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Large scale structure formation and nonlinearity onset

  1. Sep 20, 2004 #1


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    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.

    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:

    The first two links:

    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.
    Last edited: Sep 21, 2004
  2. jcsd
  3. Oct 2, 2004 #2
    Don't know the answer to your questions, but the idea of simulate universes in a computer is really interesting.The link says that they performed 4 simulations corresponding to 4 different cosmological models, each simulation showing the behaviour of 2563 particles. This seems quite simplistic, but with the continuous power that computers are acquiring, who knows what can they simulate in the future? I imagine incredible simulations very detailed showing all the processes in the history of the universe: inflation, end of the radiation-dominated era, recombination, reionization,... Very interesting indeed
    Anecdotically, I didn't know that existed a model called the tau CDM model
  4. Oct 4, 2004 #3


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    As far as I know it is a flat model with neutrinos as the principal dark matter component (and without dark energy), which lead to a different shape of the power spectrum of density fluctuations (mainly decreasing the power on smaller scales).
    Last edited: Oct 4, 2004
  5. Oct 4, 2004 #4


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    hellfire - Thank you for those fascinating links.
    I think the difference between linear/non linear dynamics is one of epoch regime. The early universe is considered plasma/gas the later universe embedded dust.

    My question is, "The Virgo simulations are compared against other simulations, but which one matches the observed universe?"

    Last edited: Oct 4, 2004
  6. Oct 4, 2004 #5


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    I think the model which fits best with the observational data is the Lambda CDM. As far as I know, redshift distribution of mass (of clusters with a specific mass) and the temperature of the ICM (intracluster medium) are mainly the two criteria used to test the models against data from SDSS, 2dF, EMSS and RDCS surveys (these are the most important ones). I think this paper gives a detailed description for the Hubble volume simulation (it is very deep and extensive):

    Galaxy Clusters in Hubble Volume Simulations
    (this is the first reference in the Virgo page for the Hubble Volume Project)
  7. Nov 1, 2004 #6
    1. There is something which is called primordial power spectrum which plays an important role in deciding which scale (large/small) will become nonlinear first.
    In general, power spectrum is taken to be a power law (P(k) = k^n, -3<n<1,due to practical considerations).

    2. If the universe is dominated by cold dark matter (CDM), then small structures are formed first (this case is supported by observation, although there are problems with this also). There are many good references for the CDM power spectrum, I am putting one here

    3. There are many other power spectra, but one which is the most popular, and motivated by inflationary theory is called the Harrison-Zeldovich power spectrum (n=1). This power spectrum is scale free.

    4. Now you have a power spectrum and you have to evolve it forward in time.Its evolution depends on the background cosmological model.

    6. One most important scale is called the jeans scale. If there is any inhomogeneity less than this scale then that will be wiped out by pressure.

    7. So there are two scales, one is the size of horizon and the second jeans scale.

    8. According to inflationary theory perturbations on different scales entered within horizon at different times. Growth of any scale depends on the era (radiation/matter dominated) in which that is entering the horizon.

    The main things which are important for the structure formation are as follows.

    a). Power spectrum (P(k))
    b). How fast the universe is expanding (Hubbles constant).
    c). Total matter content (omega_total)

    Last edited: Nov 1, 2004
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