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

Abstract

We generalize the well-known analogies between m^2 ϕ^2 and R + R^2 theories to include the selfinteraction λϕ^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.

16 pages, LaTeX

Cited by in corpus (19)

• Extended Theories of Gravity
• Palatini form of 1/R gravity
• Higher order gravity theories and scalar tensor theories
• Field-theoretical formulations of MOND-like gravity
• Fourth order gravity: equations, history, and applications to cosmology
• On Wormhole Throats in $f(R)$ Gravity Theory
• Exact solutions of three dimensional black holes: Einstein gravity vs F(R) gravity
• Primordial Gravitational Wave Signals in Modified Cosmologies
• F(R) gravity's rainbow and its Einstein counterpart
• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
• Gauss-Bonnet lagrangian G ln G and cosmological exact solutions
• Gravitoelectromagnetism and other decompositions of the Riemann tensor
• Eguchi-Hanson like space-times in F(R) gravity
• Effective gravitational equations for f(R) braneworld models
• The dynamical equivalence of modified gravity revisited
• Asymptotically Lifshitz black hole solutions in F(R) gravity
• Restricting Fourth Order Gravity via Cosmology
• Testing theories of Gravity and Supergravity with inflation and observations of the cosmic microwave background
• Generalized unimodular gravity as a form of k-essence