34. Several questions about de Sitter

Posted by Dmitry

May 2, 2008

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As it (probably) follows from my FireStats statistics, quite an impressive number of experts on the field are reading this blog. If this is indeed so, I have several questions about QFT in de Sitter space that you may be able to answer.

Here they are:

1) Consider d-dimensional de Sitter in global coordinates, where linear element looks like $ds^2=-dt^2+{\rm cosh}^2t{}d\Omega^2_{d-1}$ and QFT of a single massive free scalar field. Why $|in\rangle$ and $|out\rangle$ coinside, if d is odd? In other words, why dS_d is stable if is odd and unstable if is even?

2) Consider a general Green’s function of a massive scalar field in de Sitter space. As you know, it has a form

$\langle\phi(x)\phi(x') \rangle=c_1F\left(h_+,h_-,d/2,\frac{1+P}{2}\right)+c_2F\left(h_+,h_-,d/2,\frac{1-P}{2}\right)$ ,

where $P=\cos\Theta(x,x')$ and $\Theta$ is a geodesic distance between points and on de Sitter.

This Green’s function has a singularity at antipodal points ( P=-1 ) apart from the usual singularity at coincident points ( P=1 ). What is the physical meaning of singularity at antipodal points?

While giving answer to this question, please, don’t say anything like “antipodal singularity is beyond horizon” and/or do not mention “elliptic De Sitter”, because it is stupid.

3) This Green’s function has two branch cuts in the complex plane of : one at $-\infty<P<-1$ , another – at $1<P<+\infty$ . What is the physical meaning of these two branch cuts?

Cheers.

Cosmology, Lectures on de Sitter spacetime, Quantum field theory, String theory

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