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We introduce 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. This review focuses on tests of gravity and is intended to be of use primarily to observers, but also to theorists with interest in the development of experimental tests. It is twinned with a separate review on tests of dark matter self-interactions (Adhikari et al., in prep.). Our focus is on astrophysical probes of gravity in the weak-field regime, ranging from stars to quasilinear cosmological scales. These are complementary to both strong-field tests 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 signals specifically on astrophysical scales. The constraining power of these signals is not limited by cosmic variance, but comes with the challenge of building robust theoretical models of the nonlinear dynamics of stars, galaxies, clusters and large scale structure. In this review we lay the groundwork for a thorough exploration of the astrophysical regime with an eye to using the current and next generation of observations for tests of gravity. We begin by setting the scene for how theories beyond General Relativity are expected to behave, focusing primarily on screened fifth forces. We describe the analytic and numerical techniques for exploring the pertinent astrophysical systems, as well as the signatures of modified gravity. With these in hand we present a range of observational tests, and discuss prospects for future measurements and theoretical developments., Comment: 108 pages; matches Reviews of Modern Physics accepted version; project website at https://www.novelprobes.org/

Cosmological models with Galileon gravity are an alternative to the standard $\Lambda {\rm CDM}$ paradigm with testable predictions at the level of its self-accelerating solutions for the expansion history, as well as large-scale structure formation. Here, we place constraints on the full parameter space of these models using data from the cosmic microwave background (CMB) (including lensing), baryonic acoustic oscillations (BAO) and the Integrated Sachs-Wolfe (ISW) effect. We pay special attention to the ISW effect for which we use the cross-spectra, $C_\ell^{\rm T g}$, of CMB temperature maps and foreground galaxies from the WISE survey. The sign of $C_\ell^{\rm T g}$ is set by the time evolution of the lensing potential in the redshift range of the galaxy sample: it is positive if the potential decays (like in $\Lambda {\rm CDM}$), negative if it deepens. We constrain three subsets of Galileon gravity separately known as the Cubic, Quartic and Quintic Galileons. The cubic Galileon model predicts a negative $C_\ell^{\rm T g}$ and exhibits a $7.8\sigma$ tension with the data, which effectively rules it out. For the quartic and quintic models the ISW data also rule out a significant region of the parameter space but permit regions where the goodness-of-fit is comparable to $\Lambda {\rm CDM}$. The data prefers a non zero sum of the neutrino masses ($\sum m_\nu\approx 0.5$eV) with $ \sim \! 5\sigma$ significance in these models. The best-fitting models have values of $H_0$ consistent with local determinations, thereby avoiding the tension that exists in $\Lambda {\rm CDM}$. We also identify and discuss a $\sim \! 2\sigma$ tension that Galileon gravity exhibits with recent BAO measurements. Our analysis shows overall that Galileon cosmologies cannot be ruled out by current data but future lensing, BAO and ISW data hold strong potential to do so., Comment: 26 pages, 7 Figures; published version

Self-consistent ${\it N}$-body simulations of modified gravity models are a key ingredient to obtain rigorous constraints on deviations from General Relativity using large-scale structure observations. This paper provides the first detailed comparison of the results of different ${\it N}$-body codes for the $f(R)$, DGP, and Symmetron models, starting from the same initial conditions. We find that the fractional deviation of the matter power spectrum from $\Lambda$CDM agrees to better than $1\%$ up to $k \sim 5-10~h/{\rm Mpc}$ between the different codes. These codes are thus able to meet the stringent accuracy requirements of upcoming observational surveys. All codes are also in good agreement in their results for the velocity divergence power spectrum, halo abundances and halo profiles. We also test the quasi-static limit, which is employed in most modified gravity ${\it N}$-body codes, for the Symmetron model for which the most significant non-static effects among the models considered are expected. We conclude that this limit is a very good approximation for all of the observables considered here., Comment: 31 pages, 16 figures. Version to appear in MNRAS

We show that Solar System tests can place very strong constraints on K-mouflage models of gravity, which are coupled scalar field models with nontrivial kinetic terms that screen the fifth force in regions of large gravitational acceleration. In particular, the bounds on the anomalous perihelion of the Moon imposes stringent restrictions on the K-mouflage Lagrangian density, which can be met when the contributions of higher-order operators in the static regime are sufficiently small. The bound on the rate of change of the gravitational strength in the Solar System constrains the coupling strength $\beta$ to be smaller than $0.1$. These two bounds impose tighter constraints than the results from the Cassini satellite and Big Bang Nucleosynthesis. Despite the Solar System restrictions, we show that it is possible to construct viable models with interesting cosmological predictions. In particular, relative to $\Lambda$-CDM, such models predict percent-level deviations for the clustering of matter and the number density of dark matter haloes. This makes these models predictive and testable by forthcoming observational missions., Comment: 15 pages

We present a comprehensive derivation of linear perturbation equations for different matter species, including photons, baryons, cold dark matter, scalar fields, massless and massive neutrinos, in the presence of a generic conformal coupling. Starting from the Lagrangians, we show how the conformal transformation affects the dynamics. In particular, we discuss how to incorporate consistently the scalar coupling in the equations of the Boltzmann hierarchy for massive neutrinos and the subsequent fluid approximations. We use the recently proposed K-mouflage model as an example to demonstrate the numerical implementation of our linear perturbation equations. K-mouflage is a new mechanism to suppress the fifth force between matter particles induced by the scalar coupling, but in the linear regime the fifth force is unsuppressed and can change the clustering of different matter species in different ways. We show how the CMB, lensing potential and matter power spectra are affected by the fifth force, and find ranges of K-mouflage parameters whose effects could be seen observationally. We also find that the scalar coupling can have the nontrivial effect of shifting the amplitude of the power spectra of the lensing potential and density fluctuations in opposite directions, although both probe the overall clustering of matter. This paper can serve as a reference for those who work on generic coupled scalar field cosmology, or those who are interested in the cosmological behaviour of the K-mouflage model., Comment: 22 pages, 4 figures

We develop a numerical algorithm to solve the high-order nonlinear derivative-coupling equation associated with the quartic Galileon model, and implement it in a modified version of the RAMSES N-body code to study the effect of the Galileon field on the large-scale matter clustering. The algorithm is tested for several matter field configurations with different symmetries, and works very well. This enables us to perform the first simulations for a quartic Galileon model which provides a good fit to the cosmic microwave background (CMB) anisotropy, supernovae and baryonic acoustic oscillations (BAO) data. Our result shows that the Vainshtein mechanism in this model is very efficient in suppressing the spatial variations of the scalar field. However, the time variation of the effective Newtonian constant caused by the curvature coupling of the Galileon field cannot be suppressed by the Vainshtein mechanism. This leads to a significant weakening of the strength of gravity in high-density regions at late times, and therefore a weaker matter clustering on small scales. We also find that without the Vainshtein mechanism the model would have behaved in a completely different way, which shows the crucial role played by nonlinearities in modified gravity theories and the importance of performing self-consistent N-body simulations for these theories., Comment: 22.15 pages, 4 figures; minor corrections, version accepted for publication in JCAP

We present the first constraints on the full parameter space of the Galileon modified gravity model, considering both the cosmological parameters and the coefficients which specify the additional terms in the Lagrangian due to the Galileon field, which we call the Galileon parameters. We use the latest cosmic microwave background measurements, along with distance measurements from supernovae and baryonic acoustic oscillations, performing a Monte Carlo Markov Chain exploration of the 9-dimensional parameter space. The integrated Sachs-Wolfe signal can be very different in Galileon models compared to standard gravity, making it essential to use the full CMB data rather than the CMB distance priors. We demonstrate that meaningful constraints are only possible in the Galileon parameter space after taking advantage of a scaling degeneracy. We find that the Galileon model can fit the WMAP 9-year results better than the standard \Lambda-Cold Dark Matter model, but gives a slightly worse fit overall once lower redshift distance measurements are included. The best-fitting cosmological parameters (e.g. matter density, scalar spectral index, fluctuation amplitude) can differ by more than 2\sigma\ in the Galileon model compared with \Lambda CDM. We highlight other potential constraints of the Galileon model using galaxy clustering and weak lensing measurements., Comment: 21 pages, 7 figures and 2 tables v2. Presentational changes in some figures. References added. Matches version published in PRD

We study the cosmology of Galileon modified gravity models in the linear perturbation regime. We derive the fully covariant and gauge invariant perturbed field equations using two different methods, which give consistent results, and solve them using a modified version of the {\tt CAMB} code. We find that, in addition to modifying the background expansion history and therefore shifting the positions of the acoustic peaks in the cosmic microwave background (CMB) power spectrum, the Galileon field can cluster strongly from early times, and causes the Weyl gravitational potential to grow, rather than decay, at late times. This leaves clear signatures in the low-$l$ CMB power spectrum through the modified integrated Sachs-Wolfe effect, strongly enhances the linear growth of matter density perturbations and makes distinctive predictions for other cosmological signals such as weak lensing and the power spectrum of density fluctuations. The quasi-static approximation is shown to work quite well from small to the near-horizon scales. We demonstrate that Galileon models display a rich phenomenology due to the large parameter space and the sensitive dependence of the model predictions on the Galileon parameters. Our results show that some Galileon models are already ruled out by present data and that future higher significance galaxy clustering, ISW and lensing measurements will place strong constraints on Galileon gravity., Comment: version 2. Minor changes to figures and text, and typo corrected in Eq. (A7). References added. Published in PRD