One-loop gravitational wave spectrum in de Sitter spacetime

Abstract

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 i prescription 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.

Massless scalar field vacuum in de Sitter spacetime

“…Cf. similar results by Fröb, Roura, and Verdaguer that include the effect of one-loop corrections from matter fields [37] and apply for the full Riemann tensor [38].…”

One-loop quantum electrodynamic correction to the gravitational potentials on de Sitter spacetime

“…The same framework (with zero source) has been employed to investigate corrections to graviton mode functions from massless, minimally coupled (MMC) scalars [20,21]. There have also been studies of the effect of a loop of massless, conformally invariant scalars on the graviton mode function [22,23] and on the background geometry [24]. This paper contains six sections, of which the first is this introduction.…”

Noise kernel for a quantum field in Schwarzschild spacetime under the Gaussian approximation

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