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The two-point correlation function of metric fluctuations in de Sitter space is calculated. The results are expressed in a gauge-invariant and O(4,1)-invariant form in terms of elementary functions of z(x,x′) (a biscalar variable simply related to the invariant distance between x and x′). The Feynman functions for the transverse, trace-free, and scalar metric fluctuations grow without bounds, as ln z and z ln z, respectively, for large z. The consequences of this bad infrared behavior are discussed and it is shown that it leads to divergences in physical quantities at both the classical and quantum levels.
Antoniadis et al. (Mon,) studied this question.