Page 91 - swp0000.dvi

by equation (4.3)

The lowest-order equations in  for the cold dust are

(1)
 (1) = −    0   (1)  (1) = −     (4.6)
 2 
 

(1) (1) (1) (1)
       
= − and = −  (4.7)
  2 Θ   
whereas for the hot one are given by

(1)    0 (1)
 =  
 23 2
 − 
0
(1)
 (1) =     (4.8)

 23 −  2
0
  (1)    (1)  (1)    (1)

= − and = −  (4.9)
2
2
  −   23 Θ   −  23 
0
0
The Poisson equation provides the compatibility condition
4
(− (   0 − ( − 1)  (   0 +  0 +    0 )) +
   
        0        0
− )=0  (4.10)
 2  23 −  2
0

with
53 0
 = 
 23  
0
At the next order of , the compatibility condition for the second-order

quantities leads to an evolution equation for the first order approximation

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