In this short article I am going to briefly discuss the distribution of matter in the Universe at different scales as well as to give some basics of modern cosmology.
Let me start with the first smallest scale interesting from the cosmological point of view - the size of the Solar system. This size is about 50 AU (Astronomical Units) ≈ 7.5 billion km (kilometers) if we decide to set the boundary of the Solar system at the Pluto's orbit. The gravitational field of the Sun dominates over the field of nearest stars up to the scale ≈ 2×10^13 km = 20000 billion km. This scale can be also considered as the size of the Solar system in some sense, although the average density of matter (gas, dust, etc.) is extremely low beyond 100 billion km distance from the Sun.
The main source of visible light in the Universe is nuclear fusion within stars (mainly, hydrogen into helium). Our Sun is a typical yellow dwarf star with approximate mass 10^30 kg - 100 times more massive than all planets of the Solar system combined. One can say that we live in the gravitational well of a rather small star, since there exist stars within our Galaxy 100 times heavier than the Sun. If we consider only nearest stars, the scale of the box containing them is of the order 1 light year, the length of the path passed by a ray of light during one year. For example, the closest star, Proxima Centauri, is 3.261 light years ≈ 1 parsec (Pc) away from us. The name of the unit "Parsec" comes from the fact that Proxima Centauri has a parallax of approximately 1 arcsecond. Taking into account that the velocity of light is about 300000 km/second, one can check that 1 light year ≈ 10^13 km, while 1 parsec is ≈ 3×10^13 km.
The size of the box containing nearby stars is therefore about 1 parsec. If we increase the size of this box 1000-fold, we find that clusters of stars, interstellar gas, dark matter are combined into gravitationally bound conglomerates of matter called galaxies. The Solar system is located way off center in our Galaxy within what is called the Orion spiral arm. The name is due to the fact that stars from the Orion constellation such as the red giant Betelgeuse - the ninth brightest star on the sky - belong to the same arm.
The typical number of stars within a galaxy is extremely large. For example, our native Galaxy (the Milky Way) contains 100 billion (thous. million) stars. It has a form of disk with the radius 12500 parsecs and the thickness of only about 300 parsecs. This extremely thin disk is rotating differentially with the full period of about 200 million years - so, dinosaurs were wiped out from the face of the Earth during the previous galactic year. Large old galaxies (including the Milky Way) have usually a form of spiral. The reason is that rotating disk of gravitationally interacting dust particles is unstable, and this gravitational instability breaks the disk into a spiral-like structure. The characteristic length scale of the box containing only our Galaxy but not other galaxies is 10000 light years.
Let us now again increase the size of the box, 10-fold this time. We will find that the Milky Way resides within a small concentrated group of galaxies (LGG). All the adjacent galaxies in this box are much smaller than the Milky Way being located within its gravitational well (in other words, they are satellites of our Galaxy in the same sense as the Moon is the satellite of the Earth). The closest galaxy to the Milky Way is Large Magellanic Cloud (50 kiloparsecs, that is, 50000 parsecs ≈ 1.5×10^18 km away). The nearest galaxy of the size of our own (actually slightly larger) is 770000 parsecs away and is named the Andromeda galaxy. A typical local group of galaxies occupies a volume of few cubic Megaparsecs, i.e., millions of parsecs. Megaparsec is a cosmologist's favorite unit, 1 MPc ≈ 10^22 m. These groups of galaxies in turn are grouped themselves into galaxy clusters (some of these clusters contain more than 10000 galaxies). Our local group is within the gravitational well of the so called Virgo Cluster.
Let us again increase the size of the box 10-fold. Not surprisingly, it turns out that galaxy clusters are combined into superclusters, but surprising it is that the latter are the largest gravitationally-collapsed objects in Nature - in other words, there is no such thing as supersuperclusters of galaxies in the Universe. The structure of superclusters and their interplay due to the gravitational interaction becomes noticeable at scale about several hundreds of millions of light years or hundreds of megaparsecs. Namely, superclusters are joined by filaments and walls of galaxies creating a foam-like structure of matter and gravitational potential called the Cosmic Web. Voids in this Web are as large as 50 megaparsecs across.
Understanding that the structure of the Cosmic Web is defined by the gravitational instability and the latter needs some time to develop, on can conclude from the fact that superclusters are the largest collapsed objects that the age of the universe was finite and, moreover, its initial state was highly symmetric. Indeed, let us again increase 10 times the scale of the box. What we will find is the map of the Universe (approx. 2 million of nearby galaxies) with characteristic scale about 3000 megaparsecs. This coincides with the size of the observable patch of the Universe - that is, we are unable to probe the physics beyond this scale even with the best astronomical instruments we currently have (like Hubble Space Telescope). Within this patch of the 1 gigaparsec size, the Universe is extremely smooth, homogeneous and isotropic. In a sense, that is why qualitative discussion of the evolution of the Universe is possible at all and cosmology can be considered a legitimate daughter of astronomy. Of course, fluctuations of the matter density are present in this homogeneous Universe (we are living within one such fluctuation), but their relative amplitude is about 10^-4 ∼ 10^-5 at scales of the order 1 gigapersec.
Although cosmologists do not have any data on the distribution of matter and gravitational potential at scales larger than 1 gigaparsec, theory shows that the qualitative picture above does not change up to the scale of 13 billion light years (the cosmological horizon scale) , although the relative amplitude of fluctuations starts to slightly grow while the scale gets larger and larger. Standard inflationary paradigm predicts as well that the relative amplitude of fluctuations of the gravitational potential keeps growing until it becomes of the order of 1 at the so called eternal inflation scale LvEI ∼ 13 billion light years × e^N, where the number N is more than 60 and depends on particular inflationary model. While the Universe is homogeneous and isotropic at scales below, it again ceases to be homogeneous and isotropic at L > L^EI. Moreover, it can be considered fractal in a certain sense - the structure of the gravitational potential at these huge scales turns out to be self-reproducing.
Thinking in terms of propagating light and recalling that the speed of light is the largest possible speed in Nature, one can understand that distance or length scale in general relativity - theory governing physics at astronomical scales - is quite the same thing as time scale. In other words, larger distances correspond to earlier stages in the evolution of our Universe because more time had to pass for light from distant objects to reach us. Observing the Universe, we are watching a movie, its first shot corresponding to extremely distant objects on the sky and the last - to physics at scales of the order of the Solar system's size.
