Spontaneous decompactification

Positive vacuum energy together with extra dimensions of space imply that our fourdimensional Universe is unstable, generically to decompactification of the extra dimensions. Either quantum tunneling or thermal fluctuations carry one past a barrier into the decompactifying regime. We give an overview of this process, and examine the subsequent expansion into the higher-dimensional geometry. This is governed by certain fixed-point solutions of the evolution equations, which are studied for both positive and negative spatial curvature. In the case where there is a higher-dimensional cosmological constant, we also outline a possible mechanism for compactification to a four-dimensional de Sitter cosmology. † Email address: [email protected] ∗ Current address. ‡ Email address: [email protected]