Apparent Size of CMB Primordial Anisotropies

[fab13]

Hello,

i wrote a Matlab program which calculate the apparent angle of an anisotropy with a size equal to "380.000 light-years" , i.e "0.1166 Mpc".

For this, i have used the following equation defining the apparent angle ( in arcminute unit) as a function of the redshift "z" with "D_anisotropy=size of the anisotropy" :

$$\theta= \dfrac{180*60}{\pi}\,D_{anisotropy}\,\big[\dfrac{c}{H_{0}\,(1+z)} \ ,\int_{z_{begin}}^{z} \,(\Omega_{m}\,(1+z)^{3}+\Omega_{\Lambda}+\Omega_{k}\,(1+z)^{2})^{-1/2}\,dz\big]^{-1}$$

For $$\Omega_{m}=0.3$$ and $$\Omega_{\Lambda}=0.7$$, i get the figure in attachment. For "z=1100", I have an angle apparent equal to about 30 arcminutes for D_anisotropy=380.000 ly , i.e 0.5 degrees.

This value is relatively quite far from the first peak in CMB power spectrum which is localized at "l=200", i.e "theta= 1 degree".

Does the relation between multipole "l" and "theta" angle take the form : "theta(°)=200/l" ?

If it does, then my calculation is the value of one of the others peaks which are localized for smaller angles ?

If anyone could explain me to which peak corresponds this result,

Thanks in advance.

ps: here is the Matlab code :

function dist_diam_ang

c=3*10^(5);
H0=71;

Omega2_m=0.3;
Omega2_red=0.7;
Omega2_k=1-Omega2_m-Omega2_red;

z_begin=0.1;
z_final=1100;

size1=(380000/3.26)*10^(-6); % Megaparsec
inter=1;

j=1;
for z=z_begin:inter:z_final
theta1(j)=(180*60/(pi))*size1*(c/(H0*(1+z))*(quad(@(x)myfunc(x,Omega2_m,Omega2_red,Omega2_k),z_begin,z)))^(-1);
j=j+1;
end



plot(z_begin:inter:z_final,theta1);
ylim([0 60]);
xlabel('Redshift z');
ylabel('Apparent Angle (arcminute)');


%-------------------%
function y = myfunc(x,Omega_m,Omega_red,Omega_k)
y=(Omega_m*(1+x).^(3)+Omega_red+Omega_k*(1+x).^(2)).^(-1/2);
end
%-------------------%


end

 

[Chalnoth]

Why did you pick out 380,000 light years?

P.S. This calculation looks correct to me. I think there's just an issue with your interpretation.

 

[fab13]

I thought this anisotrpy size (380,000 ly) seemed to be typical because i saw a conference where the speaker told us to put this size .

Which peak am I supposed to find with my previous calculation of theta at z=1100 ? (the first peak at L=200, the second one at L=500, ... ?

How to choose a good value for this anisotropy size to find a value corresponding to this peak ?

Thanks in advance.

 

[Chalnoth]

I thought this anisotrpy size (380,000 ly) seemed to be typical because i saw a conference where the speaker told us to put this size .

Which peak am I supposed to find with my previous calculation of theta at z=1100 ? (the first peak at L=200, the second one at L=500, ... ?

How to choose a good value for this anisotropy size to find a value corresponding to this peak ?

Thanks in advance.

Might be easier to take the angular size and convert that to a length scale. You'll get a number about twice that.

Which should make sense: the CMB was emitted when the universe was around 380,000 years old or so. So an initial perturbation would have been able to expand in one direction some 380,000 light years, and 380,000 light years in the other direction, leading to a peak-to-peak distance of about 760,000 light years (very roughly).

Granted, one would have to investigate the precise nature of the expansion in those first 380,000 years to get a good handle as to why the sound horizon works out to be close to this intuitive calculation.

 

[fab13]

Which should make sense: the CMB was emitted when the universe was around 380,000 years old or so. So an initial perturbation would have been able to expand in one direction some 380,000 light years, and 380,000 light years in the other direction, leading to a peak-to-peak distance of about 760,000 light years (very roughly).

Yes, taking an anisotropiy size equal to 760.000 ly, i find with this calculation the double of my previous result , i.e an angle equal to 60 arcminutes, so 1°. This corresponds roughly to the first "accoustic peak" in cmb power spectrum (l =200).

Granted, one would have to investigate the precise nature of the expansion in those first 380,000 years to get a good handle as to why the sound horizon works out to be close to this intuitive calculation.

My calculation is very simple and as you say, only the physical models before the first 380.000 years can explain the precise value of the first acoustic peak, in this case, i mean the photon-baryon plasma models. Nevertheless, i don't think that it's a coincidence.

Thanks.

 

[Chronos]

It only proves the current model is incomplete, not incorrect. We already knew that. That is only one of a number of anomalies in the LCDM model. No need to despair, it is what preserves jobs for scientists - scientists too have children they are trying to put through college before they become obsolete.

 

[TrickyDicky]

It only proves the current model is incomplete, not incorrect. We already knew that. That is only one of a number of anomalies in the LCDM model. No need to despair, it is what preserves jobs for scientists - scientists too have children they are trying to put through college before they become obsolete.

Could there be a more cynical view?! Nevermind the science and that models are full of anomalies as long as jobs are assured and money keeps flowing in, right?
I hope this is not a generalized attitude but explains a lot.