Cosmology and the Universe: The Big Bang, Dark Matter and Dark Energy 265
be due to a long-range repulsive force, which is being attributed to dark
energy and dark matter. We will discuss these possibilities when we
return to the cosmological implications of Einstein’s General Relativity
Theory and the role of the cosmological constant Λ.
Cosmological Implications of General Relativity
Cosmology endeavors to understand the properties of the universe in
space and time. Consideration of Einstein’s General Theory of Relativity
is essential for understanding why the expansion of the universe is
accelerating and for determining if the universe is finite and closed or
infinite and open. General relativity fuses space and time into a four
dimensional continuum. The properties of the space-time continuum are
related to the gravitational interaction of matter, which is the one
interaction that determines the structure of the universe as a whole. As
we will see the other three basic forces of the strong, electromagnetic and
the weak interactions play an important role in the dynamics of the early
universe.
Einstein showed that the gravitation interaction of matter warps,
curves or bends the four-dimensional space-time continuum changing the
very structure of space and time. Using this notion he successfully
predicted the bending of starlight by the Sun and explained the advance
of the perihelion of Mercury.
Einstein adopted his field equations to deal with the universe as a
whole and found a solution to these equations corresponding to a static
universe. A static universe is one whose size remains fixed. De Sitter
found a second solution to Einstein’s equation also corresponding to a
static universe. Both these models were found to be in contradiction with
observations, however, and had to be abandoned. At approximately the
same time Hubble was demonstrating experimentally that the universe is
expanding, the Russian mathematician A. Fuedman showed that
solutions in which the universe was either expanding or shrinking were
consistent with Einstein’s field equations. From this result, as well as
Hubble’s experimental work, the notion of the expanding universe
developed.
The question of the finiteness or infiniteness of the universe within
the framework of general relativity depends on the nature of the
curvature of the four dimensional space-time continuum. If the curvature
of the space-time continuum is negative, then the universe is open and