Cosmological Tests of Gravity

TL;DR

This review surveys modifications to general relativity as potential explanations for cosmic acceleration, emphasizing screening mechanisms (chameleon, symmetron, Vainshtein) and massive/resonance gravity. It outlines how scalar-tensor reductions emerge in MG theories, how screening enables GR on solar-system scales, and how modified Friedman equations manifest in these models. The second half synthesizes observational tests from the lab to large-scale structure, detailing how lensing, ISW, and dynamical probes constrain the ratio of metric potentials and the growth of structure, and it highlights current constraints and the promise of upcoming surveys (DES, LSST, Euclid, SKA). The synthesis underscores that while no significant deviations from GR have been detected yet, planned observations and improved modeling of nonlinear and screening effects offer substantial potential to test or falsify MG scenarios. Overall, the article maps the landscape of gravity theories relevant to cosmology and outlines a roadmap for empirical discrimination in the near future.

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.

Figures (8)

• Figure 1: The chameleon effective potential $V_{\rm eff}$ (solid curve) is the sum of two contributions: the actual potential $V(\phi)$ (dashed curve), plus a density-dependent term from its coupling to matter (dotted curve).
• Figure 2: Plot of the $D=7$ cascading solution for the gravitational potential $\hat{\Phi}(y,z,w)$ resulting from a small tension on the codimension-3 brane. The solution is shown for $w=0$ and $w=2m_7^{-1}$ in the case where $m_6=m_7$. In terms of the extra-dimensional coordinates $y,z$ and $w$, the codimension-1 brane is located at $w=0$, the codimension-2 brane at $z=w=0$, and the codimension-3 brane at $y=z=w=0$.
• Figure 3: Power spectra for $f(R)$ (left panel) and DGP (right panel) theories. The fractional deviation from $\Lambda$-CDM are shown for the present day linear and nonlinear power spectra nbody2. At high-$k$ (small scales), nonlinear gravitational clustering and the screening of massive halos alters the power spectrum. The limited resolution of the simulations precludes a definitive statement about the high-$k$ limit of the power spectra.
• Figure 4: Examples of the shear-shear and galaxy-shear power spectra for the DES (left panel) and a Stage-IV survey similar to LSST (right panel) Guzik09. The upper (green) curves show the galaxy-shear cross power spectrum $C_{g\kappa}$, with foreground galaxies at $z=0.4$ and background galaxies at $z=1$. The lower two curves show the shear-shear power spectrum $C_{\kappa \kappa}$ with two choices of redshift bins as indicated. The error bars include the sample variance and shape noise for the two surveys (see Table 1 for survey parameters). The shape noise contribution to $C_{\kappa \kappa}$ for $z=1$ is shown separately as well (dashed lines).
• Figure 5: Simulation slices showing the density, potential $\Psi$ and $f_R$ field for two different values of $f_{R0}$Oyaizu08. Along the line of sight through a 2D slice, the maximum of the density and minimum values of $\Psi$ and $f_R$ are shown using a grayscale. In the upper panels the chameleon mechanism is more evident -- it suppresses the deviations (from GR) in the potential gradients in massive structures. In the lower panel the chameleon effect is much weaker due to the choice of a larger value of the $f_{R0}$ parameter. These images show qualitatively the coupling between the Newtonian potential and the scalar field in MG gravity theories, and how small scale structure can vary depending on the details of the model.