Look around right now. You may have a computer in front of you, a coffee cup to the left, a wall to the right. There is probably a light of some sort in your immediate vicinity, and a door you can point to. Now think about things that are further away. The building you are in is situated in a particular place, the sun or moon are somewhere in the sky, the night sky is filled with stars and planets you can point to. We live within a particular galaxy, and this galaxy has neighbors with the Andromeda galaxy being the largest. This is all to say that the universe as it looks now is inhomogeneous– it looks different in different places. Its what allows the phrases ‘over there’ or ‘I am here’ to make sense. If we were to run the history of the universe backwards to the big bang we would see this inhomogeneity slowly disappear: stars would disperse into the gas and dust clouds from which they were born, galaxies would get closer and closer until they appeared to be an indistinguishable mush of gas and dark matter, and the light from the afterglow of the big bang would have (nearly) the same intensity in all directions. Far enough back in time, the universe would look like a thick and completely disorienting omnidirectional fog; there would be no sense of ‘here’ or ‘there’.
But if you looked close enough the seeds which would grow into galaxies, and stars, and planets, and computers, and coffee cups, and buildings with doors are there. These seeds take the form of minute fluctuations in the density of this primordial fog. Over time gravity does the job of causing those regions which are more dense to collapse and coagulate into things, and those regions which are less dense to become the vast cosmic voids that separate galaxies.
As a cosmologist I have been interested in quantifying these initial (small) fluctuations in the density of the universe. To get a visual sense of what it might mean to quantify these fluctuations, imagine just looking at a two dimensional slice of the universe. Using a paper to represent this slice, place dots on the paper where the density is higher than at other locations. You could think of this as identifying the highest points (peaks) on a topographical map. Maybe these peaks form a regular pattern, like a grid. Or, possibly they are at random locations. We can use the observed location of galaxies in the universe to distinguish between these two possibilities, and from actual observations, it is clear that the density peaks are clustered together in an otherwise random distribution.
I have worked on several aspects of cosmological perturbations including: