What's the connection between cosmic strings and the strings hypothesized in string theory? I read somewhere that Edward Witten, the (once) big hotshot of string theory, said that the discovery of cosmic strings (at the beginning of this Wikipedia article it is written: "Not to be confused with strings in string theory")  would provide evidence in favor of string theory. 
Now, a cosmic string is a concept that follows from the Standard Model of elementary particles and speculation about such an entity appeared on the scene before string theory did.
Their length can span the entire Universe, they have a thickness of about $10^{-17}$ (but please correct me if I'm wrong), and inside the string, the conditions are like the conditions were before the spontaneous symmetry breaking occurred (likewise there could be much thinner cosmic strings, in the light of GUT's, inside which the conditions were like the conditions before the SSB of the strong and electroweak force).
In a nutshell: I can't see any resemblances between cosmic strings and the strings in string theory, except that they are both called strings.
My question is simple: what is the connection (if there is any) between cosmic strings and the strings used in string theory?
 A: I am not an expert in string theory, but I do have general knowledge around the notion of a cosmic string. A cosmic string is a kind of structure that has been discussed in theoretical physics for quite a while. I think most attempts to think about quantum gravity allow such things, so I don't think a cosmic string would necessarily distinguish among quantum gravity theories. In that sense it would not necessarily support string theory over other approaches. However, depending on what the data was, it would constrain theories and might rule some out.
A: A fundamental string is the building block of string theory. By definition, the string cannot be defined in more elementary terms. Except perhaps as the elementary excitation of a string theory field.
In contrast, a cosmic strings are topological defects. They are the result of phase transitions and arise from spontaneous symmetry breaking phenomena in ordinary quantum field theory.
Some string theorists have hypothesized the possibility that "tiny" fundamental strings can be made into strings of a huge size (of the order of the Hubble radius) due to the early universe inflation. The spectrum and dynamics of cosmic and fundamental strings differ and those differences could be experimentally tested if cosmic strings were found; raising the exciting possibility of detect the macroscopic fundamental superstrings of string theory. That's why Witten says that maybe finding "cosmic strings" could give the opportunity to test string theory.
References:
Seeking String Theory in the Cosmos
Divulgative video on cosmic strings
A: What I said above still holds, but for some reason this has been missed, the idea of a cosmic seed is not unique to string theory.If a vacuum is not truly Newtonian and it does indeed expand (new space appearing) then there will be new fluctuations added to spacetime as well. Fluctuations can also act as the seeds of the universe to explain a primordial gravitational clumping, giving rise to the large scale structure, albeit, this uses the notion of some rapid expansion phase. In fact, Wald and Harren have shown it is possible to retrieve the cosmic seeds without inflation.
In their model the inhomogeneities of the universe arises while in the radiation phase – their model also requires that all fluctuation modes would have been in their ground state and that the ﬂuctuations are “born” in the ground state at an appropriate time which is early enough so that their physical length is very small compared to the Hubble radius, in which case, they can “freeze out” when these two lengths become equal.
It has been noted in literature that there is clearly a need for some process that would be responsible for the so called “birth” of the ﬂuctuation but today I want to show how you can talk about fluctuations within the context of expanding space, which is required within a sensible approach to unify the cosmic seeds with the dynamics of spacetime. It is possible to construct a form of the Friedmann equation with what is called the Sakharov fluctuation term, which is the modes of the zero point fluctuations
$m\dot{R}^2 + 2\hbar c R \int k\ dk = \frac{8 \pi GmR^2}{3}\rho$
When $R \approx 0$ (but not pointlike) then the fluctuations are in their ground state. Though inflation is not required to explain the cosmic seeding, there are alternatives themselves to cosmic inflation such as one particular subject I have investigated with a passion; rotation can mimic dark energy perfectly which is thought to explain the expansion and perhaps even acceleration (if such a thing exists). It is possible to expand the Langrangian of the zero point modes on the background spacetime curvatuture in a power series
$\mathcal{L} = \hbar c R \int k\ dk... + \hbar c\ R^n\ \int \frac{dk}{k^{n-1}} + C$
Where C is a renormalizing constant which is set to zero for flat space. It had been believed at one point that the forth power over the momenta of the particles would be zero
$\hbar c\ \int k\ dk^3 = 0$
But interesting things happen in the curvature of spacetime, such a condition doesn't need to hold. The anisotropies may arise in an interesting way when I refer back to equations I investigated in the rotating model. An equation of state with thermodynamic definition can be given as:
$T k_B \dot{S} = \frac{\dot{\rho}}{n} + \frac{\rho + P}{n}\frac{\dot{T}}{T}$
The last term $\frac{\dot{T}}{T}$ calculates the temperature variations that arise, even in the presence of the cosmic seed and we can therefore change the effective density coefficient in the following way:
$\frac{\dot{R}}{R}\frac{\ddot{R}}{R} = \frac{8 \pi G}{6}(\rho + \frac{3P}{c^2} + \hbar c \int k^3\ dk)\frac{\dot{T}}{T}$
REFERENCES
See Sakharovs fluctuations in curved space and how he applies gravitational corrections.
