## CMB radiation Power Spectrum Calculation

In the previous document the CMB radiation is a superposition/summation for l = 1 to 100 for alpha going from 0 to 360 of the function:
R(l)*sin(l * alpha * pi/180 + beta(l)).
In this document the same function but for l = 0 to 100 is studied. In the case of l = 0 the function is simplified to R(0).
R(0) can be positive or negative

• Figure 6 show the combined R results for 2 WMAP and 4 Planck simulations for l = 0 to 20.
• The 2 WMAP simulations are for the Hours 10 and 45. The same for the 2 Planck simulations.
• Each column with R values is a combination of different simulations.
• For example column 3 "WMAP 45" shows the combined results of the data in Picture 10 and 11
When you compare the results of both WMAP and Planck for Hour = 10 than they are almost identical
The same for the WMAP and Planck results for Hour = 45.
But when you compare the results for Hour = 10 and Hour = 45 than they are different.
This is more or less as expected because the WMAP and Planck results are generally speaking identical, but if you compare the results for different meridians than they are different.
 l WMAP 10 Planck 10 WMAP 45 Planck 45 Planck 45* Planck 90 0 -2,19 -34,09 -11,81 -55,78 -51,40 -34,94 1 31,98 35,39 9,01 12,70 12,16 26,54 2 24,58 36,53 25,01 39,95 36,11 4,23 3 5,72 1,81 7,19 7,43 6,26 9,62 4 14,75 17,35 10,39 6,53 7,03 9,38 5 5,25 3,79 24,66 24,01 19,47 16,51 6 20,75 20,76 5,68 6,99 3,29 20,76 7 9,78 5,63 3,46 6,01 4,53 13,92 8 11,44 9,72 18,88 14,83 11,40 9,59 9 24,51 22,27 3,03 12,95 6,74 11,49 10 0,70 8,39 16,14 13,76 12,31 10,62 11 2,90 13,43 13,57 10,27 10,76 2,51 12 5,41 3,61 2,79 2,41 2,39 5,63 13 25,97 31,06 2,20 7,06 7,56 10,73 14 9,33 20,56 15,12 10,00 11,76 7,15 15 16,60 18,64 4,14 1,87 3,93 17,87 16 5,22 6,70 2,04 4,22 3,96 8,05 17 1,75 1,24 4,41 13,48 8,15 9,48 18 15,24 14,63 5,43 4,80 2,84 13,19 19 0,41 5,68 19,24 19,35 11,76 16,36 20 2,99 2,01 12,66 9,80 10,80 4,43
R values
figure 6
 WMAP 10 39,98 Planck 10 91,31 WMAP 45 41,06 Planck 45 97,47 Planck 45* 84,05 Planck 90 94,97
Average error values
figure 7
• Figure 7 Show the average error values for 2 WMAP simulations and 4 Planck simulations for 3 different Hour values.
• In most cases l goes from 1 to 60. In Planck 45* l goes from 1 to 500.
The reason that the average error for the Planck results is higher (compared with the WMAP results) comes because the positive temperature values are higher and the negative values are lower. Specific the peaks are higher and the valleys are lower.

The Planck 45* value is lower than the Planck 45 value because much more sinus functions are included (500 compared to 60)

Created: 2 June 2013

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