Introduction to Cosmology

On cosmological scales (that is, on scales greater than 100 Mpc or so), the dominant force determining the evolution of the universe is gravity. The weak and strong nuclear forces are short-range forces; the weak force is effective only on scales of or less, and the strong force on scales of or less. Both gravity and electromagnetism are long-range forces. On small scales, gravity is negligibly small compared to electromagnetic forces; for instance, the electrostatic repulsion between a pair of protons is larger by a factor than the gravitational attraction between them. However, on large scales, the universe is electrically neutral, so there are no electrostatic forces on large scales. Moreover, intergalactic magnetic fields are sufficiently small that magnetic forces are also negligibly tiny on cosmological scales.

In referring to gravity as a force, we are implicitly adopting a Newtonian viewpoint. In physics, the two useful ways of looking at gravity are the Newtonian (classical) viewpoint and the Einsteinian (general relativistic) viewpoint. In Isaac Newton's view, as formulated by his laws of motion and law of gravity, gravity is a force that causes massive bodies to be accelerated. By contrast, in Einstein's view, gravity is a manifestation of the curvature of spacetime. Although Newton's view and Einstein's view are conceptually very different, in most contexts they yield the same predictions. The Newtonian predictions differ significantly from the predictions of general relativity only in the limit of deep potential minima (to use Newtonian language) or strong spatial curvature (to use general relativistic language). In these limits, general relativity yields the correct result.

In the limit of shallow potential minima and weak spatial curvature, it is permissible to switch back and forth between a Newtonian and a general relativistic viewpoint, adopting whichever one is more convenient. I will frequently adopt the Newtonian view of gravity in this book because, in many contexts, it is mathematically simpler and conceptually more familiar.