Straight and Wiggly Cosmic Strings in Horndeski Theory

TL;DR

The paper analyzes straight and wiggly cosmic strings in the linearized Horndeski theory with massless and massive scalar fields. It derives the linearized field equations and exact weak-field solutions, expressing them through a conformal factor A(r) and an angular deficit, and then analyzes test-particle geodesics, effective potentials, and circular orbits. A key finding is the screening effect: a massive scalar field drives A(r) toward unity at large distances, recovering GR, while a massless scalar induces long-range scalar modifications and bound geodesics near the string. The study also computes velocity kicks imparted to fast particles crossing the strings, showing additive contributions from topology, wiggles, and scalar couplings, with explicit expressions that illustrate how screening modifies these kicks in the massive case.

Abstract

In this article, the behavior of a straight cosmic string is studied for the linearized version of Horndeski theory in cases where the scalar field is massless or massive. Several physical properties of such solutions are discussed in detail regarding the effects of the scalar field of this theory. The mass of the scalar field induces a screening effect such that, in the massive theory, the string solution approaches to the general relativistic one. We also consider wiggly cosmic strings, obtain the solutions for both massless and massive cases, discuss their properties and observe similar screening effects.

Figures (6)

• Figure 1: Behavior of the conformal factors of massless, massive with $m=0.1$, $m=0.5$ and general relativity cases. It is clear that in the massive case, the conformal factor approaches to unity, i.e., the GR limit for large $r$ values, whereas in the massless case it increases by increasing $r$. The general behavior of massive and massless cases agrees with small values of $r$ as the mass of the scalar field decreases. Note that plots are not scaled; We choose constant values such that these behaviors are clear to see on a single graph.
• Figure 2: Behavior of the effective potential of massless Horndeski theory with $\mu=0.1$ and $\mu=0.2$. Observe that, when we double the string tension $\mu$, the trapping energy of a particle decreases and the depth of the trapping region increases. Meaning, a particle that is trapped in a gravitational region with a higher string tension in massive Horndeski theory has a low chance of escaping from that field. The graph is plotted for $L=0.01$. Other constants are chosen such that the behavior is reflected on a single graph.
• Figure 3: Behavior of the effective potential for massive Horndeski theory. Both graphs are plotted for $L=0.1$ and have the same range. In (\ref{['fig3:a']}), $\mu =0.1$ and in (\ref{['fig3:b']}), $m=0.2$. Note that plots are not scaled; We choose constant values such that these behaviors are clear to see on a single graph.
• Figure 4: Behavior of the conformal factors for wiggly cosmic strings in linearized Horndeski theory. We observe the same graphical trend as the straight string! Here $\Omega$ represents the conformal factors of wiggly cosmic string solutions of the corresponding cases (\ref{['wigglycsmassless']}) and (\ref{['wigglycsmassive']}).
• Figure 5: Behavior of the effective potential of massless Horndeski theory with $\tilde{\mu}=0.2, \tilde{T}=0.1$ and $\tilde{\mu}=0.3, \tilde{T}=0.15$. Graph is plotted for $L=0.01$. Other constants are chosen such that the behavior is reflected on a single graph.