Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Role of Domain Walls in the Early Universe in the Context of Mode Matching

K. K. Venkataratnam

Abstract

We study the role of domain walls and their relics in the very early Universe within the framework of the mode-matching technique. Domain walls formed during the spontaneous breaking of discrete symmetries are modelled as a short lived contribution to the background energy density, leading to a controlled deviation from standard slow-roll inflation. Solving the modified Friedmann equation, we obtain a smooth, time-dependent Hubble parameter that asymptotically approaches the standard inflationary value. We analyze the evolution of scalar perturbations using the gauge-invariant Mukhanov variable and perform mode matching across the transition between the domain wall affected phase and standard inflation. We find that only modes exiting the horizon near the transition experience a modified evolution, while modes far from the transition remain unaffected. As a result, the primordial scalar power spectrum exhibits localized, scale-dependent deviations from scale invariance, while preserving the overall success of inflation. These results demonstrate that unstable domain-wall relics can leave subtle imprints on primordial fluctuations, potentially providing a probe of early-Universe phase transitions.

Role of Domain Walls in the Early Universe in the Context of Mode Matching

Abstract

We study the role of domain walls and their relics in the very early Universe within the framework of the mode-matching technique. Domain walls formed during the spontaneous breaking of discrete symmetries are modelled as a short lived contribution to the background energy density, leading to a controlled deviation from standard slow-roll inflation. Solving the modified Friedmann equation, we obtain a smooth, time-dependent Hubble parameter that asymptotically approaches the standard inflationary value. We analyze the evolution of scalar perturbations using the gauge-invariant Mukhanov variable and perform mode matching across the transition between the domain wall affected phase and standard inflation. We find that only modes exiting the horizon near the transition experience a modified evolution, while modes far from the transition remain unaffected. As a result, the primordial scalar power spectrum exhibits localized, scale-dependent deviations from scale invariance, while preserving the overall success of inflation. These results demonstrate that unstable domain-wall relics can leave subtle imprints on primordial fluctuations, potentially providing a probe of early-Universe phase transitions.
Paper Structure (11 sections, 22 equations, 3 figures)

This paper contains 11 sections, 22 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Domain Wall Dynamics in an Expanding Universe
  3. Formation of domain walls from discrete symmetry breaking
  4. Field-theoretic realization and wall properties
  5. Cosmological evolution and equation of state
  6. Domain Walls and Inflationary Background Evolution
  7. Motivation for mode matching
  8. Scalar Perturbations and Mode Matching in the Presence of Domain Walls
  9. Primordial Power Spectrum and Domain-Wall Signatures
  10. Discussion and Conclusions
  11. Acknowledgments

Figures (3)

  • Figure 1: Evolution of the Hubble parameter in the presence of a transient domain-wall contribution. The deviation from constant $H_0$ is localized around the matching time, after which standard slow-roll inflation is recovered.
  • Figure 2: Time evolution of the Mukhanov variable $|Q_k|$ for representative modes. Modes exiting the horizon near the matching time exhibit deviations due to the domain-wall phase, while modes far from the transition remain unaffected.
  • Figure 3: Fractional modification of the primordial scalar power spectrum induced by a transient domain-wall phase. Deviations are localized around modes exiting the horizon near the matching time, while scale invariance is recovered at larger and smaller scales.