Aequitas Field Theory - A Dust-Time Based Conceptual Approach to Vacuum-Energy Sequestering (Hypothetical Construct)

A conceptual approach illustrating how constant vacuum-energy terms may be neutralized without introducing new dynamical degrees of freedom.

This work presents a hypothetical construct that explores how Brown–Kuchař dust fields may be used to define a covariant dust-time foliation and to support a sequestering mechanism for constant contributions to vacuum energy. Dust fields serve as relational reference variables, allowing comoving energy densities to be defined in a covariant way. Within this setting, a local algebraic condition is imposed that ties the comoving energy density of a selected matter–scalar sector to a function of dust time. A second, semi-global condition enforces the vanishing of the dust-measured spatial average of this combination on each dust-time slice.

In the Hamiltonian formulation, the associated multiplier sector forms, after gauge fixing, a second-class pair that removes the multiplier and its momentum from the reduced phase space. No additional propagating degrees of freedom arise beyond those of general relativity with the given matter content. The covariant field equations, ADM structure, and the behavior of homogeneous FLRW solutions are outlined, including the observation that constant vacuum-energy contributions cancel in the effective Friedmann equations while allowing for late-time accelerated expansion.

The analysis also provides a qualitative discussion of linear perturbations and comparisons with related ideas such as unimodular gravity, four-form sequestering, and mimetic constructions. The framework is intended as an exploratory and incomplete conceptual approach rather than a finished physical theory.