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 sectional curvature for the Einstein metric) the scalar field Lagrangian combines a cubic kinetic term similar to the "a-quadratic" Lagrangian used in the first covariant generalization of MOND (RAQUAL) [3] and a second order derivative term introduced by Novello et al. in the context of a Weyl geometric approach to cosmology [38,17]. In varying with regard to 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 Brazilian term 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. Contents

Gauging the spacetime metric -- looking back and forth a century later

“…A review of the cosmological investigations of the Brazilian group initiated by M. Novello and its external Greek contributor J. Miritzis (see sec. 3.2) has been given at another place.74 Here I add a short discussion of studies by a group of authors around J. Jiménez and T. Koivisto (later also including L. Heisenberg) (Jiménez/Koivisto, 2014, 2016bJiménez et al, 2016a) and supplement it by a remark on a recent proposal for modelling galactic and cluster dynamics in a Weyl geometric scalar tensor theory with an unconventional kinetic term (Scholz, 2019). A comparison of the Weyl geometric approach(es) with conformal cosmological models of a more general type, in particular C. Wetterich's "universe without expansion" (Wetterich, 1988(Wetterich, , 2013, would be an interesting task, but cannot be carried out here.…”

“…The approach in (Scholz, 2019) has a different motivation. It deals with the question whether a Weyl geometric linear gravity theory (β 1 = β 2 = β 3 = 0 in ( 21)) with scalar field can reproduce the deviation of galactic dynamics from the Newtonian expectation, i.e.…”

A Weyl geometric scalar field approach to the dark sector

“…The scalar field equation in the Milgrom regime can be calculated like in [52]. Like in JBD theory one subtracts the traced Einstein equation from the variational equation of φ; in this way the trace of the baryonic matter tensor enters the dynamical equation of the scalar field without presupposing a Lagrangian coupling of the latter to matter (see app.…”

“…The energy momentum tensor Θ = (8πG)T (φ) of the scalar field and the scalar field equation come out differently from the analogous Lagrangian in a Riemannian framework. From [57,13,21,52] we know:…”