Inflation and Nonsingular Spacetimes of Cosmic Strings

TL;DR

The paper numerically investigates inflation in cosmic strings by solving the Einstein–scalar–gauge system for gauge and global strings in 3+1 dimensions. It shows that for symmetry-breaking scales above critical values, the string cores inflate radially and axially, and that static, supermassive strings exhibit exterior singularities which disappear when treated dynamically. It provides quantitative thresholds, $η_c≈0.25 m_p$ for gauge strings (n=1, β=1) and $η_c≈0.23 m_p$ for global strings, with η_c decreasing for larger winding and different couplings, and demonstrates that time dependence yields nonsingular, de Sitter-like cores. Overall, the work highlights the necessity of time-dependent analysis to obtain physically sensible spacetimes around supermassive cosmic strings and clarifies the inflationary regime for both gauge and global defects.

Abstract

Inflation of cosmic gauge and global strings is investigated by numerically solving the combined Einstein and field equations. Above some critical symmetry-breaking scales, the strings undergo inflation along the radial direction as well as the axial direction at the core. The nonsingular nature of the spacetimes around supercritical gauge and global strings is discussed and contrasted to the singular static solutions that have been discussed in the literature.

Figures (14)

• Figure 1: A plot of $\delta/H_0^{-1}$ vs. $n$ for the $\eta=0.1,0.5,1.0,2.0,3.0m_p$ gauge strings (from the bottom to the top) in the flat spacetime. The dashed line corresponds to $\sqrt{n}$ as a reference. $H_0^{-1}$ is the horizon size at the center of the string.
• Figure 2: The scalar field configurations as functions of the proper radius $CH_0r$ at $H_0t=0,2,4$ (from the left to the right) for the $\eta=0.5m_p$ gauge string ($n=1$, $\beta=1$). The rapid growth of the proper radius in the core region indicates inflation.
• Figure 3: Plots of (a) $\log_{10}B$, $\log_{10}C$, and (b) $\log_{10}H$ vs. $H_0r$ at $H_0t=1,3,5$ (from the bottom to the top) for the $\eta=0.5m_p$ gauge string ($n=1$, $\beta=1$). The metric terms behave regularly in $r$ and $t$.
• Figure 4: A plot of $R_{\alpha\beta\gamma\delta}R^{\alpha\beta\gamma\delta}/H_0^4$ vs. $H_0r$ at $H_0t=2,4,6$ (from the right to the left) for the $\eta=0.5m_p$ gauge string ($n=1$, $\beta=1$). The scalar invariant is finite everywhere. The generic picture is not very different for different $\eta$'s.
• Figure 5: A plot of ${\dot{H} \over H}/{\dot{B} \over B}$ vs. $H_0r$ at $H_0t=2,3,4,5$ (from the bottom to the top) for the $\eta=0.5m_p$ gauge string ($n=1$, $\beta=1$). The ratio stays close to a constant ($\approx 1$) in the core region ($H_0r\lesssim 0.5$).