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Field Equations
The equation of motion for a scalar field in an expanding universe is

(6.1) 
To begin with we will assume a general form for the variable rescalings

(6.2) 
The position coordinates shouldn't be modified by any powers of the
scale factor so that the same comoving wavelengths stay in the box
throughout the run. In principle the coefficient could be
different for and but it is simpler and more useful to
keep them the same, thus giving an initial sound speed of one. Below
we will derive expressions for these rescaling coordinates in terms of
parameters in the potential of the model being solved. To express the
field equation in program variables note that

(6.3) 

(6.4) 
Finally define a new potential

(6.5) 
(The potential rescaling is chosen to be consistent with an energy
rescaling that gives
.) Then putting
in all rescalings the equation of motion becomes

(6.6) 
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