What is this thing we call the universe? Sounds like a trivial question, nothing to worry about. Or, as a cynic would say, "Who cares?"
It turns out that understanding the nature of the universe goes hand in hand with our understanding of who we are and how we fit into nature. To see this, consider how a person of the 16th century thought of the world.
Earth was the center of creation, immobile, while everything else turned around it: moon, planets, sun, stars. The universe was spherical, onion-like, and finite: outside the celestial orbs was the Primum Mobile, the sphere responsible for imparting motion to the inner spheres. Outside the Primum Mobile was the Empyrean, the realm of God and his court of divine beings, made of pure light. People lived in a finite, spherical cosmos, with a clear vertical hierarchy: the goal of earthly life was to pave the way to the final ascendancy into Heaven. In other words, people's lives and ambitions mirrored, in a direct way, the geometry of the universe.
Of course, everything changed after Copernicus and, more dramatically, after Kepler, Galileo, Descartes, and Newton established the sun-centered cosmos.
Newton, in particular, opened the cosmos from its finiteness, proposing that only an infinite universe could be stable against gravitational collapse (albeit only through the occasional action of God). In an infinite universe, the verticality that defined people's spiritual quest was lost. Still, the Newtonian cosmos was static: space was simply the background arena, the stage wherein natural phenomena unfolded.
When we get to Einstein and 20th-century cosmology, things get subtle. Space and time are now a single entity called spacetime. This four-dimensional mesh is not a simple background anymore but has a dynamic nature, sensitive to the distribution of matter and energy. With Einstein, space and time gained plasticity.
To study the universe meant not only studying the things that exist within the universe, but studying the universe itself. In a very real sense, there was no longer a clear separation of the universe and the things it contains.
Here things get a bit confusing. How then do we define the universe? A first answer could be "the set of things within the volume of space we can measure." What things? Galaxies, stars, planets, galaxy clusters, black holes, that is, objects that we can probe with our instruments and clearly determine their physical properties: mass, chemical composition, velocity, rotation, etc. This collection of objects is the focus of most of astronomy and astrophysics. We can then think of the universe, at this first level of definition, as the set of objects it comprises.
Of course, there are also things we can measure but don't know what they are. I'm thinking of dark matter—particles of an unknown nature that have so far eluded detection but that pull gravitationally on galaxies and clusters of galaxies—and of dark energy—the mysterious force that is increasing the rate of cosmic expansion. There is also the energy of the vacuum, which may or not be related to dark energy. And there are certainly things we haven't measured yet.
So, we could make a long shopping list of cosmic objects and claim that they are the universe. Or is that pushing it too far? The universe is not just the things it contains, right?
What, then, is the universe? The difficulty is that the universe is not a "thing" in the sense that a star or a galaxy is a thing. We can measure physical quantities that define properties of the universe, such as the temperature fluctuations of the cosmic microwave background radiation (CMB)—the left-over radiation from the time the first atoms appeared some 400,000 years after the Big Bang—or the cosmic rate of expansion. But even these measures are not of the universe but of things in the universe. The CMB is like water in the bathtub, not the bathtub itself; the cosmic expansion rate is really the measurement of the redshift of distant galaxies, based on their spectra. The inference that it relates to the expansion of the cosmic geometry comes a posteriori, once we see that Einstein's theory of general relativity predicts that the cosmic geometry as a whole could expand or contract.
So, is what we call the universe a solution to an equation obtained through Einstein's theory? Not really, since to get to this equation we go through a series of approximations. Einstein's equations model the universe, that is, they attempt to describe its most salient features, so that we can establish a connection between the theory (that generates the equation) and the observations that test it. But we should never equate the solution to a model equation to the real thing.
The universe, then, is more a concept than a thing.
The usual parlance equates the word universe to the things it contains (galaxies, CMB ... ) and to its geometry (curved, flat, static, expanding ... ) In fact, even at the more abstract level of the theories that attempt to model the origin of the universe as a physical process, part of so-called quantum cosmology, when we compute the probability that a given universe will appear from "nothing," we equate the universe with an entity with a given geometry and material content.
Other geometries and matter content imply other model universes. However, these models are far from being the real thing. Physics is the art of approximations, a device we have to describe the world we measure. Sometimes, however, we get carried away, and ascribe reality to what are, in essence, thinking tools.
I know this may sound heretic, but it seems that the universe is one of these thinking tools.
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