A topological origin for Dark Energy

Cosmology struggles with the theoretical problems generated by the observed value and recent emergence of a cosmological constant, in the standard model of cosmology, i.e. the concordance model. We propose to provide a more natural explanation for its value than the conventional quantum vacuum energy in the guise of topological invariants. Introducing topological classes densities as Lagrange multipliers, an effective cosmological constant is generated. General Relativity is reestablished by cancelling the torsion thus generated, which provides constraints on the invariants and yield the form of the effective cosmological constant. As it is divided by the total volume of spacetime, its small value compared to the Planck scale is therefore natural. It also provides a direct measurement of the global Euler number.
Comment: The problem presented is ill-defined and therefore the solutions are not consistent as claimed. First, the variational problem is not redefined after the characteristic classes are added into the action, which is necessary. Secondly, the paper assumes certain restrictions over the contortion that forces the topology in a very cumbersome way which is, as we see it, still very poorly justified