Abstract
Cosmology's standard model posits an infinite flat universe forever expanding
under the pressure of dark energy. First-year data from the Wilkinson Microwave
Anisotropy Probe (WMAP) confirm this model to spectacular precision on all but
the largest scales (Bennett et al., 2003 ; Spergel et al., 2003).
Temperature correlations across the microwave sky match expectations on scales
narrower than $60^\circ$, yet vanish on scales wider than $60^\circ$.
Researchers are now seeking an explanation of the missing wide-angle
correlations (Contaldi et al., 2003 ; Cline et al., 2003). One
natural approach questions the underlying geometry of space, namely its
curvature (Efstathiou, 2003) and its topology (Tegmark et al., 2003). In
an infinite flat space, waves from the big bang would fill the universe on all
length scales. The observed lack of temperature correlations on scales beyond
$60^\circ$ means the broadest waves are missing, perhaps because space itself
is not big enough to support them.
Here we present a simple geometrical model of a finite, positively curved
space -- the Poincaré dodecahedral space -- which accounts for WMAP's
observations with no fine-tuning required. Circle searching (Cornish, Spergel
and Starkman, 1998) may confirm the model's topological predictions, while
upcoming Planck Surveyor data may confirm its predicted density of $Ømega_0
1.013 > 1$. If confirmed, the model will answer the ancient question of
whether space is finite or infinite, while retaining the standard
Friedmann-Lema\^ıtre foundation for local physics.
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