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.
