Induced-gravity inflation

In a Ginzburg-Landau model of induced gravity based on the Lagrangian density L=-ε${\phi }^2$R/2-${\partial }^{\mu }$φ${\partial }_{\mu }$φ/2 -λ(${\phi }^2$-$v^2$ ${)}^2$/8, we investigate the semiclassical evolution of φ from φ≠v to the spontaneous-symmetry-breaking minimum φ=v [v≡${\epsilon }^{\mathrm{-}1/2}$(8πG${)}^{\mathrm{-}1/2}$]. We show that for ε, λ≪1 the transition is inflationary, both in the case that the initial value of φ=0 (‘‘ordinary new inflation’’) and in the case that the initial value of φ≫v (Linde’s ‘‘chaotic’’ inflation). The value of λ required to ensure density inhomogeneities of the proper size is ε dependent and typically ≤${10}^{\mathrm{-}12}$.