A cosmic string is a hypothetical 1-dimensional (spatially) topological defect in various fields. Cosmic strings are hypothesized to form when the field undergoes a phase change in different regions of spacetime, resulting in condensations of energy density at the boundaries between regions. This is somewhat analogous to the imperfections that form between crystal grains in solidifying liquids, or the cracks that form when water freezes into ice. The phase changes that produce cosmic strings may have occurred in the earliest moments of the universe's evolution.
Cosmic strings, if they exist, would be extremely thin with diameters on the same order as a proton. They would have immense density, however, and so would represent significant gravitational sources. A cosmic string 1.6 kilometers in length would exert more gravity than the Earth. Cosmic strings would form a network of loops in the early universe, and their gravity could have been responsible for the original clumping of matter into galactic superclusters.
A cosmic string's vibrations, which would oscillate near the speed of light, can cause part of the string to pinch off into an isolated loop. These loops have a finite lifespan due to decay via gravitational radiation.
It was once thought that the gravitational influence of cosmic strings might contribute to the large-scale clumping of matter in the universe, but all that is known today through galaxy surveys and precision measurements of the cosmic microwave background fits an evolution out of random, gaussian fluctuations. These precise observations therefore tend to rule out a significant role for cosmic strings.
Gravitational lensing of a galaxy by a straight section of a cosmic string would produce two identical, undistorted images of the galaxy. In 2003 a group led by Mikhail Sazhin reported the accidental discovery of two seemingly identical galaxies very close together in the sky, leading to speculation that a cosmic string had been found. However, observations by the Hubble Space Telescope in January 2005 showed them to be a pair of similar galaxies, not two images of the same galaxy. A cosmic string would produce a similar duplicate image of fluctuations in the cosmic microwave background, which might be detectable by the upcoming Planck Surveyor mission.
A second piece of evidence supporting cosmic string theory is a phenomenon observed in observations of the "double quasar" called Q0957+561A,B. Originally discovered by Dennis Walsh, Bob Carswell, and Ray Weymann in 1979, the double image of this quasar is caused by a galaxy positioned between it and the Earth. The gravitational lens effect of this intermediate galaxy bends the quasar's light so that it follows two paths of different lengths to Earth. The result is that we see two images of the same quasar, one arriving a short time after the other (about 417.1 days later).
However, a team of astronomers at the Harvard-Smithsonian Center for Astrophysics led by Rudolph Schild studied the quasar and found that during the period between September 1994 and July 1995 the two images appeared to have no time delay; changes in the brightness of the two images occurred simultaneously on four separate occasions. Schild and his team believe that the only explanation for this observation is that a cosmic string passed between the Earth and the quasar during that time period traveling at very high speed and oscillating with a period of about 100 days.
The Laser Interferometer Gravitational-Wave Observatory (LIGO) and upcoming gravitational wave observatories will search for cosmic strings as well as other phenomenon with the byproduct of gravitational waves.
Superstrings, D-strings or other stringy objects stretched to intergalactic scales would radiate gravitational waves, which could presumably be detected using experiments like LIGO. They might also cause slight irregularities in the cosmic microwave background, too subtle to have been detected yet but possibly within the realm of future observability.
Note that most of these proposals depend, however, on the appropriate cosmological fundamentals (strings, branes, etc.), and no convincing experimental verification of these has been performed.