In everyday life there are many forces that strongly affect the world around us: friction, electric, magnetic, etc. But in the universe at large there is only one predominant force: gravity. It is gravity that determines the structure of the universe at large.
The (visible) universe is filled with galaxies (see Fig.8.12) each containing a billion suns (more or less) tightly bound by their mutual gravitational atraction. Because of this we can think of a galaxy as a solid object of a given mass (in the same way that when you look at the gravitational pull of the Earth on the Moon you don't have to worry about the fact that they are made of atoms; the stars are the ``atoms'' which make up galaxies).
In this simplified picture the visible matter in the universe (that which shines) is concentrated in a dusting of galaxies. In addition the universe can contain matter which does not shine, such as planet-sized objects, cold dust and, perhaps, other more exotic objects (see Sect. 8.5). The universe also contains electromagnetic radiation: for example, stars continuously give off light and heat (infrared radiation) which then disperses throughout the universe (this is why we can see them!). Finally the universe contains a significant amount of microwaves (see Sect. 8.4.2) and neutrinos, (see Sect. 8.5.1), both relics from a very early time.
The first person to look at the cosmos through the eyes of the General Theory of Relativity was Einstein himself. He took the above picture of a universe filled with matter and radiation he added two assumptions
To Einstein's initial surprise there were no steady solutions: the universe according to the General Theory of Relativity must expand or contract. He compared this result with the best observational data of the time and found, to his dismay, that the observations strongly favored a steady universe. He then made what he called ``the greatest scientific blunder of my life'': he modified the equations of the General Theory of Relativity by adding a term that countered the expansion or contraction present in his initial solutions . With this ad hoc modification he did find a steady universe and was (temporarily) satisfied.
Not long afterwards Hubble published his now famous observations that demonstrated that our universe is, in fact, expanding; and the manner in which it expands agrees with the predictions of the solutions first obtained by Einstein. It was then that Einstein, to his satisfaction, dropped his modification of the equations. But this was not the end of this saga: the added term, like the genie from the bottle, refused to disappear, showing up in many models (recent observations suggest that it must be included in order to account for the observations). I will come back to this in Sect. 8.5.2.
What Hubble did was to measure the red-shift of a group of galaxies whose distances he knew (there were no blue-shifted galaxies, which means that these galaxies were receding from the Milky Way). Using the measured red-shift and the formulas for the Doppler effect, he found the speed at which they receded. Then he made a plot ( called now a ``Hubble plot'') of velocity vs. distance and found that, as predicted by the General Theory of Relativity all points fall in a straight line (see Fig. 8.13); the slope of this line is called Hubble's constant. General Relativity then predicts that the distance d to an object is related to its velocity v (both measured with respect to the Earth) by
which is called Hubble's law and Ho is Hubble's constant, its value is approximately
It is the above relation between distance and velocity that is used to measure distances beyond 109 l.y.: the final step in the cosmic distance ladder. Needless to say astronomers have verified Hubble's law for distances below 109 l.y. using supernovae (Sect. 8.3). In order to find the distance to the farthest objects in the universe one first obtains their redshift and, using Doppler's formulas, derives the velocity v of the object. The distance is then v/Ho.