f(R) Gravities à la Brans-Dicke

Abstract

We extend f(R) theories via the addition of a fundamental scalar field. The approach is reminiscent of the dilaton field of string theory and the Brans-Dicke model. f(R) theories attracted much attention recently in view of their potential to explain the acceleration of the universe. Extending f(R) models to theories with scalars can be motivated from the low energy effective action of string theory. There, a fundamental scalar (the dilaton), has a non-minimal coupling to the Ricci scalar. Furthermore beyond tree level actions will contain terms having higher (or lower) powers of R compared to the canonical Einstein-Hilbert term. Theories with f(R) will contain an extra scalar degree on top of the ad-hoc dilaton and mixing of these two modes around a stable solution is a concern. In this work we show that no mixing condition mandates the form $V_1(\varphi )f(R)+V_2(\varphi )R^2$ for the action.

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Cited by in corpus (10)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• On the Stability of a class of Modified Gravitational Models
• Power-law cosmic expansion in f(R) gravity models
• On the co-existence of matter dominated and accelerating solutions in f(G)-gravity
• Compactifying the state space for alternative theories of gravity
• Homogeneous cosmologies in generalized modified gravity
• Symmetry analysis and exact solutions of modified Brans-Dicke cosmological equations