Recently I attend a course on quantum field theory in curved space and find it's very difficult for me to understand vacuum state in curved spacetime properly.(adsbygoogle = window.adsbygoogle || []).push({});

For example, as I try to recover the Gibbons-Hawking temperature in dS space, I was told to solve Klein-Gordon equation in both planar and static coordinates (I use the textbook by Birrell and Davies (5.54) and (5.76)), then the spectrum of radiation detected by static observer can be deduced from Bogoliubov coefficient which are used to related the distinct vacuum states (Bunch-Davies vacuum and static vacuum) in two coordinates.

It is very confuse for me that, do the comoving observer in planar coordinates should define BD vacuum as a no-particle state ? If a comoving observer (w.r.t conformal time) in BD vacuum could see nothing, is this correct to say that he would detect a thermal spectrum when he turns to be static (comoving w.r.t cosmic time) since BD vacuum appears thermal then from the view of new static vacuum?

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# Vacua in de Sitter

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