Invariant quantities in the multiscalar-tensor theories of gravitation

Abstract

The aim of the current paper is to study the multiscalar-tensor theories of gravity without derivative couplings. We construct a few basic objects that are invariant under a Weyl rescaling of the metric and transform covariantly when the scalar fields are redefined. We introduce rules to construct further such objects and put forward a scheme that allows to express the results obtained either in the Einstein frame or in the Jordan frame as general ones. These so called translation rules are used to show that the parametrized post-Newtonian approximation results obtained in the aforementioned two frames indeed are the same if expressed in a general frame.

11 pages, references added and updated, a few typos corrected

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• Scalar-torsion theories of gravity III: analogue of scalar-tensor gravity and conformal invariants
• Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories
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• Frame-invariant approach to higher-dimensional scalar-tensor gravity
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• Post-Newtonian parameter $\gamma$ for multiscalar-tensor gravity with a general potential
• A minimal model of inflation and dark radiation
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• Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories
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• Multiple point criticality principle and Coleman-Weinberg inflation
• Conformal frames in cosmology
• Static spherically symmetric configurations with N non-linear scalar fields: global and asymptotic properties
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• Global Portraits of Nonminimal Inflation: Metric and Palatini
• Field transformations and invariant quantities in scalar-teleparallel theories of gravity
• Global Portraits of Inflation in Nonsingular Variables
• On Conformal Transformation with Multiple Scalar Fields and Geometric Property of Field Space with Einstein-like Solutions