By Steven Weinberg
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Additional info for The First Three Minutes - A Moderm View of the Origin of the Universe
In the early era of the universe, the size of the universe varied as a Figure 3. Birkhoff's Theorem and the Expansion of the Universe. A number of galaxies are shown, together with their velocities relative to a given galaxy G, indicated here by the lengths and directions of the attached arrows. ) Birkhoff's theorem states that in order to calculate the motion of a galaxy A relative to G, it is only necessary to take into account the mass contained within the sphere around G that passes through A, shown here by the dashed line.
The universe is symbolized here as a sphere, at four moments separated by equal time intervals. The 'horizon' of a given point P is the distance from beyond which light signals would not have had time to reach P. The part of the universe within the horizon is indicated here by the unshaded cap on the sphere. The distance from P to the horizon grows in direct proportion to the time. On the other hand, the 'radius' of the universe grows like the square root of the time, corresponding to the case of a radiationdominated universe.
De Sitter. Although this solution appeared to be static, and was therefore acceptable according to the cosmological ideas of the times, it had the remarkable property of predicting a red shift proportional to the distance! The existence of large nebular red shifts was not then known to European astronomers. However, at the end of World War I news of the observation of large red shifts reached Europe from America, and de Sitter's model acquired instant celebrity. In fact, in 1922 when the English astronomer Arthur Eddington wrote the first comprehensive treatise on general relativity, he analysed the existing red-shift data in terms of the de Sitter model.
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