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These integrations are much easier to do, owing to the fact that for de Sitter spacetime, the relation (Formula presented) can be explicitly inverted. On the other hand, special care must be taken with the regular center (Formula presented): The boundary condition (Formula presented) must be imposed, ensuring the regularity of the scalar field (Formula presented) at (Formula presented)
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These integrations are much easier to do, owing to the fact that for de Sitter spacetime, the relation (Formula presented) can be explicitly inverted. On the other hand, special care must be taken with the regular center (Formula presented): The boundary condition (Formula presented) must be imposed, ensuring the regularity of the scalar field (Formula presented) at (Formula presented).
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29
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85037237013
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More precisely, the overdot on g denotes differentiation with respect to t, while the overdot on (Formula presented) denotes differentiation with respect to (Formula presented), which is set to zero in Eq. (4.4). The fact that g depends on (Formula presented) explains why the two terms within the square brackets are added instead of subtracted
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More precisely, the overdot on g denotes differentiation with respect to t, while the overdot on (Formula presented) denotes differentiation with respect to (Formula presented), which is set to zero in Eq. (4.4). The fact that g depends on (Formula presented) explains why the two terms within the square brackets are added instead of subtracted.
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34
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85037216733
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It should be noted that if (Formula presented) the two poles at (Formula presented) are equally near to the real axis, so that both contributions should be taken into account. We leave this subtlety aside, as it does not affect the following discussion
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It should be noted that if (Formula presented) the two poles at (Formula presented) are equally near to the real axis, so that both contributions should be taken into account. We leave this subtlety aside, as it does not affect the following discussion.
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