Theoretical Aspects of Gravitational Lensing in TeVeS

Abstract

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.

The halos of satellite galaxies: the companion of the massive elliptical lens SL2S J08544−0121

“…Nonetheless, Mortlock & Turner (2001) showed that for a typical elliptical galaxy, the thin-lens approximation holds; the deflection angles are the same as the GR predictions in the inner parts (where the projected distances are < ∼ 2 kpc) and approach an asymptotic value in the outer parts. Chiu et al (2006) found qualitatively similar trends for the deflection angles in a relativistic formulation of MOND by Bekenstein (2004;the tensorvector-scalar theory). Therefore, modelling the satellite galaxy in MOND can be seen as modelling the satellite galaxy in GR with a different deflection angle field, or equivalently, a different mass radial profile.…”

Mass discrepancy–acceleration relation in Einstein rings

“…The angle of deflection has the same formulation in TeVe S as in GR but using MONDian gravitational potential instead (see, e.g., Chiu, Ko & Tian (2006); Tian et al (2013) for details). For other relativistic MOND theories, such as GEA (Zlosnik et al 2007) and BIMOND (Milgrom 2009), gravitational lensing result is the same as in Chiu, Ko & Tian (2006) for spherical symmetry case. Thus, one may expect the mass discrepancy in relativistic MOND will have the same trend as in non-relativistic MOND.…”

“…When comparing with initial mass function (IMF), MOND can explain this small discrepancy without dark matter (Chen & Zhao 2006;Chiu, Ko & Tian 2006;Chiu et al 2011;Sanders & Land 2008;Sanders 2014).…”

Post-Newtonian parameters in the tensor-vector-scalar theory

“…While the difficulty has been reported in explaining gravitational lensing of colliding galaxy clusters 1E0657-56 in modified gravities [3]. Evolution of the universe and cosmological perturbation have also been studied in [4,5,6]. These results tell us that TeVeS can explain the observed spectrum of the spatial distribution of galaxies and of the cosmic microwave radiation without dark matter if we include the contributions by neutrinos and the cosmological constant.…”