Modified gravity, Dark Energy and MOND

Abstract

We propose a class of actions for the spacetime metric that introduce corrections to the Einstein-Hilbert Lagrangian depending on the logarithm of some curvature scalars. We show that for some choices of these invariants the models are ghost free and modify Newtonian gravity below a characteristic acceleration scale given by a_0 = cμ, where c is the speed of light and μis a parameter of the model that also determines the late-time Hubble constant: H_0 \sim μ. In these models, besides the massless spin two graviton, there is a scalar excitation of the spacetime metric whose mass depends on the background curvature. This dependence is such that this scalar, although almost massless in vacuum, becomes massive and effectively decouples when one gets close to any source and we recover an acceptable weak field limit at short distances. There is also a (classical) ``running'' of Newton's constant with the distance to the sources and gravity is easily enhanced at large distances by a large ratio. We comment on the possibility of building a model with a MOND-like Newtonian limit that could explain the rotation curves of galaxies without introducing Dark Matter using this kind of actions. We also explore briefly the characteristic gravitational phenomenology that these models imply: besides a long distance modification of gravity they also predict deviations from Newton's law at short distances. This short distance scale depends on the local background curvature of spacetime, and we find that for experiments on the Earth surface it is of order \sim 0.1mm, while this distance would be bigger in space where the local curvature is significantly lower.

24 pages, 2 figures. References and comments on the external field effect added in subsect. 3.3.3

References in corpus (5)

• Ghosts, Instabilities, and Superluminal Propagation in Modified Gravity Models
• The History and Present Status of Quantum Field Theory in Curved Spacetime
• Alternatives to Dark Matter (?)
• Globular Clusters as a Test for Gravity in the Weak Acceleration Regime
• Dark energy, MOND and sub-millimeter tests of gravity

Cited by in corpus (8)

• Matter instability in modified gravity
• The (pseudo)issue of the conformal frame revisited
• A viability criterion for modified gravity with an extra force
• On the growth of structure in theories with a dynamical preferred frame
• Collider Signals of Gravitational Fixed Points
• Generalized Einstein-Aether theories and the Solar System
• Dark Energy, scalar-curvature couplings and a critical acceleration scale
• Long distance modifications of gravity in four dimensions