Replacing dark energy by silent virialisation

Standard cosmological $N$-body simulations have background scale factor evolution that is decoupled from non-linear structure formation. Prior to gravitational collapse, kinematical backreaction ($Q_D$) justifies this approach in a Newtonian context. However, the final stages of a gravitational collapse event are sudden; a globally imposed expansion rate thus forces at least one expanding region to suddenly decelerate. This is relativistically unrealistic. Instead, we allow non-collapsed domains to evolve in volume according to the $Q_D$ Zel'dovich Approximation (QZA). We study the inferred average expansion under this "silent" virialisation hypothesis. We set standard (mpgrafic) EdS cosmological $N$-body initial conditions. Using RAMSES, we call DTFE to estimate the initial values of the three invariants of the extrinsic curvature tensor in Lagrangian domains $D$. We integrate the Raychaudhuri equation in each domain using inhomog, adopt the stable clustering hypothesis (VQZA), and average spatially. We adopt an early-epoch--normalised EdS reference-model Hubble constant $H_1^{bg} = 37.7$ km/s/Mpc and an effective Hubble constant $H_0^{eff} = 67.7$ km/s/Mpc. From 2000 simulations at resolution $256^3$, a unity effective scale factor is reached at 13.8~Gyr (16% above EdS) for an averaging scale of $L_{13.8}=2.5^{+0.1}_{-0.4}$ Mpc/$h^{eff}$. Relativistically interpreted, this corresponds to strong average negative curvature evolution. The virialisation fraction and super-EdS expansion correlate strongly at fixed cosmological time. Thus, starting from EdS initial conditions and averaging on a typical non-linear structure formation scale, the VQZA dark-energy--free average expansion matches $\Lambda$CDM expansion to first order. The software packages used here are free-licensed.