Lectures on de Sitter spacetime

271. Continuing dS/CFT – correspondence. Part 2

Posted by Dmitry

February 18, 2009

News: It seems that there are good news for science funding in US. Cosmic Variance points out that science funding in the stimulus package was largely restored: with 3 bill. for NSF, 1.6 bill. for DOE and 1 bill. for NASA. I really hope this is final

254. Continuing dS/CFT – the correspondence. Part 1

Posted by Dmitry

February 12, 2009

When I’ve discussed dS/CFT correspondence last time, I listed several criticisms of it, but probably had to explain in the first place what is the essence of dS/CFT

According to Bousso, Maloney and Strominger, the correspondence works as follows.

234. Continuing dS/CFT. Why it is so hard to prove?

Posted by Dmitry

February 6, 2009

I continue today the discussion of dS/CFT correspondence started a week ago.

As you probably remember, I finished last time pointing out the discrepancy between non-perturbative and perturbative values of the dimension of the dS Hilbert space. Namely, since the entropy of dS space is finite, the dimension of of the Hilbert space is finite as well since

223. Starting dS/CFT: Hilbert space

Posted by Dmitry

February 2, 2009

Since I was recently thinking of the dS/CFT correspondence, I find it natural to also start discussing facts and hypotheses related to dS/CFT and other gauge theory – gravity dualities on the blog. In what follows, we will mostly discuss 4-dimensional gauge theories.

152. Volume of the Universe after inflation

Posted by Dmitry

December 27, 2008

Back to work after a way too short Xmas break Since we were recently a bit into black hole complementarity and information loss paradox, maybe it is also worth discussing a bit the physics of de Sitter space.

125. From quarks to strings. On Liouville mode, instantons and confinement in abelian theories

Posted by Dmitry

December 6, 2008

Alexander Polyakov have released this week a preprint about history of string theory, which is also so full of non-trivial physical ideas that I decided to list some of them in this post as well as to include my comments (or rather my ramblings )

124. Talk in Munich. Regularizing correlators of curvature perturbation

Posted by Dmitry

December 5, 2008

This post is hopefully the last one in the series devoted to my seminar in Munich Last time I have explained why correlation functions of the scalar field on de Sitter background should be actually infrared finite. This time, using similar trick, I will argue that the correlation functions of the curvature perturbation $\zeta$ (by curvature perturbation, as usual, I mean curvature of the 3-dimensional slice) should be also infrared finite due to the effects of eternal inflation.

120. Talk in Munich. Regularizing inflaton correlation functions

Posted by Dmitry

December 1, 2008

Let me get again back from confinement to eternal inflation , or more precisely, to the infrared behavior of correlation functions of a self-interacting massless scalar field on de Sitter background. In what follows, I will consider the case $M_P\to\infty$ (a QFT in fixed dS spacetime).

115. Talk in Munich. Leading logs

Posted by Dmitry

November 28, 2008

Last time I have claimed that the leading IR divergences in the loop expansion for the inflaton pair correlation function in $\lambda\phi^4$ theory contribute in the form of expansion

$\langle\phi^2\rangle=\frac{H^2}{(2\pi)^2}\log{}a\sum_{n=0}^\infty(c_n\lambda\log^2{}a)$ .

Let me now show how these divergences appear. First of all, let us forget about the interaction term $\lambda\phi^4$ and show that the correlation function $\langle\phi^2\rangle$ for the free field $\phi$ on dS background diverges in the IR.

112. Talk in Munich. Other two interesting infrared scales

Posted by Dmitry

November 27, 2008

As Instanton figured out in comments to the previous post, the scale $L_\Phi\sim{}L_\zeta$ is related to the self-reproduction scale. How to show this? Well, recall that the classical displacement of the inflaton field during one efolding is

111. Talk in Munich. One interesting infrared scale in inflationary cosmology

Posted by Dmitry

November 26, 2008

I am back to Helsinki, was not this visit really short? :-)

For those of you how were unable to come to the Sommerfeld Center in Munich to hear my talk and for those of you who were there but did not understand it ? I decided to put the outline of my talk on the blog.

99. Eternal inflation with many light scalar fields

Posted by Dmitry

November 16, 2008

I am going to briefly discuss one result from the recent paper by Peter Adshead, Richard Easther and Eugene Lim.

One subject of the authors’ study is the interplay between stochastic and eternal N-flation. Let us recall what is N-flation (or assisted inflation). Suppose that we have a large number $N\gg 1$ of scalar fields with equal potentials $V(\phi_i)=m^2 \phi_i^2$ and relatively large vacuum expectation values. How large? We want to have the ordinary slow roll inflation in this setup. While one needs an expectation value of the inflaton to be superplanckian in single field inflationary models in order for slow roll conditions to hold, expectation values of any one among N scalar fields can be rather small and still the inflationary slow roll regime will not be spoiled. Indeed, we have

58. Stability of de Sitter space: dS as a perfect interferometer

Posted by Dmitry

June 13, 2008

Let us now show that QFT of a massive scalar field in de Sitter space features instabilities if the number of dimensions is odd. The expression for the two-point function found in the previous post will be of no help, so we will have to switch to the language of Bogolyuov coefficients and modes.

57. Stability of de Sitter space: statement of the problem 1

Posted by Dmitry

June 12, 2008

Ok, friends, I feel that the time has come to let you know about things I am currently involved in – namely, understanding of intrinsic stability of the de Sitter space.

55. Eternal inflation: stochastic approach 3 (Inflationary perturbations 7)

Posted by Dmitry

June 5, 2008

Last time we have found that dynamics of the inflaton field (more precisely, its expectation value w.r.t. to the distribution among different Hubble patches) is determined by the Langevin equation.

As we know, there are two descriptions of the Brownian motion: in terms of the Langevin equation and in terms of the Fokker-Planck equation describing diffusion of the probability distribution to find a randomly moving particle at given $\Phi$ in a given moment of time . This Fokker-Planck equation has the form

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Lectures on de Sitter spacetime

271. Continuing dS/CFT – correspondence. Part 2

254. Continuing dS/CFT – the correspondence. Part 1

234. Continuing dS/CFT. Why it is so hard to prove?

223. Starting dS/CFT: Hilbert space

152. Volume of the Universe after inflation

125. From quarks to strings. On Liouville mode, instantons and confinement in abelian theories

124. Talk in Munich. Regularizing correlators of curvature perturbation

120. Talk in Munich. Regularizing inflaton correlation functions

115. Talk in Munich. Leading logs

112. Talk in Munich. Other two interesting infrared scales

111. Talk in Munich. One interesting infrared scale in inflationary cosmology

99. Eternal inflation with many light scalar fields

58. Stability of de Sitter space: dS as a perfect interferometer

57. Stability of de Sitter space: statement of the problem 1

55. Eternal inflation: stochastic approach 3 (Inflationary perturbations 7)

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