We discuss finite-size effects on symmetry breaking in curved space-times with some compact dimensions, and the implications for inflationary cosmologies. Infrared behavior in the de Sitter universe is studied by examination of the lowest-mode contribution to the effective potential for an $N$-component scalar field. We find that at the Planck energy the shape of the effective potential near the symmetric state can significantly deviate from the overall flatness condition necessary for the implementation of new inflation. This effect can in principle rule out Planck-scale inflationary transitions.

• Received 8 August 1985

DOI:https://doi.org/10.1103/PhysRevLett.56.1613