A free-singularity general relativity solution modelling a lattice universe in which the cosmological constant results from the lattice granularity

Several models have been proposed explaining the cosmological constant as a consequence of a distance-redshift relation alteration by the universe inhomogeneities. We modelled the universe as a galactic spherical mass having a gaussian radial profile repeated on the nodes of a periodic lattice. The Einstein field equations were solved at the first order for the 2-scalar and 1-tensor perturbation of the FRLW metric. When constraining the two scalar fields to be proportional to each other, the cosmological constant directly appeared in the Einstein field equations derived from the metric. The final metric solution is free of any singularity and differs by less than 1% from the conventional FRLW metric. This tiny difference results from the actual low value of the Hubble constant. This geometrically derived cosmological constant exponentially decreases when the galaxy extent tends to the inter galaxy distance. When the universe becomes homogeneous, the expanding rate equation reduces to that of the cosmological constant-free FLRW model. The model is Copernican in the sense that all galaxies share similar observational features. The model opens a new research track to explain the origin of the cosmological constant within the pure general relativity framework.