In chameleon f (R)-gravity, the fifth force will lead to 'upturns' in galaxy rotation curves near the screening radius. The location of the upturn depends on the cosmic background value of the scalar fieldf R0 , as well as the mass, size and environment of the galaxy. We search for this signature of modified gravity in the SPARC sample of measured rotation curves, using an MCMC technique to derive constraints onf R0 . Assuming NFW dark matter haloes and withf R0 freely varying for each galaxy, most galaxies prefer f (R) gravity to ΛCDM, but there is a large spread of inferredf R0 values, inconsistent with a single global value. Requiring instead a consistentf R0 value for the whole sample, models with log 10 |f R0 | > −6.1 are excluded. On the other hand, models in the range −7.5 < log 10 |f R0 | < −6.5 seem to be favoured with respect to ΛCDM, with a significant peak at -7. However, this signal is largely a result of galaxies for which the f (R) signal is degenerate with the core/cusp problem, and when the NFW profile is replaced with a cored halo profile, ΛCDM gives better fits than any given f (R) model. Thus, we find no convincing evidence of f (R) gravity down to the level of |f R0 | ∼ 6 × 10 −8 , with the caveat that if cored halo density profiles cannot ultimately be explained within ΛCDM, a screened modified gravity theory could possibly provide an alternative solution for the core/cusp problem. However, the f (R) models studied here fall short of achieving this.

Current constraints on gravity are relatively weak on galactic and intergalactic scales. Screened modified gravity models can exhibit complex behaviour there without violating stringent tests of gravity within our Solar System. They might hence provide viable extensions of the theory of gravity. Here, we use galaxy kinematics to constrain screened modified gravity models. We focus on chameleon f (R) gravity and predict its impact on galaxy rotation curves and radial acceleration relations. This is achieved by post-processing state-of-the-art galaxy formation simulations from the auriga project, using the mg-gadget code. For a given galaxy, the surface dividing screened and un-screened regions adopts an oblate shape, reflecting the disc morphology of the galaxy's mass distribution. At the 'screening radius'-the radius at which screening is triggered in the disc plane-characteristic 'upturns' are present in both rotation curves and radial acceleration relations. The locations of these features depend on various factors, such as the galaxy mass, the concentration of the density profile and the value of the background field amplitudef R0 . Self-screening of stars and environmental screening also play a role. For Milky Way-size galaxies, we find that a model with |f R0 | = 10 −7 results in rotation curves that are indistinguishable from ΛCDM, while for |f R0 | ≥ 2 × 10 −6 the simulated galaxies are entirely unscreened, violating Solar System constraints. For intermediate values, distinct upturns are present. With a careful statistical analysis of existing samples of observed rotation curves, including lower mass objects, constraints on f (R) gravity with a sensitivity down to |f R0 | ∼ 10 −7 should be possible.

The advent of datasets of stars in the Milky Way with six-dimensional phase-space information makes it possible to construct empirically the distribution function (DF). Here, we show that the accelerations can be uniquely determined from the DF using the collisionless Boltzmann equation, providing the Hessian determinant of the DF with respect to the velocities is non-vanishing. We illustrate this procedure and requirement with some analytic examples. Methods to extract the potential from datasets of discrete positions and velocities of stars are then discussed. Following Green & Ting, we advocate the use of normalizing flows on a sample of observed phase-space positions to obtain a differentiable approximation of the DF. To then derive gravitational accelerations, we outline a semi-analytic method involving direct solutions of the over-constrained linear equations provided by the collisionless Boltzmann equation. Testing our algorithm on mock datasets derived from isotropic and anisotropic Hernquist models, we obtain excellent accuracies even with added noise. Our method represents a new, flexible and robust means of extracting the underlying gravitational accelerations from snapshots of six-dimensional stellar kinematics of an equilibrium system.

Theories of gravity that incorporate new scalar degrees of freedom typically require "screening mechanisms" to ensure consistency with Solar System tests. One widely studied mechanism-the chameleon mechanism-can lead to violations of the equivalence principle (EP), as screened and unscreened objects fall differently. If the stars are screened but the surrounding dark matter is not, EP violation can lead to asymmetry between leading and trailing streams from tidally disrupted dwarf galaxies in the Milky Way halo. We provide analytic estimates of the magnitude of this effect for realistic Galactic mass distributions, demonstrating that it is an even more sensitive probe than suggested previously. Using a restricted N-body code, we simulate four satellites with a range of masses and orbits, together with a variety of strengths of the fifth force and screening levels of the Milky Way and satellite. The ratio of the cumulative number function of stars in the leading and trailing stream as a function of longitude from the satellite is computable from simulations and measurable from the stellar data and can provide a direct test of chameleon gravity. We forecast constraints for streams at large Galactocentric distances, which probe deeper into chameleon parameter space, using the specific example case of Hu-Sawicki fðRÞ gravity. Streams in the outer reaches of the Milky Way halo (with apocenters between 100 and 200 kpc) provide easily attainable constraints at the level of jf R0 j ¼ 10 −7. Still more stringent constraints at the level of 10 −7.5 or even 10 −8 are plausible provided the environmental screening of the satellite is accounted for, and screening of the Milky Way's outer halo by the Local Group is not yet triggered in this range. These would be among the tightest astrophysical constraints to date. We note three further signatures of chameleon gravity: (i) the trailing stellar stream may become detached from the dark matter progenitor if all the stars are lost, (ii) in the extreme fifth force regime, striations in the stellar trailing tail may develop from material liberated at successive pericentric passages, and (iii) if the satellite is fully screened, its orbital frequency is lower than that of the associated dark matter, which is preferentially liberated into the leading tidal tail.

We have mapped the number density and mean vertical velocity of the Milky Way's stellar disk out to roughly two kiloparsecs from the Sun using Gaia Data Release 3 (DR3) and complementary photo-astrometric distance information from StarHorse. For the number counts, we carefully masked spatial regions that are compromised by open clusters, great distances, or dust extinction and used Gaussian processes to arrive at a smooth, non-parametric estimate for the underlying number density field. We find that the number density and velocity fields depart significantly from an axisymmetric and mirror-symmetric model. These departures, which include projections of the Gaia phase-space spiral, signal the presence of local disturbances in the disk. We identify two features that are present in both stellar number density and mean vertical velocity. One of these features appears to be associated with the Local Spiral Arm. It is most prominent at small heights and is largely symmetric across the mid-plane of the disk. The density and velocity field perturbations are phase-shifted by roughly a quarter wavelength, suggesting a breathing mode that is propagating in the direction of Galactic longitude l ∼ 270 deg. The second feature is a gradient in the stellar number density and mean vertical velocity with respect to galactocentric radius. This feature, which extends across the entire region of our analysis, may be associated with the extension of the Galactic warp into the solar neighbourhood in combination with more localised bending waves.