Multiscalar-metric gravity: merging gravity, dark energy and dark matter

TL;DR

The work introduces Spontaneously Broken Relativity (SBR) as a modification of GR that merges gravity with dark energy and dark matter through a multiscalar-metric spacetime. It formulates metagravity as an EFT based on a basic metric $g_{\\mu\\nu}$ and an auxiliary metric $\\zeta_{\\mu\\nu}$ encoded via scalar fields $Z^a$, yielding a scalar graviton $\\sigma$ and a traceless DE-like sector $\\tilde{\\AE}^ abla_\mu$; two realizations, SBGR and SBWTR, are analyzed alongside their field equations. An explicit SBGR solution combining a GR-like black hole with a scalar graviton halo demonstrates possible rotation-curve behavior, yielding asymptotically constant $v_{rot}$ that can model dark-matter halos in dwarf galaxies for small $\\Upsilon$. The framework outlines a path toward a deeper unification of gravity with matter and internal symmetries, while highlighting key open challenges such as finite vacuum (dark-hole) solutions, matter coupling, gravitational-wave signatures, and global solutions with DE/DM sources.

Abstract

The status of a modification of General Relativity (GR) -- Spontaneously Broken Relativity (SBR) -- for merging gravity, dark energy (DE) and dark matter (DM) is presented. The modification is principally grounded on a multiscalar-metric concept of spacetime endowed with two dynamical structures: a basic metric and a set of the reversible multiscalar fields. The latter ones serve geometrically as exceptional dynamical coordinates among arbitrary kinematical/observer's ones and physically as a kind of gravitational Higgs fields producing possible spontaneous breaking of the symmetry (SSB) of relativity. The effective field theory (EFT) of the extended gravity based on the multiscalar-metric spacetime -- the metagravity -- is discussed and some of its particular realizations beyond GR as SBR are explicated. Physically, SBR results in appearance of massive tensor and scalar gravitons. Some of the emerging consequences, problems and prospects for SBR for future deeper unification of gravity with matter in the context of the relativity and internal symmetries breaking are shortly discussed.