A scalar field inducing a non-metrical contribution to gravitational acceleration and a compatible add-on to light deflection

Abstract

A scalar field model for explaining the anomalous acceleration and light deflection at galactic and cluster scales, without further dark matter, is presented. It is formulated in a scale covariant scalar tensor theory of gravity in the framework of integrable Weyl geometry and presupposes two different phases for the scalar field, like the superfluid approach of Berezhiani/Khoury. In low acceleration regimes of static gravitational fields (in the Einstein frame) with accordingly low values of the scalar field gradient, the scalar field Lagrangian combines a cubic kinetic term similar to the “a-quadratic” Lagrangian used in the first covariant generalization of MOND (RAQUAL) (Bekenstein and Milgrom in Astrophys J 286:7–14, 1984) and a second order derivative term introduced by Novello et al. in the context of a Weyl geometric approach to cosmology (Novello et al. in Int J Mod Phys D 1:641–677, 1993; de Oliveira et al. in Class Quantum Gravity 14(10):2833–2843, 1997). In varying with regard to $$\phi $$ ϕ the latter is variationally equivalent to a first order expression. The scalar field equation thus remains of order two. In the Einstein frame it assumes the form of a covariant generalization of the Milgrom equation known from the classical MOND approach in the deep MOND regime. It implies a corresponding “non-metrical” contribution to the acceleration of free fall trajectories. In contrast to pure RAQUAL, the second order derivative term of the Lagrangian leads to a non-negligible contribution to the energy momentum tensor and an add-on to the light deflection potential in beautiful agreement with the dynamics of low velocity trajectories. Although the model takes up important ingredients from the usual RAQUAL approach, it differs essentially from the latter.—In higher sectional curvature regions, respectively for higher accelerations in static fields, the scalar field Lagrangian consists of a Jordan–Brans–Dicke term with sufficiently high value of the JBD-constant to satisfy empirical constraints. Here the dynamics agrees effectively with the one of Einstein gravity.

Light cone and Weyl compatibility of conformal and projective structures

“…8 In principle, a Weylian metric on spacetime can thus be read off from sufficiently detailed knowledge of the free fall trajectories of test particles and of the gravitational bending of light. This fact may give support for a modified gravity approach to the problem of dark matter at the astrophysical level (galaxies and galaxy clusters) [9,18]. The central physical question for such an approach is then whether a theoretical coherent and empirically confirmed dynamics of the underlying field content can be found.…”

Dark Matter Realism

“…10 Since the authors conceive of the particle phase as consisting of axionlike particles-which, as bosons, naturally condense below a critical temperature-superfluid dark matter theory is arguably a version of one of the mainstream dark matter candidates. 11 [12,13,15,[18][19][20][21][22][23][24][25][26][27][28][29]. 12 Some examples are the small-scale challenges [31,32], the Bullet Cluster (which, despite usually being put forward as a smoking gun against modified gravity explanations of dark matter data, is potentially also problematic for ΛCDM) [33][34][35], and the tension between different measurements of the Hubble constant.…”

Cartography of the space of theories: an interpretational chart for fields that are both (dark) matter and spacetime

“…Another interesting follow-up would be to determine which modifications of SFDM would make Φ more or less of a dark matter field, and more or less of 40 Read et al seem to suggest that TeVeS itself may be a hybrid theory [90]. For potential further, interesting case studies, see [91][92][93][94][95][96][97][98][99][100][101][102]. 41 A particularly interesting example could be the dilaton in string theory.…”