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Standard cosmological $N$-body simulations have background scale factorevolution that is decoupled from non-linear structure formation. Prior togravitational collapse, kinematical backreaction ($Q_D$) justifies thisapproach in a Newtonian context. However, the final stages of a gravitationalcollapse event are sudden; a globally imposed expansion rate thus forces atleast one expanding region to suddenly decelerate. This is relativisticallyunrealistic. Instead, we allow non-collapsed domains to evolve in volumeaccording to the $Q_D$ Zel'dovich Approximation (QZA). We study the inferredaverage expansion under this "silent" virialisation hypothesis. We set standard(mpgrafic) EdS cosmological $N$-body initial conditions. Using RAMSES, we callDTFE to estimate the initial values of the three invariants of the extrinsiccurvature tensor in Lagrangian domains $D$. We integrate the Raychaudhuriequation in each domain using inhomog, adopt the stable clustering hypothesis(VQZA), and average spatially. We adopt an early-epoch--normalised EdSreference-model Hubble constant $H_1^{bg} = 37.7$ km/s/Mpc and an effectiveHubble constant $H_0^{eff} = 67.7$ km/s/Mpc. From 2000 simulations atresolution $256^3$, 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 averagenegative curvature evolution. The virialisation fraction and super-EdSexpansion correlate strongly at fixed cosmological time. Thus, starting fromEdS initial conditions and averaging on a typical non-linear structureformation scale, the VQZA dark-energy--free average expansion matches$\Lambda$CDM expansion to first order. The software packages used here arefree-licensed.

Replacing dark energy by silent virialisation