34. Several questions about de Sitter

Posted by Dmitry
May 2, 2008

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 d is odd and unstable if d 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 x and x' 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 P: one at -\infty<P<-1, another - at 1<P<+\infty. What is the physical meaning of these two branch cuts?

Cheers.

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

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