On the consistency of universally non-minimally coupled $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ theories

Abstract

We discuss the consistency of a recently proposed class of theories described by an arbitrary function of the Ricci scalar, the trace of the energy-momentum tensor and the contraction of the Ricci tensor with the energy-momentum tensor. We briefly discuss the limitations of including the energy-momentum tensor in the action, as it is a non fundamental quantity, but a quantity that should be derived from the action. The fact that theories containing non-linear contractions of the Ricci tensor usually leads to the presence of pathologies associated with higher-order equations of motion will be shown to constrain the stability of this class of theories. We provide a general framework and show that the conformal mode for these theories generally has higher-order equations of motion and that non-minimal couplings to the matter fields usually lead to higher-order equations of motion. In order to illustrate such limitations we explicitly study the cases of a canonical scalar field, a K-essence field and a massive vector field. Whereas for the scalar field cases it is possible to find healthy theories, for the vector field case the presence of instabilities is unavoidable.

Minor changes, version published matching Phys. Rev. D 91 (2015) 104003. 15 pages, no figures

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• Role of $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ Model on the Stability of Cylindrical Stellar Model
• Study of Decoupled Anisotropic Solutions in $f(R,T,R_{\rho \eta }{T}^{\rho \eta })$ Theory
• Effects of Non-minimal Matter-geometry Coupling on Embedding Class-one Anisotropic Solutions
• Extended Decoupled Anisotropic Solutions in $f(\mathcal{R},\mathcal{T},{\mathcal{R}}_{\gamma \chi }{\mathcal{T}}^{\gamma \chi })$ Gravity
• Cosmological implications of Rastall-$f(R)$ theory
• Particle creation and decay in nonminimally coupled models of gravity
• Non-minimal Energy-momentum squared gravity
• Role of $\sigma R^2+\gamma R_{\mu \nu }{T}^{\mu \nu }$ Model on Anisotropic Polytropes