According to the big-bang model, it is assumed that when the universe was young enough (lets say z > 1100), the density fluctuations did evolve in the linear regime. Due to this fact, one can make use of simple linearized formulas such as the continuity, Poisson and Euler equations to model the dynamics of the perturbations on a background (aka Jeans analysis). The solution to this equations can be split into Fourier modes, which evolve independently.(adsbygoogle = window.adsbygoogle || []).push({});

The non-linear regime is entered when the gravitational collapse becomes strong, or equivalently when the density contrast (fluctuation vs. mean density of the universe) approaches to one (or, at least, when it is not << 1 anymore). In this regime, the Fourier modes become coupled and the perturbation theory is not longer a valid description.

My assumption is that two factors are mainly relevant to determine the onset of nonlinearity: on the one hand the spatial scale (when considering smaller scales one is forced to take non-linearity into account) and on the other hand the time (the more the redshift approaches to zero, the more need to take non-linearity into account). My guess was that non-linearity takes place with the formation of the galaxy clusters, which starts to take place more or less at z ~ 5.

But this seams to be wrong. I had a look to the webpage of the Virgo project here:

http://www.mpa-garching.mpg.de/galform/virgo/index.shtml

The first two links:

http://www.mpa-garching.mpg.de/galform/virgo/hubble/index.shtml

http://www.mpa-garching.mpg.de/galform/virgo/int_sims/index.shtml

describe the simulation made for the whole Hubble volume (first link) and the "intermediate simulations" of 200 Mpc (second link). In the second link it is explicitely stated that a N-body simulation was done.

This is confusing. If my assumption is right, it is not clear why it is necessary to make use of complicated N-body simulations to model large scale structure formation at 200 Mpc, instead of linear perturbation theory of fluids as mentioned before. So it seams that the "transition" between the linear and non-linear regime takes place before and may be also on larger scales.

I would like to know whether my qualitative understanding is correct and when this transition takes place and on which scales. Also it would be nice to know how the cosmological model influences the onset of nonlinearity, e.g. whether universes with less dark energy became earlier (and at greater scales) nonlinear.

Comments regarding the Virgo simulations are also wellcome.

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# Large scale structure formation and nonlinearity onset

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