Calculating the power spectra of scalar perturbation

  • #51
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Well, you originally asked for the spectrum as a function of ##k##, remember?
No, I just want ##P_S## AT the horizon crossing (which now we say at ##N=60##), because my main goal is to get ##r## at the horizon crossing.
 
  • #52
bapowell
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Yes. Refer to posts #4 and #5 where you confirm that you desire to find ##P(k)##. And to be clear: your main goal here is to find ##r## on a particular observable scale (not simply "at horizon crossing"), which you've selected to be N=60. But, as is standard, we quote observables on a given scale ##k##, and so you need the ##k=aH## mapping to go from ##k## to ##N##.
 
  • #53
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Yes. Refer to posts #4 and #5 where you confirm that you desire to find ##P(k)##. And to be clear: your main goal here is to find ##r## on a particular observable scale (not simply "at horizon crossing"), which you've selected to be N=60. But, as is standard, we quote observables on a given scale ##k##, and so you need the ##k=aH## mapping to go from ##k## to ##N##.
So you mean, choosing ##N=60## is enough to calculate ##r## at that point though I should state it as you've mentioned in the latter part? Or you mean I should still show ##k=aH## vs ##N## even though I've decided already to compute ##r## at ##N=60##?
 
  • #54
bapowell
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If you wish to find ##r## at N=60, you're done.
 
  • #55
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If you wish to find ##r## at N=60, you're done.
Ok, so that is settled. What is the corresponding formula for the spectral index NOT in terms of ##k##? I mean, like the one I posted for ##P_S##, it is the lowest order in slow roll.
 
  • #56
bapowell
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Check out that Stewart and Lyth references I posted earlier.
 

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