In this paper we investigate a model of an inflationary universe in Kaluza-Klein theory , which is a four-dimensional de Sitter space plus a one-dimensional compactified internal space .
We find that the energy scale for inflation can be predicted from the fine-structure constant in a self-consistent solution of the semi-classical Einstein equations including the Casimir effect .
From the observed value of the fine-structure constant , we obtain an energy scale for inflation of \epsilon = 1.84 \times 10 ^ { 16 } g _ { * } ^ { 1 / 4 } Gev , where g _ { * } is a dimensionless number depending on the spin and number of matter fields existing in the universe .
This value is consistent with the values often discussed for inflation and grand unification .
The wave function for this model predicts a high probability for forming such universes , independent of the value of the cosmological constant .
The tunneling probability favors the creation of inflationary universes with a compactified dimension , over those with all macroscopic dimensions .