Anisotropic singularities in modified gravity models

TL;DR

This paper demonstrates that anisotropic singularities in modified gravity models with scalar fields are fundamentally linked to hypersurfaces where certain functions vanish, leading to unavoidable instabilities that challenge model viability.

Contribution

It reveals the physical origin of singularities in complex modified gravity models and shows their connection to anisotropic instabilities at specific hypersurfaces.

Findings

Anisotropic instabilities are tied to the hypersurface F(φ)=0.

Such instabilities lead to unavoidable singularities.

Models with ∂f/∂R=0 hypersurfaces are generally not physically viable.

Abstract

We show that the common singularities present in generic modified gravity models governed by actions of the type $S=\int d^4x \sqrt{-g}f(R,\phi,X)$, with $X= -{1/2}g^{ab}\partial_a\phi\partial_b\phi$, are essentially the same anisotropic instabilities associated to the hypersurface $F(\phi)=0$ in the case of a non-minimal coupling of the type $F(\phi)R$, enlightening the physical origin of such singularities that typically arise in rather complex and cumbersome inhomogeneous perturbation analyses. We show, moreover, that such anisotropic instabilities typically give rise to dynamically unavoidable singularities, precluding completely the possibility of having physically viable models for which the hypersurface $\frac{\partial f}{\partial R}=0$ exists. Some examples are explicitly discussed.