Present models of the universe hold two fundamental premises: the cosmological principle and the dominant role of gravitation. Derived by Hubble, the cosmological principle holds that if a large enough sample of galaxies is considered, the universe looks the same from all positions and in all directions in space. The second point of agreement is that gravitation (or an antigravitation force, called dark energy) is the most important force in shaping the universe. According to Einstein's general theory of relativity, which is a geometric interpretation of gravitation, matter produces gravitational effects by actually distorting the space about it; the curvature of space is described by a form of non-Euclidean geometry. A number of cosmological theories satisfy both the cosmological principle and general relativity. The two main theories are the big-bang hypothesis and the steady-state hypothesis, with many variations on each basic approach.

The earliest pre-Ptolemaic theories assumed that the earth was the center of the universe (see Ptolemaic system). With the acceptance of the heliocentric, or sun-centered, theory (see Copernican system), the nature and extent of the solar system began to be realized. The Milky Way, a vast collection of stars separated by enormous distances, came to be called a galaxy and was thought to constitute the entire universe with the sun at or near its center. By studying the distribution of globular star clusters the American astronomer Harlow Shapley was able to give the first reliable indication of the size of the galaxy and the position of the sun within it. Modern estimates show it to have a diameter of about 100,000 light-years with the sun toward the edge of the disk, about 28,000 light-years from the center.

During the first two decades of the 20th cent. astronomers came to realize that some of the faint hazy patches in the sky, called nebulae, are not within our own galaxy, but are separate galaxies at great distances from the Milky Way. Willem de Sitter of Leyden suggested that the universe began as a single point and expands without end. After studying the red shift (see Doppler effect) in the spectral lines of the distant galaxies, the American astronomers Edwin Hubble and M. L. Humason concluded that the universe is expanding, with the galaxies appearing to fly away from each other at great speeds. According to Hubble's law, the expansion of the universe is approximately uniform. The greater the distance between any two galaxies, the greater their relative speed of separation.

At the end of the 20th cent. the study of very distant supernovas led to the belief that the cosmic expansion was accelerating. To explain this cosmologists postulated a repulsive force, dark energy, that counteracts gravity and pushes galaxies apart. It also appears that the universe has been expanding at different rates over its cosmic history. This led to a variation of the big-bang theory in which, under the influence of gravity, the expansion slowed initially and then, under the influence of dark energy, suddenly accelerated. It is estimated that this cosmic jerk occurred five billion years ago, about the time the solar system was formed. This theory postulates a flat, expanding universe with a composition of c.70% dark energy, c.30% dark matter, and c.0.5% bright stars.

A number of questions must be answered, however, before cosmologists can establish a single, comprehensive theory. The expansion rate and age of the universe must be established. The nature and density of the missing mass, the dark matter and dark energy that is far more abundant than ordinary, visible matter, must be identified. The total mass of the universe must be determined to establish whether it is sufficient to support an equilibrium condition—a state in which the universe will neither collapse of its own weight nor expand into diminishing infinity. Such an equilibrium is called omega equals one, where omega is the ratio between the actual density of the universe and the critical density required to support equilibrium. If omega is greater than one, the universe would have too much mass and its gravity would cause a cosmic collapse. If omega is less than one, the low-density universe would expand forever. Today the most widely accepted picture of the universe is an omega-equals-one system of hundreds of billions of galaxies, many of them clustered in groups of hundreds or thousands, spread over a volume with a diameter of at least 10 billion light-years and all receding from each other, with the speeds of the most widely separated galaxies approaching the speed of light. On a more detailed level there is great diversity of opinion, and cosmology remains a highly speculative and controversial science.