Cosmological Tests of Gravity

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Abstract

Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher dimensional approaches and chameleon/f(R) theories. We classify these models in terms of the screening mechanisms that enable such theories to approach general relativity on small scales (and thus satisfy solar system constraints). We describe general features of the modified Friedman equation in such theories. The second half of this review describes experimental tests of gravity in light of the new theoretical approaches. We summarize the high precision tests of gravity on laboratory and solar system scales. We describe in some detail tests on astrophysical scales ranging from ~kpc (galaxy scales) to ~Gpc (large-scale structure). These tests rely on the growth and inter-relationship of perturbations in the metric potentials, density and velocity fields which can be measured using gravitational lensing, galaxy cluster abundances, galaxy clustering and the Integrated Sachs-Wolfe effect. A robust way to interpret observations is by constraining effective parameters, such as the ratio of the two metric potentials. Currently tests of gravity on astrophysical scales are in the early stages --- we summarize these tests and discuss the interesting prospects for new tests in the coming decade.

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An Alternative to Compactification

Raman Sundrum, Lisa Randall (1999)

Conventional wisdom states that Newton's force law implies only four non-compact dimensions. We demonstrate that this is not necessarily true in the presence of a non-factorizable background geometry. The specific example we study is a single 3-brane embedded in five dimensions. We show that even without a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and general relativistic gravity is reproduced to more than adequate precision.

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The galileon as a local modification of gravity

Alberto Nicolis, Riccardo Rattazzi, Enrico Trincherini (2008)

In the DGP model, the ``self-accelerating'' solution is plagued by a ghost instability, which makes the solution untenable. This fact as well as all interesting departures from GR are fully captured by a four-dimensional effective Lagrangian, valid at distances smaller than the present Hubble scale. The 4D effective theory involves a relativistic scalar \pi, universally coupled to matter and with peculiar derivative self-interactions. In this paper, we study the connection between self-acceleration and the presence of ghosts for a quite generic class of theories that modify gravity in the infrared. These theories are defined as those that at distances shorter than cosmological, reduce to a certain generalization of the DGP 4D effective theory. We argue that for infrared modifications of GR locally due to a universally coupled scalar, our generalization is the only one that allows for a robust implementation of the Vainshtein effect--the decoupling of the scalar from matter in gravitationally bound systems--necessary to recover agreement with solar system tests. Our generalization involves an internal ``galilean'' invariance, under which \pi's gradient shifts by a constant. This symmetry constrains the structure of the \pi Lagrangian so much so that in 4D there exist only five terms that can yield sizable non-linearities without introducing ghosts. We show that for such theories in fact there are ``self-accelerating'' deSitter solutions with no ghost-like instabilities. In the presence of compact sources, these solutions can support spherically symmetric, Vainshtein-like non-linear perturbations that are also stable against small fluctuations. [Short version for arxiv]