Space-time is viewed as a smooth “fabric,” but that smooth fabric can be bent and manipulated in various ways. In relativity, gravity bends our four space-time dimensions, but in string theory more dimensions are bound up in other ways. In relativity and modern cosmology, the universe has an inherent curvature.
The typical approach to string theory’s extra dimensions has been to wind them up in a tiny, Planck length-sized shape. This process is called compac-tification. In the 1980s, it was shown that the extra six space dimensions of superstring theory could be compactified into Calabi-Yau spaces.
Since then, other methods of compactification have been offered, most notably G2 compactification, spin-bundle compactification, and flux compactifica-tion. For the purposes of this topic, the details of the compactification don’t matter.
The wraparound universe
Some cosmologists have considered some extreme cases of space warping in our own universe, theorizing that the universe may be smaller than we think. A new field of cosmology called cosmic topology attempts to use mathematical tools to study the overall shape of the universe.
In his 2008 topic, The Wraparound Universe, cosmologist Jean-Pierre Luminet proposes the idea that our universe wraps around so it has no particular boundary, sort of like the Klein bottle in Figure 13-5. Any direction you look, you may
be seeing an illusion, as if you were standing in a funhouse full of mirrors that appeared to go on forever. Distant stars may actually be closer than expected, but the light travels a larger path along the wraparound universe to reach us.
In this sort of a scenario, the horizon problem from topic 9 ceases to be an issue because the universe is small enough to have become uniform within the timeframe of our universe’s existence. Inflation is consistent with the wraparound universe hypothesis, but many of the problems it fixes are solved in other ways.
To picture compactification, think of a garden hose. If you were an ant living on the hose, you’d live on an enormous (but finite) universe. You can walk very far in either of the length directions, but if you go around the curved dimension, you can only go so far. However, to someone very far away, your dimension — which is perfectly expansive at your scale — seems like a very narrow line with no space to move except along the length.
This is the principle of compactification — we can’t see the extra universes because they’re so small that nothing we can do can ever distinguish them as a complex structure. If we got close enough to the garden hose, we’d realize that something was there, but scientists can’t get close to the Planck length to explore extra compactified dimensions.
Of course, some recent theories have proposed that the extra dimensions may be larger than the Planck length and theoretically in the range of experiment.
Still other theories exist in which our region of the universe only manifests four dimensions, even though the universe as a whole contains more. Other regions of the universe may exhibit additional dimensions. Some radical theories even suppose that the universe as a whole is curved in strange ways.