Scaling from gauge and scalar radiation in Abelian Higgs string networks (1703.06696v3)

Abstract: We investigate cosmic string networks in the Abelian Higgs model using data from a campaign of large-scale numerical simulations on lattices of up to $4096^3$ grid points. We observe scaling or self-similarity of the networks over a wide range of scales, and estimate the asymptotic values of the mean string separation in horizon length units $\dot{\xi}$ and of the mean square string velocity $\bar v^2$ in the continuum and large time limits. The scaling occurs because the strings lose energy into classical radiation of the scalar and gauge fields of the Abelian Higgs model. We quantify the energy loss with a dimensionless radiative efficiency parameter, and show that it does not vary significantly with lattice spacing or string separation. This implies that the radiative energy loss underlying the scaling behaviour is not a lattice artefact, and justifies the extrapolation of measured network properties to large times for computations of cosmological perturbations. We also show that the core growth method, which increases the defect core width with time to extend the dynamic range of simulations, does not introduce significant systematic error. We compare $\dot{\xi}$ and $\bar v^2$ to values measured in simulations using the Nambu-Goto approximation, finding that the latter underestimate the mean string separation by about 25%, and overestimate $\bar v^2$ by about 10%. The scaling of the string separation implies that string loops decay by the emission of massive radiation within a Hubble time in field theory simulations, in contrast to the Nambu-Goto scenario which neglects this energy loss mechanism. String loops surviving for only one Hubble time emit much less gravitational radiation than in the Nambu-Goto scenario, and are consequently subject to much weaker gravitational wave constraints on their tension.

Scaling from Gauge and Scalar Radiation in Abelian Higgs String Networks

This paper investigates cosmic string networks in the context of the Abelian Higgs model through large-scale numerical simulations. The paper focuses on understanding the scaling properties of string networks, which is crucial for interpreting their cosmological implications, particularly in generating Cosmic Microwave Background (CMB) fluctuations.

The authors employ simulations on lattices with up to $4096^3$ grid points to analyze the dynamics of cosmic strings when considering gauge and scalar radiation, which are intrinsic to the Abelian Higgs model. The central theme is the evaluation of scaling behavior or self-similarity, which arises from energy loss due to classical radiation. The research examines the mean string separation relative to horizon length $\dot{\xi}$ and mean square string velocity $\bar{v}^2$, extending these properties to large times and continuum limits.

Key Findings and Numerical Results

1. Scaling Behavior: The paper presents strong numerical evidence that string networks exhibit scaling behavior over a vast range of scales, with both radiation and matter eras considered. These observations confirm the self-similarity in network evolution driven by the consistent energy loss into gauge and scalar fields.
2. Radiative Efficiency: The authors introduce a radiative efficiency parameter, which quantifies the energy loss rate of the string network per unit length of strings. This parameter does not show significant variation with lattice spacing or string separation, suggesting that the energy loss mechanism is intrinsic rather than a lattice-induced artifact.
3. Measurements and Comparisons: The paper measures $\dot{\xi}$ and $\bar{v}^2$ using various estimators, comparing results from simulations employing the Nambu-Goto approximation. It is found that the Nambu-Goto approximation underestimates mean string separation by about 25% and overestimates $\bar{v}^2$ by approximately 10%.
4. Implications for Gravitational Radiation: String loops radiate massive fields within a Hubble time, implying less gravitational wave emission than predicted by the Nambu-Goto approximation. Consequently, gravitational wave constraints on cosmic string tension are significantly weaker than previously thought.

Implications and Future Research

This research holds implications for cosmological models that incorporate cosmic strings as sources of perturbations, particularly in the CMB. Understanding the scaling laws from these field theory simulations provides crucial parameters needed to extrapolate to the cosmological scales relevant for CMB analysis.

The paper challenges the common presumption of the Nambu-Goto framework as appropriate for describing cosmic string dynamics at cosmological scales, especially concerning energy conversion dynamics. Further studies could explore the detailed mechanisms behind the radiation from string networks, and more accurate models could be developed to better predict the gravitational radiation from cosmic strings.

In summary, the paper provides a comprehensive dataset and analysis framework for studying cosmic string networks, with profound implications for understanding the universe's symmetries and phase transitions measurable through cosmological observables. The combination of large-scale numerical simulations, careful extrapolation techniques, and robust analysis contributes significantly to the field of theoretical cosmology and the paper of topological defects.