It is known that the appearance of microscopic objects with distinct topologies and different Euler characteristics, such as instantons and wormholes, at the spacetime-foam level in Euclidean quantum gravity approaches leads to spacetime topology changes. Such changes, in principle, may affect the field equations that arise through the semiclassical variation procedure of gravitational actions. Although in the case of Einstein-Hilbert action the presence of microscopic wormholes does not lead to any nontrivial result, when the Gauss-Bonnet term is added in the gravitational action, the above effective topological variation procedure induces an effective cosmological constant that depends on the Gauss-Bonnet coupling and the wormhole density. Since the latter in a dynamical spacetime is in general time-dependent, one obtains an effective dark energy sector of topological origin.

• Received 21 December 2023
• Accepted 26 February 2024

DOI:https://doi.org/10.1103/PhysRevD.109.084010