CMB fluctuations and large scale fluctuations nowadays do not match ?

[smallphi]

CMB fluctuations and large scale fluctuations nowadays do not match ?

The CMB dark matter density fluctuations for big scales is d_rho/rho~ 10^-5 and lower.
The scale factor increased ~ 1000 times from last scattering to now.
Linear perturbation theory predicts that the density fluctuations today would be ~ 1000 times what they were at last scattering i.e. d_rho/rho ~ 10^-2 today.

That is in obvious disagreement with what we observe since density fluctuations on scales of voids for example suggest fluctuations of order d_rho/rho ~ 1. This is two orders of magnitudes off the suggested value from linear perturbation theory and such big scales like voids just entered the non-linear regime so the explanation it's nonlinear effect is not plausable.

So what is the explanation of that?

 

[Chalnoth]

The CMB dark matter density fluctuations for big scales is d_rho/rho~ 10^-5 and lower.
The scale factor increased ~ 1000 times from last scattering to now.
Linear perturbation theory predicts that the density fluctuations today would be ~ 1000 times what they were at last scattering i.e. d_rho/rho ~ 10^-2 today.

That is in obvious disagreement with what we observe since density fluctuations on scales of voids for example suggest fluctuations of order d_rho/rho ~ 1. This is two orders of magnitudes off the suggested value from linear perturbation theory and such big scales like voids just entered the non-linear regime so the explanation it's nonlinear effect is not plausable.

So what is the explanation of that?

I'd have to break out my old cosmology texts to be sure, but I don't believe there is any such problem when you look at it in detail. Everything I've seen in cosmology talks and whatnot indicates that the large-scale behavior is predicted extremely well with linear perturbation theory. It is only at small scales that things start to diverge significantly, and even then the divergence can be largely fixed with some semi-analytic approximations.

So I suspect one of three things could be the case:
1. You've got the wrong input numbers.
2. Your understanding of how d_rho/rho scales with expansion is off (I don't remember offhand what it is).
3. You're mistaking the expected output from linear perturbation theory with the observed d_rho/rho that results after non-linear behavior is taken into account.

 

[smallphi]

I'm interested in void scales, d ~ 60Mpc.
The only number that might be wrong is d_rho/rho ~ 10^-5 at last scattering but not very probable - I checked it already with semianalytical formulas. In linear regime, the growing perturbation mode in matter dominated universe is proportional to the scale factor so the perturbation grew about 1100 times since last scattering.

The void scales currently have density contrast ~-1 inside the void and ~1.5 in the dense walls, so they are just getting into nonlinear regimes. Nonlinear effects cannot provide two orders of magnitude increase over the linear regime so soon.

 

[smallphi]

I got it finally.

The delta_rho/rho of dark matter for that scale is around 0.06 at last scattering.
I was using wrong formula for it since I took for the wave vector k= Pi/60 when I should have taken k=1/60 Mpc which puts it in a different case formula.

 

[Chalnoth]

I got it finally.

The delta_rho/rho of dark matter for that scale is around 0.06 at last scattering.
I was using wrong formula for it since I took for the wave vector k= Pi/60 when I should have taken k=1/60 Mpc which puts it in a different case formula.

Ah, okay, that makes sense. Sorry I wasn't more help, as I haven't worked with structure formation in a number of years.