Comparing selfinteracting scalar fields and R + R^3 cosmological models

TL;DR

This paper explores the relationship between self-interacting scalar fields and specific modified gravity models, particularly R + R^3 theories, analyzing their properties and establishing a conformal equivalence theorem.

Contribution

It extends known analogies to include   interactions and proves a general conformal equivalence between certain Lagrangians and scalar fields.

Findings

R + R^3 models effectively represent self-interacting scalar fields.

Masses of spin 0-parts coincide in linearized models.

Established a general conformal equivalence theorem.

Abstract

We generalize the well-known analogies between m^2 \phi^2 and R + R^2 theories to include the selfinteraction \lambda \phi^4-term for the scalar field. It turns out to be the R + R^3 Lagrangian which gives an appropriate model for it. Considering a spatially flat Friedman cosmological model, common and different properties of these models are discussed, e.g., by linearizing around a ground state the masses of the resp. spin 0-parts coincide. Finally, we prove a general conformal equivalence theorem between a Lagrangian L = L(R), L'L" \ne 0, and a minimally coupled scalar field in a general potential.