ÿþ<html> <title>Albert van der Sel: A few simple notes on Cosmic Strings</title> <body> <h1>A few simple notes on "Topological Defects", like Cosmic strings, in the Universe.</h1> Version : 0.2<br> Date : 10/02/2011<br> By : Albert van der Sel<br> Type of doc : Just an attempt to decribe the subject in a few simple words. Hopefully, it's any good.<br> For who : For anyone interrested. <br> <hr/> <br> Cosmic strings and other topological defects, are hypothetical objects that may be a result of symmetry<br> breaking models in GUT theories and cosmological models.<br> <br> <font face="arial" size=2 color="blue"> <h3>1. Motivations for Defects in the Universe:</h3> <font face="arial" size=2 color="black"> <B><U>1.1. Symmetry breaking:</U></B><br> <br> There are several reasons why socalled "Topological defects" may exist in the Universe.<br> One very important reason is this: "spontaneous symmetry breaking".<br> <br> In our present (cooled down) Universe, we have a number of fundamental forces (interactions) which are believed<br> to be unified as long as the <B>energy is high enough</B>. For example, just after the inflationary period,<br> (at the birth of the Universe), the universe cooled down to the point where symmetry breaking occurred,<br> and different force manifestations came into existence.<br> <br> To illustrate this: Just consider a very "homogenic bowl of fluid". If you for example "rotate" it (apply an operator),<br> nothing changes.<br> Now, suppose you have <I>just one type of force</I>. Then no matter what set of operators you want to apply<br> to the system, it's very symmetric to those operators.<br> <br> Regrettably this is still nerd talk. Well, here is an example that may illustrate the symmetry quite well:<br> <br> Suppose you hold a ordinary magnet. If you rotate the magnet for say 90 or 180 degrees, the magnetic field lines<br> are totally different compared to the original position. So, this is not symmetric for rotations.<br> <br> Now we heat up the magnet (not while you are holding it).<br> For a magnetic material, the "long range order" (magnetic domains) abruptly disappears at a certain temperature,<br> which is called the Curie temperature for the material. If it's just a plain iron magnet, then the temerature<br> is about 1043 K. All socalled line-upped Domains inside the iron dissapears, and we have a homogenic<br> (symmetric) situation again. So, at high temperatures this system is rotationally invariant.<br> And, at low temperatures the symmetry is broken.<br> <br> Ofcourse, every example has flaws, and this one certainly has it's fair portion of it.<br> But hopefully the example conveyed the basic idea behind symmetry breaking.<br> <br> "Grant Unifying Theories" (GUT's) try to "unite" the elementary (the weak, strong, electromagnetic, and gravitational) interactions<br> into one field theory and views the known interactions as low-energy manifestations of a single unified interaction.<br> <br> In somewhat philosophical words: <I>More is different.</I> <br> The cosmological significance of symmetry breaking is the fact that symmetries are restored at high energies,<br> and for the extremely high energies in the early universe, we will even achieve a grand unified state.<br> <br> <B><U>1.2. Phase Transitions and Defects:</U></B><br> <br> At the same event as decribed above, different "regions" may be formed with respect to the "background", or the vacuum.<br> This means that sort of isolated cells may have formed, each with their own type of vacuum and conditions.<br> Figure 1 illustrate those regions, separated by socalled "domain walls".<br> <br> Fig 1.<br> <br> <img src="td1.jpg" align="centre"/> <br> Why at all, might different regions form?<br> <br> A possible answer may be found in "causality" and the finite speed of light (or information).<br> It's probably true that causal effects in the early universe can only propagate at the speed of light c.<br> This then would mean that at a certain time in the early universe, regions of the universe separated by more<br> than a distance d=ct will "know" nothing about other regions: they are causally disconnected.<br> in effect: they are not close enough "to smear out" all of their properties.<br> So, it might be expected that different regions of the universe will fall into different values in the set of possible states<br> of the vacuum.<br> <br> Topological defects are the "borders" of matter formed at those phase transitions in the very early universe.<br> These defects are likely to be in the original phase. It is assumed (and partly mathematically proven) that some<br> types of defects will decay rapidly, while others may persist.<br> Some commonly known defects are: Domain Walls (2 dimensional "sheet"), textures, and Cosmic Strings.<br> <br> So it might be said, that topological defects are a posible consequence of unification theory, during the symmetry breaking.<br> However, from all types of defects, only cosmic strings seems to be a true candidate that might really exist.<br> Why?<br> <br> Strings are indeed "string-like" (one-dimensional like) objects, which may span the entire Universe.<br> It can be shown (mathematically and from particle physics) that strings will enlarge the continous global symmetry<br> of the various GUT models. In such a framework, when then the symmetry is broken, instead of domain walls<br> the phase transitions will give rise to strings and socalled Gold-stone bosons.<br> <br> So, if the defects are for real, we might expect "Cosmic Strings" instead of other types.<br> <br> As another, rather "pictorial" way to see how Cosmic Strings may have formed, consider this example.<br> At the times the state transitions occurred, disconnected "bubbles" of true vacuum (in false vacuum) came into existence,<br> where in the "true" vacuum state, symmetry is broken and matter and fields came into existence.<br> <br> Fig 2.<br> <br> <img src="tn2.jpg" align="centre"/> <br> <br> As the bubbles grow rapidly and come in contact, there might be sharp jumps in the field values,<br> which might yield very compact string like "borders" of the original state of the Universe.<br> <br> <br> <font face="arial" size=2 color="blue"> <h3>2. Cosmic strings and the "Large Scale Structure" of the Universe:</h3> <font face="arial" size=2 color="black"> The "large scale structure" of the Universe, resembles some sort of "swiss cheese" structure.<br> Superclusters of galaxies, or large collections of galaxies, are organized in filaments with large "holes"<br> in between. The figure below illustrates the structure:<br> <br> Fig 3.<br> <br> <img src="td2.jpg" align="centre"/> <br> <br> Although the <B>"cold dark matter model"</B> has become the <B>leading</B> theoretical paradigm for the formation of <br> such a structure in the Universe, some researchers still see a network of the "cosmic strings" as<br> precisely the common source for the observed large scale structure.<br> <br> Interestingly, some studies has been done, using simulations as to how a set of Cosmic Strings would<br> evolve from the early universe, up to the present. Remarkably, a similar structure as the observed<br> large scale structure of galaxies, emerged. It is indeed quite attemting to regard the strings as a sort of "attractor"<br> that lined up the the clusters as the way they do. See figure 3 as a representative result of such study.<br> <br> Fig 4.<br> <br> <img src="td3.jpg" align="centre"/> <br> <br> However, this seems to be no longer the favourite view of most cosmologists. As said before, instead<br> nowadays "Dark Matter" plays a key role in the observed structure.<br> <br> <br> <br> <br> <br> <br> </body> </html>