of infinite networks?
• RQ2 What is the dynamical fate of biased domain wall networks—do they decay, and if so, how quickly?
• RQ3 How do background fluctuations affect the stability of domain wall networks even when initial conditions are symmetric on average?
• RQ4 To what extent does the lifetime of a domain wall network depend on the parameters of the scalar potential?
• RQ5 Can the standard assumption of potential-independent wall lifetimes be invalidated by biasing effects?

Key findings

• Biased phase transitions generate compact, bag-like domain wall structures rather than infinite networks.
• The surface area of biased domain wall networks decays exponentially over time, leading to rapid disappearance.
• Even with symmetric initial conditions, fluctuations in the background induce instability and network decay.
• The lifetime of the domain wall network is sensitive to variations in the potential's height, contradicting the standard belief of independence.
• The instability mechanism is generic and does not require fine-tuning of initial conditions.
• The results suggest a viable solution to the cosmological domain wall problem through natural decay of wall networks.