2012/05/31 by Markus B. Fröb, Albert Roura, Enric Verdaguer · 1 citation
Physics and Astronomy · #gr-qc #hep-th
paper · pdf · doi:10.1088/1475-7516/2012/08/009
published as JCAP08(2012)009 · 42 pages, 2 figures, includes three new paragraphs in response to referee's comments
arxiv created 2012/09/05 · arxiv updated 2012/09/06
The two-point function for tensor metric perturbations around de Sitter spacetime including one-loop corrections from massless conformally coupled scalar fields is calculated exactly. We work in the Poincaré patch (with spatially flat sections) and employ dimensional regularization for the renormalization process. Unlike previous studies we obtain the result for arbitrary time separations rather than just equal times. Moreover, in contrast to existing results for tensor perturbations, ours is manifestly invariant with respect to the subgroup of de Sitter isometries corresponding to a simultaneous time translation and rescaling of the spatial coordinates. Having selected the right initial state for the interacting theory via an appropriate iεprescription is crucial for that. Finally, we show that although the two-point function is a well-defined spacetime distribution, the equal-time limit of its spatial Fourier transform is divergent. Therefore, contrary to the well-defined distribution for arbitrary time separations, the power spectrum is strictly speaking ill-defined when loop corrections are included.