Conformal Transformations with Multiple Scalar Fields

Abstract

Many interesting models incorporate scalar fields with non-minimal couplings to the spacetime Ricci curvature scalar. As is well known, if only one scalar field is non-minimally coupled, then one may perform a conformal transformation to a new frame in which both the gravitational portion of the Lagrangian and the kinetic term for the (rescaled) scalar field assume canonical form. We examine under what conditions the gravitational and kinetic terms in the Lagrangian may be brought into canonical form when more than one scalar field has non-minimal coupling. A particular class of two-field models admits such a transformation, but models with more than two non-minimally coupled fields in general do not.

17 pages, no figures. References added to match published version.

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• Auxiliary fields representation for modified gravity models
• Inflation in models with Conformally Coupled Scalar fields: An application to the Noncommutative Spectral Action
• Primordial Perturbations from Multifield Inflation with Nonminimal Couplings
• Gauge invariant cosmological perturbations for the nonminimally coupled inflaton field
• Non-Gaussianities of Single Field Inflation with Non-minimal Coupling
• Non-minimally coupled hybrid inflation
• Gravi-Natural Higgs and Conformal New Physics