Gravitational scalar field with a RAQUAL-like cubic kinetic term and second order self-interaction. (arXiv:1906.04989v1 [astro-ph.GA])
<a href="http://arxiv.org/find/astro-ph/1/au:+Scholz_E/0/1/0/all/0/1">Erhard Scholz</a>
The consequences of two unorthodox contributions to the Lagrangian of a (real
valued) relativistic scalar field are studied: a cubic kinetic term similar to
the “a-quadratic” Lagrangian used in the first attempt of a covariant
generalization of Milgrom’s modified Newtonian dynamics (RAQUAL)
citep{Bekenstein/Milgrom:1984}, and a second order derivative term studied by
Novello et al. in the context of a Weyl geometric approach to cosmology
citep{Novello/Oliveira_ea:1993,Oliveira/Salim/Sautu:1997}. Both taken
together, analysed in a scale covariant (Weyl geometric) approach, lead to a
scalar field model which recovers the MOND kinematics for free fall
trajectories in the quasi-static weak field approximations for the Einstein
equation and the scalar field equation. In contrast to the original MOND and
RAQUAL approaches, the second order term of the Lagrangian induces a
non-negligible energy-momentum tensor of the scalar field. It results in
gravitational light deflection compatible with the additional acceleration due
to the scalar field in Einstein gauge. For clusters the scalar field halos
around the galaxies superimpose the overall scalar halo of the hot gas. It
remains to be checked whether this closes the mass gap for clusters without
assuming additional dark matter.
The consequences of two unorthodox contributions to the Lagrangian of a (real
valued) relativistic scalar field are studied: a cubic kinetic term similar to
the “a-quadratic” Lagrangian used in the first attempt of a covariant
generalization of Milgrom’s modified Newtonian dynamics (RAQUAL)
citep{Bekenstein/Milgrom:1984}, and a second order derivative term studied by
Novello et al. in the context of a Weyl geometric approach to cosmology
citep{Novello/Oliveira_ea:1993,Oliveira/Salim/Sautu:1997}. Both taken
together, analysed in a scale covariant (Weyl geometric) approach, lead to a
scalar field model which recovers the MOND kinematics for free fall
trajectories in the quasi-static weak field approximations for the Einstein
equation and the scalar field equation. In contrast to the original MOND and
RAQUAL approaches, the second order term of the Lagrangian induces a
non-negligible energy-momentum tensor of the scalar field. It results in
gravitational light deflection compatible with the additional acceleration due
to the scalar field in Einstein gauge. For clusters the scalar field halos
around the galaxies superimpose the overall scalar halo of the hot gas. It
remains to be checked whether this closes the mass gap for clusters without
assuming additional dark matter.
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