Novel Probes Project: Tests of gravity on astrophysical scales

The Novel Probes Project, an initiative to advance the field of astrophysical tests of the dark sector by creating a forum that connects observers and theorists, is introduced. This review focuses on tests of gravity and is intended to be of use primarily to observers, as well as theorists with an interest in the development of experimental tests. It is twinned with a separate upcoming review on dark matter self-interactions. The review focuses on astrophysical tests of gravity in the weak-field regime, ranging from stars to quasilinear cosmological scales. This regime is complementary to both strong-field tests of gravity and background and linear probes in cosmology. In particular, the nonlinear screening mechanisms that are an integral part of viable modified-gravity models lead to characteristic signatures, specifically on astrophysical scales. The potential of these probes is not limited by cosmic variance but comes with the challenge of building robust theoretical models of the nonlinear dynamics of stars, galaxies, and large-scale structure. The groundwork is laid for a thorough exploration of the weak-field, nonlinear regime, with an eye to using the current and next generation of observations for tests of gravity. The scene is set by showing how gravitational theories beyond general relativity are expected to behave, focusing primarily on screening mechanisms. Analytic and numerical techniques for exploring the relevant astrophysical regime are described, as are the pertinent observational signals. With these in hand a range of astrophysical tests of gravity are presented, and prospects for future measurements and theoretical developments are discussed.

Figure 1

Landscape of gravitational environments probed by known systems. The $x$ axis indicates the characteristic gravitational potential of the system, and the $y$ axis approximately quantifies the typical spacetime curvature probed by that system (note that the $y$-axis quantity is not exactly the Ricci curvature, as this vanishes for vacuum systems). For details on this figure and its implications, see [44].

Figure 2

Similar to Fig. 1, but with experimental or observational tests corresponding to each region.

Figure 3

The chameleon effective potential for both low-density (left panel) and high-density (right panel) environments. The bare potential $V(\varphi )$ is shown by the dotted black line, and the contribution from the matter coupling is indicated by the black dashed line. The effective potential is the sum of these contributions and is shown in solid black.

Figure 4

Thin-shell screening. The field minimizes its effective potential inside the screening radius but begins to roll to the minimum in the low-density background outside. Only the mass outside the screening radius contributes to the fifth force.

Figure 5

The symmetron effective potential. The red line is for $\rho <{\mu }^2{M}_{\mathrm{s}}^2$ and the blue line is for $\rho >{\mu }^2{M}_{\mathrm{s}}^2$.

Figure 6

Vainshtein screening due to a point mass located at $r=0$. The red curve shows the ratio of the fifth force to Newtonian force outside the object.

Figure 7

Timeline for future surveys.

Figure 8

A comparison of the ratios of power spectra for $f(R)$ models and an equivalent $\mathrm{\Lambda }\mathrm{CDM}$ model for $|f_{R0}|={10}^{-4}$ (top panels), ${10}^{-5}$ (middle panels), and ${10}^{-6}$ (bottom panels) at $z=0$ (left-hand column) and 1 (right-hand column). We show the power spectrum from the simulations of [356] (blue points) together with that from two versions of the halo model, that of [398] (short-dashed black lines) and [397] (solid black lines). The former does not take into account chameleon screening and thus overestimates the deviation from GR. We also show the MG-HALOFIT model ([568]) (long-dashed red lines) that was fitted to the same simulation data as shown (among others) and provides a better fit. From [397].

Figure 9

(a) Change in power spectrum due to baryonic effects as a function of scale, with a comparison among the Horizon, OWLS, Illustris, and EAGLE simulations. From [138]. (b) Competition between baryonic and modified-gravity effects: on scales $k\gtrsim 2\mathrm{h}/\mathrm{Mpc}$, baryonic effects can noticeably suppress (solid green and blue lines) the enhancement in clustering power due to the fifth force (dashed green and blue lines) in $f(R)$ models. From [32].

Figure 10

(a) Constraints on parameters $\mu$ and $\eta$ [Eq. (60)] describing deviations of the gravitational potentials from their expected values in GR. The $\mathrm{\Lambda }\mathrm{CDM}$ prediction is at the intersection of the dashed lines. From [20]. (b) Constraints on $E_G$ [Eq. (69)] from CMB and galaxy-galaxy lensing compared to $\mathrm{\Lambda }\mathrm{CDM}$ expectations of varying ${\mathrm{\Omega }}_m$. From [505].

Figure 11

(a) ISW-galaxy cross-correlation from the WISE survey ([212]) together with predictions from a number of parameter choices in the covariant Galileon model. The dashed red curve is the best-fitting cubic Galileon model to the data, which illustrates the high degree of tension plaguing this model. From [451]. (b) Time evolution of $f{\sigma }_8$ for $\mathrm{\Lambda }\mathrm{CDM}$, nDGP, and two values of growth index $\gamma$. From left to right, the data points shown correspond to the analyses of the 6DFGS survey ([77]), luminous red galaxy sample from SDSS-DR7 ([426]), BOSS DR12 ([23]), and Vipers surveys ([178]), as labeled.

Figure 12

Left panel: comparison of the splashback radius (defined as the minimum of each curve) for GR and chameleon theories. F5 models correspond to $\chi ={10}^{-5}$. The red lines correspond to particles, and the blue and black lines correspond to subhalos with masses indicated in the figure. Right panel: density slope for dark matter particles in GR (black line) and a Vainshtein-screened theory with $r_c=600\mathrm{Mpc}$ (red line). The splashback radius is the minimum of each curve. From [16].

Figure 13

(a) Comparison of the fifth-force ($y$-axis) and normal GR ($x$-axis) contributions to the total force felt at particle locations in $N$-body simulations of the nDGP model. The four panels split the particles by the type of cosmic web structure [halos, filaments, walls, and voids, as identified by the origami algorithm ([206])] where each particle lies. The solid line marks the unscreened linear expectation, which is followed in filaments, walls, and voids; in the higher-density haloes, the fifth force is suppressed. From [203]. (b) Differential surface mass density (which is related to the lensing shear) of spherically symmetric stacks of voids in the cubic Galileon model. Relative to the GR scenario (red lines; named $\mathrm{QCDM}$ because the background is not $\mathrm{\Lambda }\mathrm{CDM}$), the full model result (blue lines) displays roughly the same enhancement as a linearized unscreened version of it (green lines). This indicates that the screening mechanism is not at play and thus that the fifth force can have prominent observational signatures. From [49].

Figure 14

Maps of environmental Newtonian potential $|\mathrm{\Phi }|$, acceleration $a$, and curvature $K$ across a $300\times 300{\mathrm{Mpc}}^2$ slice of the local Universe. The Milky Way is located at $x=y=0$. From [188].

Figure 15

Tracks in the color-magnitude diagram for a solar mass and metallicity star in GR (black line) and Hu-Sawicki $f(R)$ gravity (red line) with $f_{R0}={10}^{-6}$. Here $L$ is normalized to the solar luminosity and $T_{\mathrm{eff}}$ is measured in kelvins.

Figure 16

Excluded region in the $\chi$-$\alpha$ plane derived by comparing Cepheid and TRGB distance estimates to 22 unscreened galaxies. The black dashed line corresponds to $f(R)$ theories. Recall that $f_{R0}=2\chi /3$. From [286].

Figure 17

Schematic illustration of disk warping in an unscreened galaxy in thin-shell-screened modified gravity. From [186].

Figure 18

Left panel: displacement between H i and optical centroids for $\sim 11\hspace{0.17em}000$ ALFALFA galaxies predicted by a fifth-force model with ${\lambda }_C=5\mathrm{Mpc}$, $2{\alpha }^2=1$, both with and without thin-shell screening. Right panel: $1\sigma$ constraints in the $2{\alpha }^2$ ($\mathrm{\Delta }G/G$) vs ${\lambda }_C$ plane obtained by comparing the previous prediction with the measured displacements using highly conservative measurement uncertainties. From [189].

Figure 19

A galaxy falling into an external Galileon field ${\varphi }^{\mathrm{ext}}$. In the rest frame of the galaxy, the SMBH feels two forces: the outward Galileon force and the restoring force of the baryons left at the center.

Figure 20

Left panel: restoring force profile for a cored galaxy (red solid line). The blue dashed, upper line shows the case where the Galileon force exceeds the maximum restoring force and the black dotted, lower line shows the case where the Galileon force is smaller than this. In the latter case, there are two equilibrium positions labeled 1 and 2. The former point represents a stable offset; the latter is unstable. Right panel: restoring force for a cusped (NFW) profile (red solid line). The blue dashed, upper line shows the case where the Galileon force is larger than the maximum restoring force (the force at the center) and the black dashed, lower line shows the case where it is smaller than this.

Figure 21

Left panel: Newtonian and cubic Galileon force profile for a Virgo-like galaxy cluster. We use a NFW profile (with two-halo term corrections) ([193]) with concentration $c=5$ and parameters that give a total mass $M={10}^{15}{M}_{\odot }$ ([216]; [439]), which is consistent with observations. The blue line shows the Newtonian force and the red and black solid lines show the cubic Galileon force for $\alpha =1$ and $r_c=500$ and 6000 Mpc (cosmological Galileons), respectively. The black dashed line shows the rms cosmological Galileon force for the fiducial values shown in Eq. (102) and is shown for comparative purposes only. Right panel: SMBH offset for typical infalling satellite galaxies for cluster masses and satellite central densities indicated in the caption. The $x$ axis shows the distance between the satellite galaxy and the cluster’s center. From [468].

Figure 22

Constraints on the coupling $\alpha$ and crossover scale $r_c$ for cubic (left panel) and quartic (right panel) Galileon models. The pink region is excluded because it would predict a larger offset than is observed in M87, which is falling toward the center of the Virgo cluster. The red dashed line in the left panel indicates the previous constraints from lunar laser ranging ([196]). LLR constraints on the quartic Galileon are not competitive with SMBH constraints, and hence they are omitted from the right-hand panel.