P(k)

[Boud Roukema]

Hi again, Bartek, everyone,

On Tue, 7 Jan 2003, Bartosz Lew wrote:

>
>  what is the true meaning of P(k) ???

It only has a true meaning if:

(1) the curvature of comoving space is zero (it is perfectly flat)

(2) the topology of comoving space is an equal-sided, right-angled,
hypertorus

If either (1) or (2) is false, then P(k) is only an *approximation*,
and if you forget this you may make errors. (If everyone makes the
same error, it is still an error. It's OK politically, but not OK
scientifically.)


I did a quick search using

http://www.google.com

"power spectrum density perturbations"

and found a fairly standard definition by Pedro Viana:

http://nedwww.ipac.caltech.edu/level5/Viana/Viana2_1.html

What seems to be missing is the definition of  delta_[k (scalar)]
in terms of  delta_[k (vector)].


My guess is that

|delta_[k (scalar)]|^2  in the definition of P(k)

should be replaced by

< | delta_[k (vector)] | ^2 >

where the average is taken over all [k (vector)] pointing in different
directions, for the same fixed magnitude of  k > 0 .

But you should check, where you take an averages or absolute value can
make a difference...

boud