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Abstract: I show how to reintroduce velocity dispersion into perturbation theory PTcalculations of structure in the Universe, i.e., how to go beyond thepressureless fluid approximation, starting from first principles. Thisaddresses a possible deficiency in uses of PT to compute clustering on theweakly non-linear scales that will be critical for probing dark energy.Specifically, I show how to derive a non-negligible value for the initiallytiny velocity dispersion of dark matter particles, <\delta v^2>, where \deltav is the deviation of particle velocities from the local bulk flow. Thecalculation is essentially a renormalization of the homogeneous zero orderdispersion by fluctuations 1st order in the initial power spectrum. For powerlaw power spectra with n>-3, the small-scale fluctuations diverge andsignificant dispersion can be generated from an arbitrarily small startingvalue - the dispersion level is set by an equilibrium between fluctuationsgenerating more dispersion and dispersion suppressing fluctuations. For ann=-1.4 power law normalized to match the present non-linear scale, thedispersion would be ~100 km-s. This n corresponds roughly to the slope on thenon-linear scale in the real \LambdaCDM Universe, but \LambdaCDM contains muchless initial small-scale power - not enough to bootstrap the small startingdispersion up to a significant value within linear theory viewed very broadly,structure formation has actually taken place rather suddenly and recently, inspite of the usual -hierarchical- description. The next order PT calculation,which I carry out only at an order of magnitude level, should drive thedispersion up into balance with the growing structure, accounting for smalldispersion effects seen recently in simulations.



Author: Patrick McDonald

Source: https://arxiv.org/



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