Cosmological Consequences of Unconstrained Gravity and Electromagnetism

Motivated by the quantum description of gauge theories, we study the cosmological effects of relaxing the Hamiltonian and momentum constraints in general relativity and Gauss' law in electromagnetism. We show that the unconstrained theories have new source terms that mimic a pressureless dust and a charge density that only follows geodesics. The source terms may be the simplest explanation for dark matter and generically predict a charged component. We comment that discovery of such terms would rule out inflation and be a direct probe of the initial conditions of the universe.