Dark Matter as the leftover of historical violations of the Hamiltonian constraint

Abstract

If the Hamiltonian constraint were ever violated (in the early Universe, at high energies, etc), its subsequent restoration could never erase a memory effect of the original violation. Depending on the technicalities of restoration, the memory effect may be as boring as something which mimics standard dark matter, or an anisotropic extension of dark matter... Or, as crazy as something that acts like a dust fluid capable of attracting other matter but being attracted to nothing. Attracting without being attracted: we discuss how it might be possible in a relativistic theory of gravity, its implications to the foundations of physics (specifically Dirac's algebra of constraints underpinning relativistic physics), and what its observational hallmarks might be.