Recent developments in the physics of extra dimensions have opened up new avenues to test such theories. We review cosmological aspects of brane world scenarios such as the Randall–Sundrum brane model and two-brane systems with a bulk scalar field. We start with the simplest brane world scenario leading to a consistent cosmology: a brane embedded in an anti-de Sitter space–time. We generalize this setting to the case with a bulk scalar field and then to two-brane systems.We discuss different ways of obtaining a low-energy effective theory for two-brane systems, such as the moduli space approximation and the low-energy expansion. A comparison between the different methods is given. Cosmological perturbations are briefly discussed as well as early universe scenarios such as the cyclic model and the born-again brane world model. Finally we also present some physical consequences of brane world scenarios on the cosmic microwave background and the variation of constants.

Brane world cosmology

We analyze the cosmological signatures visible to an observer in a Coleman-de Luccia bubble when another such bubble collides with it. We use a gluing procedure to generalize the results of Freivogel, Horowitz and Shenker to the case of a general cosmological constant in each bubble and study the resulting spacetimes. The collision breaks the isotropy and homogeneity of the bubble universe and provides a cosmological 'axis of evil' which can affect the cosmic microwave background in several unique and potentially detectable ways. Unlike more conventional perturbations to the inflationary initial state, these signatures can survive even relatively long periods of inflation. In addition, we find that for a given collision the observers in the bubble with smaller cosmological constant are safest from collisions with domain walls, possibly providing another anthropic selection principle for small positive vacuum energy.

When Worlds Collide

Non-abelian gauge theories in the Higgs phase admit a startling variety of BPS solitons. These include domain walls, vortex strings, confined monopoles threaded on vortex strings, vortex strings ending on domain walls, monopoles threaded on strings ending on domain walls, and more. After presenting a self-contained review of these objects, including several new results on the dynamics of domain walls, we go on to examine the possible interactions of solitons of various types. We point out the existence of a classical binding energy when the string ends on the domain wall which can be thought of as a BPS boojum with negative mass. We present an index theorem for domain walls in non-abelian gauge theories. We also answer questions such as: Which strings can end on which walls? What happens when monopoles pass through domain walls? What happens when domain walls pass through each other?

Monopoles, vortices, domain walls and D-branes: The Rules of interaction

In the context of eternal inflation we discuss the fate of Lambda = 0 bubbles when they collide with Lambda< 0 crunching bubbles. When the Lambda = 0 bubble is supersymmetric, it is not completely destroyed by collisions. If the domain wall separating the bubbles has higher tension than the BPS bound, it is expelled from the Lambda = 0 bubble and does not alter its long time behavior. If the domain wall saturates the BPS bound, then it stays inside the Lambda = 0 bubble and removes a finite fraction of future infinity. In this case, the crunch singularity is hidden behind the horizon of a stable hyperbolic black hole.

https://escholarship.org/content/qt0ns9z82h/qt0ns9z82h.pdf?t=lnqrbk

Colliding with a crunching bubble

In the picture of eternal inflation as driven by a scalar potential with multiple minima, our observable universe resides inside one of many bubbles formed from transitions out of a false vacuum. These bubbles necessarily collide, upsetting the homogeneity and isotropy of our bubble interior, and possibly leading to detectable signatures in the observable portion of our bubble, potentially in the cosmic microwave background or other precision cosmological probes. This constitutes a direct experimental test of eternal inflation and the landscape of string theory vacua. Assessing this possibility roughly splits into answering three questions: What happens in a generic bubble collision? What observational effects might be expected? How likely are we to observe a collision? In this review we report the current progress on each of these questions, improve upon a few of the existing results and attempt to lay out directions for future work.

A Status report on the observability of cosmic bubble collisions

It is intriguing to consider the possibility that the big bang of the standard (3+1)-dimensional cosmology originated from the collision of two branes within a higher dimensional spacetime, leading to the production of a large amount of entropy. In this paper we study, subject to certain well-defined assumptions, under what conditions such a collision leads to an expanding universe. We assume the absence of novel physics, so that ordinary (4+1)-dimensional Einstein gravity remains a valid approximation. It is necessary that the fifth dimension not become degenerate at the moment of collision. First the case of a symmetric collision of infinitely thin branes having a hyperbolic or flat spatial geometry is considered. We find that a symmetric collision results in a collapsing universe on the final brane unless the preexisting expansion rate in the bulk just prior to the collision is sufficiently large in comparison to the momentum transfer in the fifth dimension. Such prior expansion may either result from negative spatial curvature or from a positive five-dimensional cosmological constant. The relevance of these findings to the colliding bubble braneworld universe scenario is discussed. Finally, results from a numerical study of colliding thick-wall branes is presented, which confirm the results of the thin-wall approximation.

Frederic Glanois

Papers

When do colliding bubbles produce an expanding universe