Editing M-theory (section)

===Heterotic M-theory===

Because of the difficulties with {{math|''G''<sub>2</sub>}} manifolds, most attempts to construct realistic theories of physics based on M-theory have taken a more indirect approach to compactifying eleven-dimensional spacetime. One approach, pioneered by Witten, Hořava, [[Burt Ovrut]], and others, is known as heterotic M-theory. In this approach, one imagines that one of the eleven dimensions of M-theory is shaped like a circle. If this circle is very small, then the spacetime becomes effectively ten-dimensional. One then assumes that six of the ten dimensions form a Calabi–Yau manifold. If this Calabi–Yau manifold is also taken to be small, one is left with a theory in four-dimensions.<ref name="Yau and Nadis 2010, p. 150"/>

Heterotic M-theory has been used to construct models of [[brane cosmology]] in which the observable universe is thought to exist on a brane in a higher dimensional ambient space. It has also spawned alternative theories of the early universe that do not rely on the theory of [[cosmic inflation]].<ref name="Yau and Nadis 2010, p. 150"/>