Unimodular bimode gravity and the coherent scalar-graviton field as galaxy dark matter

TL;DR

This paper proposes a modified gravity theory with a scalar graviton to explain galaxy dark matter phenomena, leading to solutions that resemble galaxy structures with dark halos and black hole-like cores.

Contribution

It introduces a unimodular bimode gravity framework with a scalar graviton, providing a new model for galaxy dark matter without dark matter particles.

Findings

Derivation of a static spherically symmetric solution called dark lacuna.

Dark lacunas exhibit gravitational confinement and flat rotation curves.

Model predicts galaxy-like structures with dark halos and scalar-modified black holes.

Abstract

The explicit violation of the general gauge invariance/relativity is adopted as the origin of dark matter and dark energy of the gravitational nature. The violation of the local scale invariance alone, with the residual unimodular one, is considered. Besides the four-volume preserving deformation mode -- the transverse-tensor graviton -- the metric comprises a compression mode -- the scalar graviton, or the systolon. A unimodular invariant and general covariant metric theory of the bimode/scalar-tensor gravity is consistently worked out. To reduce the primordial ambiguity of the theory a dynamical global symmetry is imposed, with its subsequent spontaneous breaking revealed. The static spherically symmetric case in the empty, but possibly for the origin, space is studied. A three-parameter solution describing a new static space structure -- the dark lacuna -- is constructed. It enjoys the property of gravitational confinement, with the logarithmic potential of gravitational attraction at the periphery, and results in the asymptotically flat rotation curves. Comprising a super-massive dark fracture (a scalar-modified black hole) at the origin surrounded by a cored dark halo, the dark lacunas are proposed as a prototype model of galaxies, implying an ultimate account for the distributed non-gravitational matter and a putative asphericity or rotation.