Primordial spectral indices from generalized Einstein theories

Abstract

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 \ensuremath{\xi} alone, with ${\mathit{n}}_{\mathit{s}}$(\ensuremath{\xi})\ensuremath{\le}1, although the constraints on \ensuremath{\xi} 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.