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The equation of motion for a scalar field in an expanding universe
is
|
(5.10) |
To define an adiabatic invariant occupation number for this field
we need to switch to conformal variables in which this equation
becomes a more standard oscillator equation. These variables are
|
(5.11) |
Using conformal time and noting that
|
(5.12) |
the equation of motion becomes
|
(5.13) |
Then switching to conformal field values note that
|
(5.14) |
and thus
|
(5.15) |
This equation can be approximated in Fourier space by
|
(5.16) |
where
and
|
(5.17) |
Next: Occupation Number and Energy
Up: Definitions of Number and
Previous: Rescaled Fourier Transforms
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This
documentation was generated on 2008-01-21