On Conformal Transformation with Multiple Scalar Fields and Geometric Property of Field Space with Einstein-like Solutions

Abstract

Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar fields are usually not canonical, which makes analytic treatment difficult. Here we investigate under what conditions the theories can be transformed to the quasi-canonical form, in which case the effective metric tensor in field space is conformally flat. We solve the relevant nonlinear partial differential equations for arbitrary number of scalar fields and present several solutions that may be useful for future phenomenological model building, including the $\sigma$-model with a particular non-minimal coupling. We also find conformal flatness can always be achieved in some modified gravity theories, for example, Starobinsky model.

1+17 pages, 1 table

References in corpus (8)

• Dynamics of dark energy
• Cosmology and the Fate of Dilatation Symmetry
• The Standard Model Higgs boson as the inflaton
• Superconformal Symmetry, NMSSM, and Inflation
• Conformal Transformations with Multiple Scalar Fields
• Higgs inflation from Standard Model criticality
• Inflation from Broken Scale Invariance
• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism

Cited by in corpus (2)

• Gravitational Waves from Preheating in Inflation with Weyl Symmetry
• Cosmic inflation from broken conformal symmetry