Ask Ethan: Are there defects in space-time tissue?

The fabric of space-time is a rather difficult concept to understand. Thanks to Einstein's general theory of relativity, we can take it up.

The most important lesson of Einstein’s GR is the fact that space is not a flat, unchanging, absolute entity. It is woven together with time into a single fabric: space-time. This fabric is continuous, smooth, it bends and deforms in the presence of matter and energy. Everything that exists in space-time moves along paths determined by its curvature, and this movement is limited by the speed of light. But what if there are defects in this fabric? This is not science fiction, but a real idea in theoretical physics, and this week our reader asks a question about it:

I would like to suggest such a topic for discussion as high-energy relics — domain walls, cosmic strings , monopoles, and so on. It would be interesting to read about what such defects are, where they come from, what properties they can have, and what is most interesting for me, how they can look and interact with the “ordinary” universe.

It turns out that it is mathematically very easy to get a defective Universe.


The gravitational behavior of the Earth around the Sun does not occur due to invisible gravitational attraction - it is better to describe it as if the Earth falls freely in a curved space, where the Sun plays the main role. But in this case, the curvature of space will be quite small, and there will be no defects in it.

Imagine the space. What does it look like? Do you imagine empty, smooth, homogeneous space? Do you think that the only deviations from this picture will be due to the masses and energy quanta? This is a good approach, commonly used by physicists. On the largest scales, it should be a three-dimensional lattice, with small deviations in the form of sections with a small spatial curvature, which creates the force of gravity well known to us. In this form, the space will be in a state with the least energy.


The fabric of space-time, with ripples and deformations caused by mass. But as far as we know, the space never folds or collapses.

What about excited states? What about other states? For simplicity, we eliminate two spatial dimensions and leave only one: a straight line. A straight line can be straight, open and endless, or it can be closed like a loop. Both of these options are direct in a state with minimal energy. What would a higher energy state look like? Take our line and make it flexible as a thread. Now imagine that we tied a knot on it - make a loop, put it crosswise and pull. A thread without knots denotes a one-dimensional space in a state with minimal energy; a single-knot thread denotes a one-dimensional space in the first excited state. This node is a zero dimensional topological defect.


The knot tied on a thread is an analogue of a zero-dimensional defect of a one-dimensional straight line. A node mirroring this may lead to the disappearance of both of them in a collision and the restoration of a level with minimal energy.

And now with a line containing knots, you can do something interesting. You can tie the exact same knot, and you will have two topological defects that summarize their impact. But if you tie a knot in the opposite direction - a mirror one, you get a node that is topologically opposite to the original one. If you bring these two nodes together, you will find that they can mutually untie each other, which will bring you back to a state with minimal energy.

These two types of zero-dimensional defects — a node and an anti-node — have physical counterparts in our Universe: magnetic monopoles. The node corresponds to an isolated north magnetic pole; the anti-node corresponds to an isolated south magnetic pole. If you bring them together, they annihilate, like matter and antimatter, and return the fabric of space-time to a state with minimal energy. Since monopoles are point particles, they would behave like ordinary matter, not much different from electrical monopoles (positive and negative electrical charges) that exist in our Universe.


The concept of a magnetic monopole emitting magnetic field lines in a similar way as an isolated electric charge emits electric field lines

Now back to our three-dimensional Universe. You can imagine not only point defects, but also defects with a large number of measurements:

• Cosmic strings: a one-dimensional straight line passes through the entire observable universe.
• Domain walls: a two-dimensional plane with irregular properties passes through the entire Universe.
• Space structures: a plot of three-dimensional space "tied into a knot."

So, among the possible defects, we have a monopole (0-D), a string (1-D), a wall (2-D), and a texture (3-D), and they all appear as a result of the work of different mechanisms, but belonging to the same class: they appear when symmetry is broken.


Differences between the Universe created within the framework of standard cosmology (left) and the one that appeared with a developed network of topological defects (right) lead to the appearance of completely different large-scale structures. Our observations confidently reject cosmic strings and domain walls as the dominant components of the modern universe.

Symmetry breaking is serious business for physics. All existing symmetries correspond to conserved quantities; therefore, if symmetry is violated, the law of conservation of this quantity ceases to work. Monopoles can be obtained by breaking the spherical symmetry; strings - breaking axial or cylindrical symmetry; domain walls - breaking the discrete symmetry (parity or mirror reflection). Defects of a different kind are more difficult to understand, but they are often encountered when working with additional dimensions. However, the first three of these — monopoles, cosmic strings, and domain walls — are particularly interesting for cosmology.


The idea of ​​combining states that all three interactions of the Standard Model, and possibly even gravity, at high energies are combined on a single platform.

You know that besides the Standard Model there must be something else, and it has many extensions, the consequences of which can be quite impressive. One of them is the idea of ​​the Great Unification , according to which electromagnetic, weak and strong nuclear interactions combine to form some kind of high energy. This would lead not only to the presence of new particles and interactions, but also to the emergence of magnetic monopoles at the moment of breaking of symmetry, keeping strong interaction together with the other two. The absence of magnetic monopoles in the observable Universe is often presented as evidence of cosmic inflation, and as additional evidence they cite the fact that the Universe, at the end of inflation, is not heated enough to restore the symmetry of the Great Unification.


If the Great Unification, restoring symmetry, was broken, a huge amount of magnetic monopoles should have appeared. But our Universe does not provide them for us; if cosmic inflation occurred after this symmetry breaking, then no more than one magnetic monopole may be present in the observable Universe.

Cosmic strings and domain walls (if they exist) should have appeared during phase transitions soon after the end of inflation. There may be additional symmetries at high energy levels, recovering in the early moments of the life of the Universe, and at the time of their destruction the described defects may appear. Cosmic strings and walls of domains — single or entire networks — would leave signs of their presence in large-scale structures of the Universe, textures would be visible in relic radiation, and magnetic monopoles in direct experiments to detect them. Some physicists ironically point to the only magnetic monopole, found on St. Day. Valentine in 1982 as evidence of cosmic inflation: there is only one monopoly in the universe, and we have seen it!


In 1982, an experiment led by Blas Cabrera with a twisted wire in eight loops discovered a change in flux of eight magnetons: evidence of the presence of a magnetic monopole. Unfortunately, no one was in the laboratory at the time of detection, and no one has yet managed to reproduce the result or find a second monopole.

And if monopoles would behave like ordinary matter, then cosmic strings, domain walls or cosmological textures would be extremely active in influencing the expansion of the Universe. Cosmic strings would behave like the curvature of space, limited to 0.4% of the total energy density, and the walls of the domains would create a kind of dark energy that accelerates the Universe - but this would be too weak an acceleration that would not explain the processes we see. The influence of cosmological textures would be comparable to the influence of the cosmological constant, but in order to explain all the available observations, one would have to accept that the entire observable Universe is inside a single defect!


The various components and contributions to the density of the energy of the universe, and the time in which they could prevail. If there were a sufficient number of cosmic strings or domain walls, they would make a significant contribution to the expansion of the Universe.

If there are monopoles, strings, walls, textures, then they must be extremely heavy. Monopoles should be the most massive of all open particles — about 10 ¹⁴ times more massive than the upper quark. Strings, walls and textures should play the role of embryos of large-scale structures, tightening matter in the period preceding the formation of any other structures, and creating very obvious traces of presence, taking into account the current capabilities of telescopes, observations and data on relict radiation. Modern restrictions indicate that such structures do not exist in large quantities, and there may be no more than a few percent of the total space energy budget.


Our relic radiation and its spectrum of fluctuations indicate scale invariance, while the network of cosmic strings would give a very steep climb in the left part of the graph.

Today there is no evidence of defects in the Universe, except for the only observation of a magnetic monopole made 35 years ago. And although we cannot disprove their existence (we can only impose restrictions on them), we need to be prepared for the possibility that these topological effects will not be forbidden, and that many extensions of the Standard Model will inevitably entail them. In many scenarios, their absence is due to the fact that they are being suppressed by something else. The lack of evidence is not proof of absence, but until we see something else that indicates the reality of the topological defects of the Universe, we will have to abandon this idea in the field of theories.

Ethan Siegel - astrophysicist, popularizer of science, blog Starts With A Bang! He wrote the books Beyond The Galaxy , and Treknologiya: Star Trek Science [ Treknology ].

FAQ: if the universe is expanding, why aren't we expanding ; why the age of the universe does not coincide with the radius of the observed part of it .