The evolution of cosmic string network is the relatively complicated
result of only three rather simple and fundamental processes: cosmological
expansion, intercommuting & loop production,
and radiation. We describe each one of them below...
The overall
expansion of the universe will `stretch' the strings, just like any
other object that is not gravitationally bound. You can easily undertand
this through the well-known analogy of the expanding balloon. If you draw
a line of the surface of the balloon and then blow it up, you will see
that the length of your `string' will grow at the same rate as the radius
of the balloon.
Whenever two long strings cross each other, they exchange ends, or `intercommute'
(case (a) in the figure below). We had already encountered this apparently
strange fact when we discussed the strings in the context of nematic
liquid crystals. In particular, a long string can intercommute with
itself, in which case a loop will be produced (this is case (b) below).
The processes of intercommuting and loop production.
Belowyou can see two movies providing numerical evidence for the intercommuting
process. The first one shows a full three-dimensional simulation of the
intercommuting of two cosmic strings....
The reconnection and `exchange of partners' when two strings intersect. In this three-dimensional simulation, the strings approach each other at half the speed of light. Notice the radiation of energy and the production of a small interaction loop in the aftermath of the collision (R. Battye & E. P. Shellard).
...while the second shows a two-dimensional section of it. The height of the surface above the plane represents the energy present at each point.
The scattering of two vortices is highly
non-trivial; the two vortices approach and form a donut from which the
emerge at right-angles have `exchanged halves' (J. Moore & E. P. Shellard).
Both long cosmic strings and small loops will emit radiation. In most cosmological
scenarios this will be gravitational radiation, but electromagnetic
radiation or axions can also be emitted in some cases (for some specific
phase transitions). Here is a single, oscillating piece of string...
... and here you can see the radiation that is being emitted. Note that
this is a cross section through the string, that is, in this movie the
string is perpendicular to the screen.
The effect of radiation is much more dramatic for loops, since they lose all their energy this way, and eventually disappear. Here you can see what happens in the case of two interlocked loops. This configuration is unlikely to happen in a cosmological setting, but it is nevertheless quite enlightening. Notice the succession of compicated dynamic processes before the loop finally disappears!
If you are not able to see the movie, here are some selected snapshots...
After formation, an initially high density string network begins to chop itself up by producing small loops. These loops oscillate rapidly (relativistically) and decay away into gravitational waves. The net result is that the strings become more and more dilute with time as the universe expands. From an enormous density at formation, mathematical modelling suggests that today there would only be about 10 long strings stretching across the observed universe, together with about a thousand small loops!
In fact the network dynamics is such that the string density will eventually stabilize at an exactly constant level relative to the rest of the radiation and matter energy density in the universe. Thus the string evolution is described as `scaling' or scale-invariant, that is, the properties of the network look the same at any particular time t if they are scaled (or multiplied) by the change in the time. This is schematically represented below:
Scale-invariant evolution of a cosmic string network. The network looks exactly the same (in a statistical sense) if it is re-scaled relative to the horizon (which grows in proportion to the time t multiplied by the speed of light c).
In order to obtain a more detailed description of the evolution, however, it is necessary to use high -resolution numerical simulations.
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