# Search Results

1. Post

### A Calculating the power spectra of scalar perturbation

Check out that Stewart and Lyth references I posted earlier.
Post by: bapowell, May 19, 2017 in forum: Cosmology
2. Post

### A Calculating the power spectra of scalar perturbation

If you wish to find $r$ at N=60, you're done.
Post by: bapowell, May 19, 2017 in forum: Cosmology
3. Post

### A Calculating the power spectra of scalar perturbation

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...
Post by: bapowell, May 19, 2017 in forum: Cosmology
4. Post

### A Calculating the power spectra of scalar perturbation

Well, you originally asked for the spectrum as a function of $k$, remember?
Post by: bapowell, May 19, 2017 in forum: Cosmology
5. Post

### A Calculating the power spectra of scalar perturbation

If N = 200 is the end, then yes. FYI, conventionally the variable $N$ is defined as the number of e-folds before the end of inflation (which is...
Post by: bapowell, May 19, 2017 in forum: Cosmology
6. Post

### A Calculating the power spectra of scalar perturbation

The duration is not relevant to the observables as long as it's sufficient to solve the horizon/flatness problems. Whether I've got an inflation...
Post by: bapowell, May 19, 2017 in forum: Cosmology
7. Post

### A Calculating the power spectra of scalar perturbation

I don't know what you mean by "whatever $N$ I got..". Got from where? You have a range of N, and for each N there is a mode leaving the...
Post by: bapowell, May 19, 2017 in forum: Cosmology
8. Post

### A Calculating the power spectra of scalar perturbation

Observable scales leave the horizon 60 e-folds before the end of inflation in cold inflation. Is that no longer the case in warm inflation? I...
Post by: bapowell, May 19, 2017 in forum: Cosmology
9. Post

### A Calculating the power spectra of scalar perturbation

1) aH must be monotonically increasing as a function of N during inflation, since it is equal to 1 over the comoving horizon size (which is...
Post by: bapowell, May 19, 2017 in forum: Cosmology
10. Post

### A Calculating the power spectra of scalar perturbation

1) I don't understand why this graph isn't monotonic: what's with the sharp rise as N descends from 140? 2) You read off the value of $aH$...
Post by: bapowell, May 19, 2017 in forum: Cosmology
11. Post

### A Calculating the power spectra of scalar perturbation

Yeah, $r$ is just another way of reporting the tensor spectrum amplitude at the scale of interest.
Post by: bapowell, May 19, 2017 in forum: Cosmology
12. Post

### A Calculating the power spectra of scalar perturbation

I learned the basics of the inflationary perturbations calculation from Section 2.3 of Will Kinney's PhD thesis (he was my PhD advisor), available...
Post by: bapowell, May 18, 2017 in forum: Cosmology
13. Post

### A Calculating the power spectra of scalar perturbation

$N=60$ is just a rule-of-thumb. Remember, as I've been saying: the mapping between k (the scale of interest observationally) and N is model...
Post by: bapowell, May 18, 2017 in forum: Cosmology
14. Post

### A Calculating the power spectra of scalar perturbation

Pick whatever you want for a(0): it's the proportionate change in $a$ that matters. Also, you've got a misplaced power of 2 in (2) (should be...
Post by: bapowell, May 18, 2017 in forum: Cosmology
15. Post

### A Calculating the power spectra of scalar perturbation

But you do have an equation for the scale factor! Can you write $a$ as a function of $N$?
Post by: bapowell, May 18, 2017 in forum: Cosmology
16. Post

### A Calculating the power spectra of scalar perturbation

Sure, that works. I only mentioned the explicit mapping so that you can see how to go from k <-> N in general. But, yes, if you have k = aH as a...
Post by: bapowell, May 18, 2017 in forum: Cosmology
17. Post

### A Calculating the power spectra of scalar perturbation

It's measured on CMB scales, which generally do not correspond to the onset of inflation. Remember, inflation can last arbitrarily long, for...
Post by: bapowell, May 18, 2017 in forum: Cosmology
18. Post

### A Calculating the power spectra of scalar perturbation

You can find the relationship by taking the derivative of k = aH wrt N...
Post by: bapowell, May 18, 2017 in forum: Cosmology
19. Post

### A Calculating the power spectra of scalar perturbation

Which N you choose depends on what length scale you wish to measure r on. The mapping between and N and k is model dependent, but for a given...
Post by: bapowell, May 18, 2017 in forum: Cosmology
20. Post

### A Calculating the power spectra of scalar perturbation

Yes. In fact, I did this for my thesis ;). See this paper for a discussion of the numerical solution: https://arxiv.org/pdf/0706.1982.pdf. In...
Post by: bapowell, May 18, 2017 in forum: Cosmology
21. Post

### A Calculating the power spectra of scalar perturbation

A few things. If you wish to compute r without reference to slow roll, you can't use the expression you posted for P_S, since it is lowest-order...
Post by: bapowell, May 18, 2017 in forum: Cosmology
22. Post

### A Calculating the power spectra of scalar perturbation

Yep. There is just one k that crossed the horizon at N = 60. But you said you wanted P(k), so presumably you are interested in the spectrum at...
Post by: bapowell, May 18, 2017 in forum: Cosmology
23. Post

### A Calculating the power spectra of scalar perturbation

What is IT? You have k vs. N. Pick an N. The associated k is crossing the horizon at that N. I think we're talking past each other...
Post by: bapowell, May 18, 2017 in forum: Cosmology
24. Post

### A Calculating the power spectra of scalar perturbation

No, you're plotting k = aH, say, as a function of N. This function tells you the value of k that is crossing the horizon at the corresponding...
Post by: bapowell, May 18, 2017 in forum: Cosmology
25. Post

### A Calculating the power spectra of scalar perturbation

Once you have k = aH as a function of N, you can obtain P(k) parametrically.
Post by: bapowell, May 18, 2017 in forum: Cosmology
26. Post

### A Calculating the power spectra of scalar perturbation

You've got two relations: the power spectrum and the horizon crossing condition. The expression for P can be solved in terms of some time...
Post by: bapowell, May 18, 2017 in forum: Cosmology
27. Post

### A Calculating the power spectra of scalar perturbation

What are you trying to do, determine P(k)?
Post by: bapowell, May 18, 2017 in forum: Cosmology
28. Post

### A Calculating the power spectra of scalar perturbation

What is the condition for horizon crossing in warm inflation? In standard inflation it's k = aH.
Post by: bapowell, May 18, 2017 in forum: Cosmology
29. Post

### I Alexander Vilenkin spontaneous creation

The universe is *close* to flat, but may still be closed.
Post by: bapowell, May 13, 2017 in forum: Cosmology