38. And again about effective QFT for inflation

Posted by Dmitry
May 8, 2008

I want again to come back to the paper “Where does effective field theory for inflation break down” by C. Armendariz-Picon et al. (kindly see the beginning of discussion here).

As David Seery immediately pointed out, the known (H/M_P)^2 * N result comes from IR effects, while C. Armedariz-Picon et al. actually discuss effective QFT and therefore deep UV effects, so the two things should be unrelated. At first sight, this indeed seems so…

Let us go back to the expression for two point correlator of the Mukhanov’s variable:

\langle{}v(k) v(k')\rangle=\frac{1}{2k}\left(\left(1+\alpha_{20}\frac{H^2}{M_P^2}+\cdots\right)+\right.

\left.\left(\alpha_{22}\frac{H^2}{M_P^2}+\alpha_{42}\frac{H^4}{M_P^4}+\cdots\right)\frac{k^2}{M_P^2}+\cdots \right) (1)

(formula (3.18) in the Armendariz-Picon et al. paper). As the authors point out, \alpha_{20} is of the order 1 while all \alpha_{nn} are generally of the order of \epsilon. So, what is the physical meaning of the smallness parameter \epsilon H^2/M_P^2?

Well, one can calculate the classical displacement of the inflaton during one efolding:

\Delta\phi\sim-\frac{1}{3H^2}\frac{\partial{}V}{\partial\phi} (2)

and the average amplitude of fluctuation generated during one efolding

\delta\phi\sim{}H (3).

(2) and (3) coinside when H\sim\sqrt{\epsilon}M_P, i.e., when inflation enters eternal selfreproducing regime.

So, it is clear to me that corrections Armedariz-Picon et al. found are due to the effects of eternal inflation. Why effective QFT expansion breaks down there? Let me repeat the answer I gave last time: this is because background cannot be described in terms of a single FRW patch.

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Cosmology, Journal club, Master Postdoc, Quantum field theory

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3 Comments »

Comment by Instanton
2008-05-08 11:56:13

Hi
Leonardo Senatore was talking about effective QFT for inflation this week in PI.
http://pirsa.org/08050006/

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Comment by Instanton
2008-05-08 12:05:53

BTW, yesterday I’ve tried to leave a comment but could not do that - pressing on Submit button I was getting a email subscription form. Everything seems to work today.

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Comment by Dmitry
2008-05-08 12:35:08

Dear Instanton

Thanks for the link. Are you from PI yourself?
As for the Submit button :-), indeed, I have to apologize.
I made the email subsription form yesterday and found only this morning that I forgot to close a /form tag. As a result, commenting did not work at all for the whole yesterday. The tag is closed now.

Cheers,
Dmitry.

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