The 3-point function in the large scale structure: I. The weakly non-linear regime in N-body simulations

A B ST R A C T Thispaperpresentsa com parison ofthe predictionsforthe 2 and 3-pointcorrelation functionsofdensity uctuations, and ,in gravitationalperturbation theory (PT) againstlargeCold Dark M atter(CDM )sim ulations.Thiscom parison ism adepossible forthe rsttim eon largeweakly non-linearscales(> 10h M pc)thanksto thedevelopm entofa new algorithm to estim ate correlation functionsform illionsofpointsin only a few m inutes.Previousstudiesin the literature com paring the PT predictions ofthe 3-pointstatisticsto sim ulationshavefocused m ostly on Fourierspace,angular space orsm oothed elds.Results in con guration space,such asthe ones presented here,werelim ited to sm allscaleswereleading orderPT givesa poorapproxim ation. Herewealsoproposeand applyam ethod forseparatingthe rstand subsequentorders contributionstoPT by com biningdi erentoutputtim esfrom theevolved sim ulations. W e nd thatin allcasesthere isa regim ewere sim ulationsdo reproduce the leading order(tree-level)predictionsofPT forthe reduced 3-pointfunction Q 3 = .For steeply decreasing correlations (such as the standard CDM m odel) deviations from the tree-levelresults are im portant even at relatively large scales,’ 20 M pc/h.O n largerscales goesto zero and theresultsaredom inated by sam pling errors.In m ore realistic m odels (like the C D M cosm ology)deviations from the leading order PT becom eim portantatsm allerscalesr’ 10 M pc/h,although thisdependson theparticular3-pointcon guration.W e characterise the range ofvalidity ofthisagreem ent and show the behaviourofthe nextorder(1-loop)corrections.