What Does Density Contrast in the Universe Mean in the Context of Chaplygin Gas?

[kptsilva]

hey people,

Can anyone tell me what density contrasts in the universe means? Is there a particular equation for this for say a model like λCDM?

 

[Bobbywhy]

kptsilva, You have asked a simple question that needs a long and complicated answer. Some folks spend their whole careers studying density contrasts in the universe. Simply put, when you compare a volume of intergalactic space with an equal volume containing a supercluster of galaxies there is a large "density contrast".

With that, I suggest you do some reading and then when you have more specific questions, come right back here and post them. Surely some members here are highly qualified and ready to assist you with any questions or doubts. I offer four references for you:

"The matter power spectrum describes the density contrast of the universe (the difference between the local density and the mean density) as a function of scale. It is the Fourier transform of the matter correlation function. On large scales, gravity competes with cosmic expansion, and structures grow according to linear theory. In this regime, the density contrast field is Gaussian, Fourier modes evolve independently, and the power spectrum is sufficient to completely describe the density field. On small scales, gravitational collapse is non-linear, and can only be computed accurately using N-body simulations. Higher-order statistics are necessary to describe the full field at small scales."
http://en.wikipedia.org/wiki/Matter_power_spectrum

"If we use the virial theorem on galaxies instead of clusters of galaxies then we get a mass-to-luminosity ratio that is about 30. Thus the mass-to-luminosity ratio appears to vary with the size of the region measured, from 3 in the solar neighborhood to 30 in galaxies to 300 in clusters of galaxies. Is there a possibility that for even larger objects the ratio could reach the critical value of 700? For such large regions we cannot use the virial theorem because these regions are still expanding with the Hubble flow. However, we can compute the gravitational acceleration due to the large density contrasts in the nearby superclusters. The density contrast, d(rho)/rho, can be measured by counting galaxies. The gravitational acceleration is proportional to d(rho) which is the measured density contrast times the unknown density. The gravitational acceleration times the age of the Universe gives our peculiar velocity relative to the CMB, which can be determined from the dipole anisotropy of the CMB. Different groups have reached different conclusions about whether the resulting Omega could reach the critical value of 1. But it definitely appears that the dark matter fraction increases with the size of objects at least up to clusters of galaxies (1 Mpc radius)."
http://www.astro.ucla.edu/~wright/density.html

"Primordial matter density contrast and the size of the very early universe in the Quantum Big Bang theory of the cosmological constant"
Authors:Budh Ram
http://arxiv.org/abs/0805.4268

"STRUCTURE FORMATION IN THE UNIVERSE"
http://ned.ipac.caltech.edu/level5/Sept02/Padmanabhan/Pad5.html

 

[kptsilva]

Thank you BobbyWhy. Is there any experimental data for density contrasts in the universe?

 

[Bobbywhy]

Yes, there are mountains of experimental data for density contrasts in the universe. Did you notice any in those four references?

 

[Simon Bridge]

Without the context, the short answer is "no"... there is no way to tell what the phrase means. It may be just referring to the contrasts of mass densities between different regions of the universe eg between the interior of a neutron star vs interstellar space.

 

[nicksauce]

Usually density contrast, in the cosmological sense means - $\delta\rho/\rho$, the difference from the average density of the universe divided by the average density. It's something you can solve for in LCDM, but not something I can easily write down a single equation for. GR Perturbation theory with microphysics is really messy. Pick up a cosmology text like Dodelson if you are really interested in it.

 

[kptsilva]

I was wondering if there is any experimental data for density contrast vs. scale factor?

 

[Bobbywhy]

If "experimental data" can be taken to be equivalent to "observational evidence" then you may Google search for "Dark Energy" and begin with the Wikipedia page which lists four types of observational evidence that address density contrasts versus scale factor. Or, is there some way you might describe exactly what it is you are searching for by writing a more clear and concise question?

 

[Chalnoth]

This is the mathematical framework used to describe the density contrasts in Cosmology on large scales:
http://en.wikipedia.org/wiki/Cosmological_perturbation_theory

The cleanest observation of this density contrast is the CMB, currently best-observed via WMAP, though Planck results should be available early next year.

 

[kptsilva]

i'm studying this paper(attached) and in the final figure(04) there is a density contrast vs. scale factor graph. i just want to check how close the values of this model agrees with the experimental data. is there any way to do that?

 

[Bobbywhy]

kptsilva, You have posted questions about Chaplygin gas here on PF twice on May 17th, once more on May 30th, and once again on June 3rd, all which demonstrate your keen interest in the subject.

On July 3rd your new post asking “what density contrasts in the universe means?” caused several members to try to guess your context. It would have been clearer to members if you had posted the paper you were studying (by Bento, Bertolami, and Sen) and asking about in your original post. Once again, the main subject is Chaplygin gas. I feel confident qualified members here could have given their responses directly addressing your doubt had they known that subject. Thank you for informing members here of the source document for your question about density contrasts versus scale factor.