Replacing dark energy by silent virialisation

Abstract

Context.Standard cosmologicalN-body simulations have background scale factor evolution that is decoupled from non-linear structure formation. Prior to gravitational collapse, kinematical backreaction (QD) justifies this approach in a Newtonian context.Aims.However, the final stages of a gravitational collapse event are sudden; a globally imposed smooth expansion rate forces at least one expanding region to suddenly and instantaneously decelerate in compensation for the virialisation event. This is relativistically unrealistic. A more conservative hypothesis is to allow non-collapsed domains to continue their volume evolution according to theQDZel’dovich approximation (QZA). We aim to study the inferred average expansion under this “silent” virialisation hypothesis.Methods.We set standard (MPGRAFIC) EdS 3-torus (T3) cosmologicalN-body initial conditions. UsingRAMSES, we partitioned the volume into domains and called theDTFElibrary to estimate the per-domain initial values of the three invariants of the extrinsic curvature tensor that determine the QZA. We integrated the Raychaudhuri equation in each domain using theINHOMOGlibrary, and adopted the stable clustering hypothesis to represent virialisation (VQZA). We spatially averaged to obtain the effective global scale factor. We adopted an early-epoch–normalised EdS reference-model Hubble constantH1EDS= 37.7km s-1∕Mpc and an effective Hubble constantHeff,0= 67.7km s-1∕Mpc.Results.From 2000 simulations at resolution 2563, we find that reaching a unity effective scale factor at 13.8 Gyr (16% above EdS), occurs for an averaging scale ofL13.8= 2.5−0.4+0.1Mpc∕heff. Relativistically interpreted, this corresponds to strong average negative curvature evolution, with the mean (median) curvature functionalΩRDgrowing from zero to about 1.5–2 by the present. Over 100 realisations, the virialisation fraction and super-EdS expansion correlate strongly at fixed cosmological time.Conclusions.Thus, starting from EdS initial conditions and averaging on a typical non-linear structure formation scale, the VQZA dark-energy–free average expansion matchesΛCDM expansion to first order. The software packages used here are free-licensed.