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No de Sitter invariant vacuum in massive gravity theory with ghost · Around

2007

No de Sitter invariant vacuum in massive gravity theory with ghost

Izumi, Keisuke, Tanaka, Takahiro

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In this letter we point out that the massive gravity theory with a graviton ghost mode in de Sitter background cannot possess a de Sitter invariant vacuum state.

In order to avoid a negative norm state, we must associate the creation operator of the ghost mode with a negative-energy mode function instead of a positive-energy one as the mode function.
Namely, we have to adopt a different procedure of quantization for a ghost.
When a theory has a symmetry mixing a ghost mode with ordinary non-ghost modes, the choice of a ghost mode is not unique.

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