Primordial spectral indices from generalized Einstein theories

Primordial spectral indices are calculated to second order in slow-roll parameters for three closely related models of inflation, all of which contain a scalar field nonminimally coupled to the Ricci curvature scalar. In most cases, ${\mathit{n}}_{\mathit{s}}$ may be written as a function of the nonminimal curvature coupling strength ξ alone, with ${\mathit{n}}_{\mathit{s}}$(ξ)≤1, although the constraints on ξ differ greatly between ‘‘new inflation’’ and ‘‘chaotic inflation’’ initial conditions. Under ‘‘new inflation’’ initial conditions, there are discrepancies between the values of ${\mathit{n}}_{\mathit{s}}$ as calculated in the Einstein frame and the Jordan frame. The sources for these discrepancies are addressed, and shown to have negligible effects on the numerical predictions for ${\mathit{n}}_{\mathit{s}}$. No such discrepancies affect the calculations under ‘‘chaotic inflation’’ initial conditions.