Nonsingular Cosmologies in Presence of String Cloud

TL;DR

The paper investigates nonsingular cosmologies in a 5D AdS bulk with a uniformly distributed string cloud whose endpoints attach to a 4D brane, sourcing matter on the brane and contributing a bulk gluonic component. By deriving the brane Friedmann equations, it shows that a critical braneworld with $ ext{``}\Lambda_4 ext{''}=0$ can exhibit a nonsingular bounce in a closed geometry, while noncritical cases yield regions of bouncing or singular behavior depending on the string density $b$, mass parameter $m$, and curvature $k$; however, bounces inside a bulk Cauchy horizon lead to instabilities for negative $m$. The shellworld (dark bubble) scenario without $ ext{``}\mathbb{Z}_2 ext{''}$ symmetry demonstrates a more robust route to nonsingular evolution, with exact solutions for $ ext{``}\Lambda_4=0 ext{''}$ and stable bouncing/cyclic behavior under suitable combinations of bulk parameters, and the possibility of stable nonsingular evolution even when $b_ abla=0$. Overall, the study shows that higher-dimensional AdS configurations with string clouds can realize nonsingular cosmologies, with shellworlds offering more stable bouncing solutions than braneworlds in certain parameter regimes, thereby providing a mechanism to evade initial singularities and horizon-related instabilities in these models.

Abstract

In the braneworld scenario, we introduce a uniformly distributed cloud of infinitely long strings in the five dimensional AdS bulk spacetime. The end points of the strings are attached to the brane and becomes the source of the four dimensional matter on the brane, while the body of the strings hang onto the radial direction of the bulk and act as the gluonic field on the brane. The presence of matter in the brane induces a nonsingular cosmological evolution for the scale factor of the brane world under certain conditions of mass and cosmological parameters. However, the nonsingular nature is unstable since the bounce occurs inside the Cauchy horizon. Further, we consider the shellworld or the dark bubble scenario for the same bulk spacetime. It shows stable nonsingular cosmological nature of the bubble universe under certain conditions on the bulk and bubble parameters.

Figures (16)

• Figure 1: Plot of mass as a function of the horizon radius for $k=1$, $l=1$ and various values of string density.
• Figure 2: Plot of $a$ vs $\eta$ for different values of $k$, $m=1$ and $b=1$.
• Figure 3: (a) Plot of $U(a)$ with respect to $a$ with $k=+1$ and $m=0.1$ for various values of $b$ and $\Lambda_4$. (b) Variation of $\dot{a}$ and $\ddot{a}$ with respect to $a$. Here, $k=+1, m=0.1$ and $\Lambda_4=+1$.
• Figure 4: Plot of $U(a)$ with respect to $a$ for various values of $\Lambda_4$, $m=0.1$, $b=0.1$ with (a) $k=-1$ and (b)$k=0$.
• Figure 5: (a) Plot of $a$ vs $\eta$ for different values of $k$. The values of parameters are $m=2$ and $b=6$. (b)Plot of $\dot a$ and $\ddot a$ vs $a$ for different values of $k$. The values of mass and string density are $m=1$ and $b=5$ respectively.