Scaling solutions for varying tension strings

Abstract

We use the Velocity-dependent One Scale Model for topological defect evolution to explore and classify the possible scaling solutions for string networks with time-varying tension, in cosmological and non-cosmological settings and under two different phenomenological assumptions for the behavior of these variations, which rely on different stretching and damping contributions to the string dynamics. We discuss how these assumptions impact the standard scaling solutions, as well as the evolution of the string network density. In addition to simple power-law cosmological epochs solutions, we also discuss the behavior of the network during the radiation-to-matter and matter-to-acceleration transitions. Overall, our results show that for the same amount of tension variation, a change in the stretching length scale tends to have a more significant impact on the network than a change in the damping length.

Figures (5)

• Figure 1: The linear scaling values of $v$ and $\epsilon$ (left and right panels respectively) for constant-tension strings, for relevant values of the expansion rate $\lambda$ and the loop chopping efficiency $\tilde{c}$. The two horizontal dotted lines identify the radiation end matter eras ($\lambda=1/2$ and $\lambda=2/3$ respectively), while the vertical dotted line identifies the numerically preferred value $\tilde{c}=0.23$. Some particular contour lines are also drawn for visual convenience.
• Figure 2: The linear scaling values of $v$ and $\epsilon$ (left and right panels respectively) for varying tension strings using the macroscopic and microscopic phenomenological approaches (top and bottom panels respectively), for relevant values of $\lambda$ and $\delta$, using $\tilde{c}=0.23$. The two horizontal dotted lines identify the radiation end matter eras ($\lambda=1/2$ and $\lambda=2/3$ respectively), while the vertical dotted line identifies the constant-tension case, $\delta=0$. To facilitate visual comparison, the colormaps for each plotted quantity are the same as those of Fig. \ref{['fig1']}. Some particular contour lines are also drawn for visual convenience.
• Figure 3: The behavior of transitions functions $f$ and $g$ (in blue and red, respectively) for $\delta=0$ (solid), $\delta=-1/10$ (dashed) and $\delta=+1/10$ (dotted). The left and right panels are for the macroscopic and microscopic cases respectively, and the black dotted line identifies the moment of equal radiation and matter densities.
• Figure 4: The behavior of transition functions $f$ and $g$ (in blue and red, left and right side panels respectively) for $\delta=0$ (solid), $\delta=-1/10$ (dashed) and $\delta=+1/10$ (dotted). The top and bottom panels are for the macroscopic and microscopic cases respectively, and the vertical dotted line identifies the present day.
• Figure 5: Same as Fig. \ref{['fig4']}, with the vertical axes in logarithmic rather than linear scale.