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.

Publisher's copyright statement:Reprinted with permission from the American Physical Society: Physical Review Letters 117, 051101 c 2016 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. In this Letter, we report the observational constraints on the Hu-Sawicki fðRÞ theory derived from weak lensing peak abundances, which are closely related to the mass function of massive halos. In comparison with studies using optical or x-ray clusters of galaxies, weak lensing peak analyses have the advantages of not relying on mass-baryonic observable calibrations. With observations from the Canada-France-HawaiiTelescope Lensing Survey, our peak analyses give rise to a tight constraint on the model parameter jf R0 j for n ¼ 1. The 95% C.L. is log 10 jf R0 j < −4.82 given WMAP9 priors on (Ω m , A s ). With Planck15 priors, the corresponding result is log 10 jf R0 j < −5.16.

We present cross-identification of archived ROSAT X-ray point sources with W UMa variable stars found in the All-Sky Automated Survey. A total of 34 W UMa stars have been found associated with X-ray emission. We compute the distances of these W UMa systems and hence their X-ray luminosities. Our data support the ''supersaturation'' phenomenon seen in these fast rotators, namely that the faster a W UMa star rotates, the weaker its X-ray luminosity.

f (R) gravity is one of the simplest theories of modified gravity to explain the accelerated cosmic expansion. Although it is usually assumed that the quasi-Newtonian approach (a combination of the quasi-static approximation and sub-Hubble limit) for cosmic perturbations is good enough to describe the evolution of large scale structure in f (R) models, some studies have suggested that this method is not valid for all f (R) models. Here, we show that in the matter-dominated era, the pressure and shear equations alone, which can be recast into four first-order equations to solve for cosmological perturbations exactly, are sufficient to solve for the Newtonian potential, Ψ, and the curvature potential, Φ. Based on these two equations, we are able to clarify how the exact linear perturbations fit into different limits. We find that the Compton length controls the quasi-static behaviours in f (R) gravity. In addition, regardless the validity of quasi-static approximation, a strong version of the sub-Hubble limit alone is sufficient to reduce the exact linear perturbations in any viable f (R) gravity to second order. Our findings disagree with some previous studies where we find little difference between our exact and quasi-Newtonian solutions even up to k = 10c −1 H0.