Evolution of Generic Varying-Tension Cosmic Strings in Expanding Spacetimes

TL;DR

The paper investigates cosmic strings with time-dependent tension and extends analyses from circular loops to non-circular loops by showing an equivalence to constant-tension strings in an FRW background with the modified scale factor $\tilde{a}(\eta)=a(\eta)\sqrt{\mu(\eta)}$, yielding a quasi-Hubble constant $\tilde{H}$. It develops two numerical approaches, physics-informed neural networks and B-splines, to solve the Nambu-Goto equations for horizon-scale loops and analyzes smooth, cusped, and non-self-intersecting configurations. The results show sublinear growth of the energy density $\epsilon$, with loop shapes largely preserved and non-self-intersection maintained in the studied regime, suggesting time-dependent tension does not trivially induce percolation. This work provides a practical framework for exploring varying-tension string dynamics in expanding spacetimes and informs future studies of string networks and complex features like kinks.

Abstract

It has recently been realised that strings with time-dependent tensions exhibit interesting dynamics; in particular, when the tension decreases loops of string can grow and possibly percolate. We extend previous analytic studies of strings with time-dependent tensions to numerical studies of non-circular loops. We show that the dynamics of a varying-tension string in expanding universe is mathematically equivalent to the evolution of a fixed-tension string in a universe with a modified scale factor. We use numerical solvers and machine learning techniques to explore the dynamics of non-circular string loops with radii close to the Hubble scale.

Figures (11)

• Figure 1: Figure illustrating training of neural networks to solve equations (\ref{['eqnofmotion']})
• Figure 2: An example of the mix of expert model.
• Figure 3: B-spline basis functions of degree $p = 1,2,3$ with $p+1$ regular knots and uniformly spaced internal knots.
• Figure 4: String shape at selected times for circular string initial condition.
• Figure 5: Average radius of the string vs conformal time for circular string initial condition.