Compactification

What the term means here

The procedure of taking a higher-dimensional theory and rolling up the extra dimensions on a small compact internal manifold, leaving an effective four-dimensional theory. In string theory the internal space is typically a Calabi-Yau manifold.

Why it matters to this question

Compactification is the bridge between a ten- or eleven-dimensional theory and any statement about four-dimensional cosmology. It is also where the trouble starts: the procedure introduces the moduli whose stabilization is the central technical problem.

What this does not establish

That compactification is a well-defined mathematical procedure does not establish that any particular compactification describes our universe, or that the resulting four-dimensional effective theory remains valid where it is being used.