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The Scale Factor Equation
The equation for the scale factor is derived from the
Friedmann equations

(6.19) 

(6.20) 
For a set of scalar fields in an FRW universe

(6.21) 
where , , and are kinetic (time derivative), gradient, and
potential energy respectively with

(6.22) 
Equations (6.19) and (6.20) and the field evolution
equations form an overdetermined system. In principle either scale
factor equation could be used but in practice it is easiest to combine
them so as to eliminate the time derivative term because in the
staggered leapfrog algorithm and are known at different
times. Eliminating we get

(6.23) 

(6.24) 
To convert to program variables note that

(6.25) 
so the scale factor equation becomes

(6.26) 
Next: Correcting for Staggered Leapfrog
Up: Scale Factor Evolution
Previous: Scale Factor Evolution
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This
documentation was generated on 20080121