Subatomic Physics

19.1. The Beginning of the Universe 583
potential and inflation terminated. By this time the radius had increased by a factor
of ∼ 10 50 . Ω is driven to unity, since, like a balloon, the surface becomes flatter
as it expands. Thus, the curvature became so small that it remains unimportant
today. In this scenario, the universe begins from a much smaller (∼ 10 −50 )region
than without inflation, and the horizon and homogeneity problems are solved. The
inflationary scenario does not tell us how the universe began, but it allows a wider
variety of early conditions, including vacuum fluctuations and a beginning from
“nothing.” (11)
Fortunately, the uniform smoothness is not complete. Figure19.1 shows the
distribution of temperatures across the sky measured by the WMAP collaboration.
The temperature non-uniformities shown in Fig. 19.1, which are at the level of 1 part
Figure 19.1: Map of temperature differences across the
whole sky. The darker regions are colder and the clearer regions
are hotter. The white lines indicate the polarization
direction. [From WMAP collaboration. (6) ]
Figure 19.2: Power spectrum corresponding
to the data shown in
Fig. 19.1 (see Eq. 19.3.) The continuous
line shows the best fit of a
model that assumes Dark Matter to
be cold (see text). [From WMAP
collaboration. (6) ]
in 105 , are tell-tales of density non-uniformities, i.e. ‘lumps’ in the early universe
matter distribution. In the inflation scenario these non-uniformities were quantum
fluctuations that were amplified by the initial rapid expansion. These lumps are
responsible for the subsequent gravitational aggregation that eventually produced
galaxies and stars. Thus, the inflationary scenario explains several observations in
a rather simple framework. The data of Fig. 19.1 is usually analyzed in terms of its
spherical harmonics:
T (n) = �
almYlm(n), (19.2)
l,m
where n is a unit vector indicating a direction in space. Fig. 19.2 shows the power
spectrum:
Cl = 1 �
|alm|
2l +1
2 . (19.3)
m
11A. H. Guth and P. J. Steinhardt, Sci. Amer. 250, 116 (May 1984); S. Y. Pi, Comm. Nucl.
Part. Phys. 14, 273 (1984); K.A. Olive and D.N. Schramm, Comm. Nucl. Part. Phys. 15, 69
(1985).