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The Initial value of the Hubble Constant
The initial value of the Hubble constant is used for setting the field
derivatives (equation (6.72)) and as an initial condition
for the second order evolution equation for the scale factor. The
derivative of is determined by the equation

(6.87) 
Initially is set to and

(6.88) 
In setting initial values we assume all inhomogeneities are small and
thus use only the homogeneous values of the fields and
. Typically the initial field values will be one for the
inflaton and zero for all other fields but they can be set to any
values by the user. In general, the initial energy density is thus

(6.89) 
Converting to program variables
where the second step uses the fact that initially . Since
initially we can plug equation (6.90) into
equation (6.88) to get an equation we can solve for
. Solving this quadratic equation gives

(6.91) 
where refers to the initial value of and each term
with field or field derivative values is understood to be summed over
all fields.
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