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Reconstruction of the local velocity field from the overdensity field and a gravitational acceleration that falls off from a point mass as r^-2 yields velocities in broad agreement with peculiar velocities measured with galaxy distance indicators. MONDian gravity does not. To quantify this, we introduce the velocity angular correlation function as a diagnostic of peculiar velocity field alignment and coherence as a function of scale. It is independent of the bias parameter of structure formation in the standard model of cosmology and the acceleration parameter of MOND. A modified gravity acceleration consistent with observed large scale structure would need to asymptote to zero at large distances more like r^-2, than r^-1.
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We study perturbation theory for large-scale structure in the most general scalar-tensor theories propagating a single scalar degree of freedom, which include Horndeski theories and beyond. We model the parameter space using the effective field theory of dark energy. For Horndeski theories, the gravitational field and fluid equations are invariant under a combination of time-dependent transformations of the coordinates and fields. This symmetry allows one to construct a physical adiabatic mode which fixes the perturbation-theory kernels in the squeezed limit and ensures that the well-known consistency relations for large-scale structure, originally derived in general relativity, hold in modified gravity as well. For theories beyond Horndeski, instead, one generally cannot construct such an adiabatic mode. Because of this, the perturbation-theory kernels are modified in the squeezed limit and the consistency relations for large-scale structure do not hold. We show, however, that the modification of the squeezed limit depends only on the linear theory. We investigate the observational consequences of this violation by computing the matter bispectrum. In the squeezed limit, the largest effect is expected when considering the cross-correlation between different tracers. Moreover, the individual contributions to the 1-loop matter power spectrum do not cancel in the infrared limit of the momentum integral, modifying the power spectrum on non-linear scales.
The coincident detection of gravitational waves (GW) and a gamma-ray burst from a merger of neutron stars has placed an extremely stringent bound on the speed of GW. We showed previously that the presence of gravitational slip ($eta$) in cosmology is intimately tied to modifications of GW propagation. This new constraint implies that the only remaining viable source of gravitational slip is a conformal coupling to gravity in scalar-tensor theories, while viable vector-tensor theories cannot now generate gravitational slip at all. We discuss structure formation in the remaining viable models, demonstrating that (i) the dark-matter growth rate must now be at least as fast as in GR, with the possible exception of the beyond Horndeski model. (ii) If there is any scale-dependence at all in the slip parameter, it is such that it takes the GR value at large scales. We show a consistency relation which must be violated if gravity is modified.
The first multi-messenger gravitational wave event has had a transformative effect on the space of modified gravity models. In this paper we study the enhanced tests of gravity that are possible with a future set of gravitational wave standard siren events. We perform MCMC constraint forecasts for parameters in Horndeski scalar-tensor theories. In particular, we focus on the complementarity of gravitational waves with electromagnetic large-scale structure data from galaxy surveys. We find that the addition of fifty low redshift ($z lesssim 0.2$) standard sirens from the advanced LIGO network offers only a modest improvement (a factor 1.1 -- 1.3, where 1.0 is no improvement) over existing constraints from electromagnetic observations of large-scale structures. In contrast, high redshift (up to $z sim 10$) standard sirens from the future LISA satellite will improve constraints on the time evolution of the Planck mass in Horndeski theories by a factor $sim 5$. By simulating different scenarios, we find this improvement to be robust to marginalisation over unknown merger inclination angles and to variation between three plausible models for the merger source population.
We develop an approach to compute observables beyond the linear regime of dark matter perturbations for general dark energy and modified gravity models. We do so by combining the Effective Field Theory of Dark Energy and Effective Field Theory of Large-Scale Structure approaches. In particular, we parametrize the linear and nonlinear effects of dark energy on dark matter clustering in terms of the Lagrangian terms introduced in a companion paper, focusing on Horndeski theories and assuming the quasi-static approximation. The Euler equation for dark matter is sourced, via the Newtonian potential, by new nonlinear vertices due to modified gravity and, as in the pure dark matter case, by the effects of short-scale physics in the form of the divergence of an effective stress tensor. The effective fluid introduces a counterterm in the solution to the matter continuity and Euler equations, which allows a controlled expansion of clustering statistics on mildly nonlinear scales. We use this setup to compute the one-loop dark-matter power spectrum.
The goal of this short report is to summarise some key results based on our previous works on model independent tests of gravity at large scales in the Universe, their connection with the properties of gravitational waves, and the implications of the recent measurement of the speed of tensors for the phenomenology of general families of gravity models for dark energy.
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