科研之友
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摘要
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 vacuum is ghost free at the perturbative level and Newtonian gravity is modified below a characteristic acceleration scale given by a(0) = c mu, where c is the speed of light and mu is a parameter of the model that also determines the late-time Hubble constant: H-0 similar to mu. 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 such actions. We also explore briefly the characteristic gravitational phenomenology that these models imply: besides a long distance modi. cation 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's surface it is of order similar to 0.1 mm, while this distance would be bigger in space where the local curvature is significantly lower.
- 出版日期2006-9
