*The recent announcement about the observation of a giant ring structure in a distant part of the universe, was widely reported as putting into question some fundamental assumptions of cosmology. But Dominik Schwarz argues such interpretations depend on a misunderstanding of the cosmological principle. *

At the recent American Astronomical Society meeting, an announcement was made about the discovery of a giant ring with a diameter of 1.3 billion light years. This follows a trend of similar claims in recent years about the discovery of larger and larger structures observed in the universe. The first difficult question to ask is of course, are these structures real or just chance patterns, like for example the constellation of Ursa Major. Our brains tend to fool us and we like to see patterns in any random assembly of points. If we can somehow convince ourselves of the reality of these, the second question to ask is, are they gravitationally formed and bound, or are they formed by some other dynamical process. Especially the second question is often very hard to answer and typically requires information in many different wavelengths. For sure there will be some debate on both of these questions, but let us assume both are answered and that the announcement is correct. The third, and deeper question to ask then is, what would it mean if these structures are both real and brought together by gravity?

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In short, the cosmological principle is an assumption that that space is maximally symmetric. In other words, whichever direction you look and from wherever you look, the universe would look roughly the same.

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Following the recent announcement about the giant ring structure, as in previous such cases, it has been argued that these structures are so large that they would challenge the **cosmological principle**. If that statement was true, it would be remarkable, as the cosmological principle is at the very foundation of our modern understanding of the structure of the Universe. The cosmological principle is a statement about the spatial symmetries of the Universe. However, such pronouncements stem from a misunderstanding of the cosmological principle itself. I argue that even the largest known structure itself cannot challenge the cosmological principle, since correctly understood it is a statement about the statistical distribution of matter and light in the Universe, and not a claim about the particular size of anything.

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The cosmological principle is a convenient starting point in modelling the Universe, as it allows us to make up for our lack of knowledge of what happened soon after the Universe came into existence. In short, the cosmological principle is an assumption that space is maximally symmetric. In other words, whichever direction you look and from wherever you look, the universe would look roughly the same. This assumption was originally invoked by Einstein in his very first attempt to find a cosmological solution in the context of his new theory of general relativity. The assumption of maximal symmetry does not come out of the blue, it is a property that also holds for space in Newtonian physics, where the Euclidean geometry is used to describe a pre-existing absolute space. That absolute space does not exhibit any preferred direction and it does not have any preferred place, thus exhibiting six possible symmetry operations, consisting of all translations (move an object) and all rotations (turn an object) that you can think of. In some sense, Einstein just assumed what was a standard assumption about space at the time.

About a decade after Einstein published his theory of General Relativity, and due to works of Lemaître, Hubble and others, it became clear that space expands and that the static picture of space should be given up, but the assumption of maximal spatial symmetry was kept. Shortly after the end or the second world war, Lifshitz and others started to study the question of gravitational stability and the formation of gravitationally bound structures (structures that are held together by the force of gravity) and it became clear that structures can form via gravitational collapse of small fluctuations of matter density. However, this model could not answer why there are just tiny seed fluctuations apart an otherwise highly symmetrical Universe and how do they would come along. In the 1980s it was then realised that if the Universe started in a state of even higher (approximate) symmetry, a so-called quasi-de Sitter space in which not only space is maximally symmetric, but actually space-time is close to being maximally symmetric. Furthermore, speculation about such an epoch of so-called cosmological inflation, a short episode of extremely rapid and accelerated expansion of space, would supposedly erase all information from any pre-existing state but at the same time seed, via unavoidable **quantum fluctuations**, tiny ripples in the fabric of space and time and matter distribution, which would much later on, grow via gravitational instability to form structures on all cosmological scales. Small structures would form first and larger structure later, a process that is known as **hierarchical structure formation**.

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In theory, large scale structures could either form after the end of cosmological inflation or before it. If cosmological inflation lasted for a relatively short time, we could in principle trace some relics from the epoch before inflation on super-large scales. But more on that later.

Returning to the cosmological principle, how can we test it and what does it actually say. Many textbooks on cosmology give a formulation that says that space is isotropic (symmetric under rotation) and homogeneous (symmetric under translations) at large enough scales, but they do not specify that any further. In my opinion that formulation is useless, and actually not testable.

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We should formulate the cosmological principle slightly differently, namely that the statistical distribution of matter and light in the Universe is homogeneous and isotropic.

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One possibility would be to assume an exact symmetry and claim it on all scales, but that is obviously wrong. In order to avoid that, often a so-called homogeneity scale is introduced, above which the symmetries of the cosmological principle should hold. The way this scale is measured is by counting the number of galaxies in a sphere of increasing radius. If matter was homogeneously distributed, then the number of galaxies should increase proportionately to the volume of the sphere. For small spheres this is actually not the case - this rule only applies once the radius of the spheres involved in this test exceeds about 300 million light years (the typical distance between two galaxies is about 3 million light years), which is then declared to be the scale of homogeneity. This homogeneity scale is actually defined by that counts-in-spheres test and does not imply that there are no larger structures. It is just a statement on how large a volume we need to sample in order to cover a fair or representative bit of the Universe. The cosmological principle does not predict how big that scale should be and thus finding a structure that is larger than that homogeneity scale does not question the cosmological principle. Another concept is the so-called Hubble scale, which is the distance that a light signal could travel from the birth of the Universe until today, assuming that the Universe was always in today’s state of expansion. That distance is about 1.2 billion light years in one direction, thus it would limit structures to 2.4 billion light years across their largest diameter. Some colleagues assume that as the upper limit for large scale structures. The newly found ring comes close to that but still does not exceed it.

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Thus, a Universe in which we can see giant rings structures is in line with the cosmological principle, as long as the probability of finding them in all directions and from any location is the same.

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But I would argue that relating any of those scales to the cosmological principle is still a wrong take. As it is obvious that the world around us on small scales is full of structures, I would instead argue that we should formulate the cosmological principle slightly differently, namely that the statistical distribution of matter and light in the Universe is homogeneous and isotropic. That means that the probability of finding a galaxy with some given properties is the same in any direction on the sky (apart from apparent obstacles, e.g. we cannot look through the centre of the Milky Way), and that an observer sitting in another galaxy would have the same probability as we do to see the Universe like we do. Thus, a Universe in which we can see giant rings structures is in line with the cosmological principle, as long as the probability of finding them in all directions and from any location is the same. However, what such giant structures put into question is the prevailing model of a long duration inflationary epoch (in which all pre-existing structures are stretched out to sizes that exceed the size of the observable Universe), followed by the hierarchical structure formation picture as outlined above, as structures well above a billion light years in size, would indeed be very hard to generate. Thus the new findings might challenge our understanding of structure formation, but I don’t see that they challenge a properly formulated cosmological principle.

To learn about the Universe we have to measure and observe, try to model what we see, and if we fail, we have to check the observations and the model until both agree with each other. The new observation of this giant ring might be the start of another of these cycles.

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