falcon32 said:
Alright thank you, didn't realize I could wiki it. I've got much to learn...exciting to see the equation that Einstein modified. Did a bit of reading...this equation was created before Hubble discovered the expanding universe, right? So do astronomers still use just this one, or have they made a special one from empirical redshift observations alone?
Yes, the Friedmann equations are derived from the
Einstein Field Equations of General Relativity, and Einstein finished formulating General Relativity in 1915, a few years before Hubble discovered that distant galaxies all appear to be moving away from us.
General Relativity is still the best theory of gravity we have. So, yes, astronomers still use the Friedmann equation in the form given there to this day. However, that is less restrictive than you would think. The Friedman equation doesn't describe a single mathematical model with a single expansion history for the universe, but rather a whole set of models called the "Friedman World Models." The reason for this is that the equations contain certain parameters, and a particular model with a particular expansion rate and history is given by one particular set of values for those parameters. Change the values of the parameters, and you change the outcome predicted by the model. A key task of modern cosmology has been using measurements and observations to figure out which set of parameter values (and hence which world model) accurately describes the universe we live in.
A concrete example may help. One of the main parameters appears in those equations in the form of the density, rho (ρ). A key result of General Relativity is that the geometry of spacetime is affected by its mass-energy content. In the context of the universe as a whole, what this means is that the dynamics of the expansion are affected by the total energy density, ρ, of the universe. This total density rho consists of contributions from all the major constituents: dark energy, dark matter, ordinary matter, and radiation (photons and relativistic particles). There is a separate density parameter for each of these, and we can measure them separately. The total density can be either larger than, equal to, or less than some critical density, ρ
cr. In the classic case (with no dark energy), these three cases lead to the following possibilities:
1. If ρ > ρ
cr, in other words, if there is enough mass in the universe, the universe's expansion slows, stops, and reverses itself, leading to a collapse (the so called "Big Crunch" scenario). You can think of it as there being enough matter in the universe that its mutual gravitation slows down the expansion enough to stop it and reverse it. In this case, there is also positive spatial curvature, meaning that the geometry of the universe is like the geometry on the surface of a sphere.
2. If ρ = ρ
cr, the universe continues to expand forever, albeit at a steadily decreasing rate (there is not enough mass to pull everything back together). In this case, the geometry of the universe is "flat" (meaning that it is Euclidean: it behaves like the geometry you learned in high school). So, at the critical density, there is just enough mass to have no spatial curvature.
3. If ρ < ρ
cr, the universe will also continue to expand forever at a steadily decreasing rate. There will also be negative spatial curvature, meaning that geometry will behave the way it does on the surface of a "saddle."
So, the Friedman equation gives you distinctly different results when you modify the parameters (in this case the total density). Notice that in all three of these scenarios (or "world models"), the universe expands, but that expansion slows down. It turns out that NONE of these three models is right, because in our inventory of the total "mass budget" of the universe, we were missing a major contributor: dark energy. When you throw dark energy into the mix, there is no longer such a straightforward relationship between the mass density of the universe, its geometry (curvature), and its ultimate fate. In the link I sent you, dark energy appears in the form of an additional constant Lambda (##\Lambda##) in the equations. This is the famous "Cosmological Constant." Einstein originally added the cosmological constant because his models predicted that the universe was not static: it could either expand or contract. At the time, this was inconceivable to him. He wanted to make the universe static, so he tried to throw in the extra ##\Lambda## term and tune it to achieve a delicate balance in which the universe neither expanded nor contracted. It turns out that this was futile, because the solutions are unstable. Even if you tune ##\Lambda## to make the universe static NOW, it will not remain so LATER. This was a rookie mistake. If Einstein had stuck to his convictions and followed his own theory to its logical conclusions (the way he did so well when he formulated Special Relativity ten years earlier), he could have
predicted the expansion of the universe before Hubble
observed it. But Einstein just wasn't thinking outside of the box in this case, and he didn't do that. That's why he later referred to the introduction of the cosmological constant as his "greatest blunder." For a long time, ##\Lambda## fell by the wayside.
Recently (in the mid to late 90's), observations of objects called Type Ia supernovae caused people to bring it back. Type Ia supernovae are thought to result from the thermonuclear explosion of a white dwarf star, and as a result, they are thought to be "standard candles" meaning that they all reach roughly the same peak brightness. So, if you look at how bright one of them
appears to be, you can infer its distance. Different Friedman models (with different values for the density parameters)
predict different variations of distance (as measured in this way) with redshift. After all, what use is a theoretical model unless if it makes
testable predictions?
Anyway, by measuring and plotting the Type Ia brightness vs redshift, and finding out which model fits the observed data the best, you can determine the values of the cosmological parameters. In the late 90's, observations of Type Ia supernovae *strongly* favoured a model with a NON-zero value for ##\Lambda##. This result has since been corroborated by observations of the Cosmic Microwave Background (CMB). The presence of ##\Lambda## in the equations was attributed to the presence of some as yet unknown and mysterious substance that astronomers termed "dark energy." Dark energy has weird properties. Even though it adds mass to the universe, it also has a repulsive, anti-gravitational effect. So, instead of pulling things together, it forces them apart. So, not only do the observations show that the universe will continue to expand forever, but it also shows that that expansion, rather than slowing down as we thought, will instead get faster and faster and faster with time. This is a crazy result (it won the 2011 Nobel Prize in physics), and it's an example of what you wanted: empirical observations that improve our understanding of the universe. But they do so
within the theoretical framework of General Relativity (for now). By the way, the observations also show that the geometry of the universe is very close to being flat (Euclidean): i.e. if you include dark energy, the total density is very close to the critical value.
