The radial acceleration relation (RAR) in galaxies describes a tight empirical scaling law between the total acceleration observed in galaxies and that expected from their baryonic mass , with a characteristic acceleration scale of m s−2. Here, we examine if such a correlation exists in galaxy clusters using weak-lensing, strong-lensing, and X-ray data sets available for 20 high-mass clusters targeted by the Cluster Lensing And Supernova survey with Hubble (CLASH). By combining our CLASH data with stellar mass estimates for the brightest cluster galaxies (BCGs) and accounting for the stellar baryonic component in clusters, we determine, for the first time, an RAR on BCG–cluster scales. The resulting RAR is well described by a tight power-law relation, , with lognormal intrinsic scatter of . The slope is consistent with the low acceleration limit of the RAR in galaxies, , whereas the intercept implies a much higher acceleration scale of m s−2, indicating that there is no universal RAR that holds on all scales from galaxies to clusters. We find that the observed RAR in CLASH clusters is consistent with predictions from a semianalytical model developed in the standard ΛCDM framework. Our results also predict the presence of a baryonic Faber–Jackson relation ( ) on cluster scales.

Since Bekenstein's creation of his tensor-vector-scalar theory (TeVeS), the modified Newtonian dynamics (MOND) paradigm has been redeemed from the embarrassment of lacking a relativistic version. One primary success of TeVeS is that it provides an enhancement of gravitational lensing, which could not be achieved by other MOND theories. Following Bekenstein's work, we investigate the phenomena of gravitational lensing including deflection angles, lens equations, and time delay. We find that the deflection angle maintains its value, while the distance of closest approach varies in the MOND regime. We also use the deflection angle law to derive magnifications and investigate microlensing light curves. We find that the difference in the magnification of the two images in the point-mass model is not a constant, as in general relativity (GR). Besides, microlensing light curves could deviate significantly from GR in the deep MOND regime. Furthermore, the scalar field, which is introduced to enhance the deflection angle in TeVeS, contributes a negative effect on the potential time delay. Unfortunately, this phenomenon is unmeasurable in lensing systems, where we can only observe the time delay between two images for a given source. However, this measurable time delay offers another constraint on the mass ratio of the dark matter and MOND scenarios, which in general differs from that given by the deflection angle. In other words, for a lensing system, if two masses, m gN and m gM , are mutual alternatives for the deflection angles in their own paradigm, regarding the time delay they are in general in an exclusive relation.

Using strong lensing data Milgrom's MOdified Newtonian Dynamics (MOND) or its covariant TeVeS (Tensor-Vector-Scalar Theory) is being examined here as an alternative to the conventional ΛCDM paradigm. We examine 10 double-image gravitational lensing systems, in which the lens masses have been estimated by stellar population synthesis models. While mild deviations exist, we do not find out that strong cases for outliers to the TeVeS

The dynamics of an elliptical galaxy within a couple of effective radii can be probed effectively by stars. However, at larger distances planetary nebulae (PNe) replace stars as the tracer of the dynamics. Making use of the motion of PNe, Romanowsky et al. (2003) measured the dynamics of three luminous elliptical galaxies (NGC821, NGC3379 and NGC4494) at large distances from the galactic center. They found that little dark matter is needed up to 6 effective radii. Milgrom & Sanders (2003) showed that this result can be understood in the framework of MOdified Newtonian Dynamics (MOND). As more data are available in the past decade, we revisit this problem. We combine PNe data (up to 6-8 effective radii) and stellar data from SAURON of 7 elliptical galaxies, including those 3 galaxies in Romanowsky et al. (2003) with updated data and 4 other galaxies which have not been analyzed before. We conclude that the dynamics of these galaxies can be well explained by MOND.

We study the Mass Discrepancy-Acceleration Relation (MDAR) of 57 elliptical galaxies by their Einstein rings from the Sloan Lens ACS Survey (SLACS). The mass discrepancy between the lensing mass and the baryonic mass derived from population synthesis is larger when the acceleration of the elliptical galaxy lenses is smaller. The MDAR is also related to surface mass density discrepancy. At the Einstein ring, these lenses belong to high-surface-mass density galaxies. Similarly, we find that the discrepancy between the lensing and stellar surface mass density is small. It is consistent with the recent discovery of dynamical surface mass density discrepancy in disk galaxies where the discrepancy is smaller when surface density is larger. We also find relativistic modified Newtonian dynamics (MOND) can naturally explain the MDAR and surface mass density discrepancy in 57 Einstein rings. Moreover, the lensing mass, the dynamical mass and the stellar mass of these galaxies are consistent with each other in relativistic MOND.