John Mather, along with George Smoot, won the Nobel Prize for his work on the Cosmic Background Explorer (COBE), the probe that first caught glimpses of fluctuations in the Cosmic Microwave Background (CMB) left over from the big bang. Those fluctuations are the product of the tiny, random, quantum fluctuations in the Universe immediately after the big bang, which are now visible in the large scale structures of the current Universe, as they produced clusters of galaxies and filaments of dark matter. For his talk at the Lindau Nobel Laureates Meeting, Mather took the audience on both a short history of the Universe, and a history of how we've come to understand it.
Mather started out with some background on the Big Bang—although he said he preferred the term used in a Calvin and Hobbes strip, the "Horrendous Space Kablooie." (We'll continue to use Big Bang for now.) He described how, in the early 1920s, Alexander Friedman applied Einstein's equations to the Universe, and figured it must be expanding. Einstein asked his friends, who told him the Universe couldn't be expanding, so he added the cosmological constant in order to preserve the static universe that everyone thought existed.
Friedman died a few years after and, within a year, Hubble published his famous paper, providing evidence of an expanding universe. ("In the same year we learned that the economy could collapse, we learned that the Universe is expanding," Mather quipped.) Mather showed Figure One of Hubble's paper, with red shift (and therefore speed) rising with a galaxy's distance from the Earth.
Once a consensus formed around the Big Bang model, things went through a bit of a slow period. Information on the stability of free neutrons let theorists calculate the expected elemental abundances of hydrogen and helium, and later, the existence of the CMB was predicted, but there wasn't any obvious way to detect it until Penzias and Wilson's famous experiment at Bell Labs found the faint hiss of the CMB. Now, according to Mather, a dedicated high school student could probably manage it. About one percent of the snowflakes you see when you tune a TV in between channels, Mather said, can be ascribed to the CMB.