Concordance cosmology without dark energy
  According to the separate universe conjecture, spherically symmetric sub-regions in an isotropic universe behave like mini-universes with their own cosmological parameters. This is an excellent approximation in both Newtonian and general relativistic theories. We estimate local expansion rates for a large number of such regions, and use a scale parameter calculated from the volume-averaged increments of local scale parameters at each time step in an otherwise standard cosmological $N$-body simulation. The particle mass, corresponding to a coarse graining scale, is an adjustable parameter. This mean field approximation neglects tidal forces and boundary effects, but it is the first step towards a non-perturbative statistical estimation of the effect of non-linear evolution of structure on the expansion rate. Using our algorithm, a simulation with an initial $\Omega_m=1$ Einstein--de~Sitter setting closely tracks the expansion and structure growth history of the $\Lambda$CDM cosmology. Due to small but characteristic differences, our model can be distinguished from the $\Lambda$CDM model by future precision observations. Moreover, our model can resolve the emerging tension between local Hubble constant measurements and the Planck best-fitting cosmology. Further improvements to the simulation are necessary to investigate light propagation and confirm full consistency with cosmic microwave background observations. 
G\'abor R\'acz, L\'aszl\'o Dobos, R\'obert Beck, Istv\'an Szapudi and   Istv\'an Csabai
astro-ph.CO