A topological origin for Dark Energy

TL;DR

This paper proposes a topological approach to explain the small value of the cosmological constant, linking it to global topological invariants and providing a natural origin for dark energy within general relativity.

Contribution

It introduces topological class densities as a mechanism to generate an effective cosmological constant, connecting topology with dark energy in a novel way.

Findings

Effective cosmological constant derived from topological invariants.

Small value of dark energy explained by division over spacetime volume.

Provides a method to measure the global Euler number.

Abstract

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.