Replacing dark energy by silent virialisation

¹ Toruń Centre for Astronomy, Faculty of Physics, Astronomy and Informatics, Grudziadzka 5, Nicolaus Copernicus University, ul. Gagarina 11, 87-100 Toruń, Poland
e-mail: boud@astro.uni.torun.pl
² Univ Lyon, ENS de Lyon, Univ Lyon1, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574, 69007 Lyon, France

Received: 19 June 2017
Accepted: 22 October 2017

Abstract

Context. 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.

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 the 𝒬_𝒟 Zel’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) cosmological N-body initial conditions. Using RAMSES, we partitioned the volume into domains and called the DTFE library 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 the INHOMOG library, 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 constant H₁^EdS = 37.7 km s⁻¹ ∕Mpc and an effective Hubble constant H_eff,0 = 67.7 km 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 of L_13.8¹³ = 2.5_−0.1^+0.1 Mpc/h_eff. Relativistically interpreted, this corresponds to strong average negative curvature evolution, with the mean (median) curvature functional Ω_ℛ^𝒟 growing 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.

Conculsions. Thus, starting from EdS initial conditions and averaging on a typical non-linear structure formation scale, the VQZA dark-energy–free average expansion matches ΛCDM expansion to first order. The software packages used here are free-licensed.