### Cosmic Acceleration from Topological Defects

A few days ago I posted a preliminary description of topological defects, as a prelude to a brief discussion of how they can lead to cosmic acceleration. In that post I focused on an analogy between field-theoretic systems and a simple mechanical system consisting of pencils, stood on their ends on a table, and connected to their nearest neighbor pencils by springs. In a field theory, it is (usually) a scalar field that picks out a specific direction in field space, spontaneously breaking the overall symmetry of the theory. In the pencil example, any direction in the plane is a vacuum, but when a pencil picks out just one, it breaks that symmetry (in this case rotational invariance in the plane).

Just as with the pencils, if the space of vacuum states, from which the field chooses, is topologically nontrivial, then the field can pick different vacua in different regions of field space. This can then result in a small region of space in which the field is not in the vacuum and, in fact, takes the value it did before the symmetry broke. We say that this region, the core of the defect, is in the unbroken symmetry phase.

Because the core is not in the vacuum, it is a region of approximately constant energy density, which is rendered metastable by topology. In broad terms, for a lone defect, this means that the core is like a small region of cosmological constant and the rest of space is in the vacuum. For example, for an infinite straight string, the energy-momentum distribution is like having a cosmological constant in the direction along the string.

If defects form during phase transitions as the universe cools, which is what we expect if the relevant field theory has the appropriate topological features, then networks of defects will form. Under certain circumstances, the defect network will frustrate; that is to say that it will form a frozen network, which you can imagine as a mesh-like configuration pervading space. Since the physical orientations of defects are random as one traverses the network, one can average over them to obtain a homogeneous, isotropic distribution of energy density on large scales.

How does this energy density evolve? You might expect that because each defect behaves, in part, like a cosmological constant, this might lead to an overall cosmic acceleration. The actual answer depends on the dimensionality of the defect. In a gauge theory one obtains the following; a system of magnetic monopoles evolves like regular matter; a network of cosmic strings evolves like a fluid with equation of state parameter w=-1/3, which is precisely on the border between decelerating and accelerating cosmologies; and a network of domain walls yields w=-2/3, which would indeed cause cosmic acceleration.

Current measurements of the equation of state of dark energy disfavor an equation of state parameter so far from w=-1. However, it is still possible that a frustrated defect network is part of the cosmic energy budget, and it is fascinating (to me at least) that nonperturbative solutions to particle physics theories can have such a profound effect of the evolution of the universe.

Just as with the pencils, if the space of vacuum states, from which the field chooses, is topologically nontrivial, then the field can pick different vacua in different regions of field space. This can then result in a small region of space in which the field is not in the vacuum and, in fact, takes the value it did before the symmetry broke. We say that this region, the core of the defect, is in the unbroken symmetry phase.

Because the core is not in the vacuum, it is a region of approximately constant energy density, which is rendered metastable by topology. In broad terms, for a lone defect, this means that the core is like a small region of cosmological constant and the rest of space is in the vacuum. For example, for an infinite straight string, the energy-momentum distribution is like having a cosmological constant in the direction along the string.

If defects form during phase transitions as the universe cools, which is what we expect if the relevant field theory has the appropriate topological features, then networks of defects will form. Under certain circumstances, the defect network will frustrate; that is to say that it will form a frozen network, which you can imagine as a mesh-like configuration pervading space. Since the physical orientations of defects are random as one traverses the network, one can average over them to obtain a homogeneous, isotropic distribution of energy density on large scales.

How does this energy density evolve? You might expect that because each defect behaves, in part, like a cosmological constant, this might lead to an overall cosmic acceleration. The actual answer depends on the dimensionality of the defect. In a gauge theory one obtains the following; a system of magnetic monopoles evolves like regular matter; a network of cosmic strings evolves like a fluid with equation of state parameter w=-1/3, which is precisely on the border between decelerating and accelerating cosmologies; and a network of domain walls yields w=-2/3, which would indeed cause cosmic acceleration.

Current measurements of the equation of state of dark energy disfavor an equation of state parameter so far from w=-1. However, it is still possible that a frustrated defect network is part of the cosmic energy budget, and it is fascinating (to me at least) that nonperturbative solutions to particle physics theories can have such a profound effect of the evolution of the universe.

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