We consider Schwinger pair production in 1+1 dimensional de Sitter space, filled with a constant electric field E. This can be thought of as a model for describing false vacuum decay beyond the semiclassical approximation, where pairs of a quantum field ϕ of mass m and charge e play the role of vacuum bubbles. We find that the adiabatic ``in" vacuum associated with the flat chart develops a space-like expectation value for the current J, which manifestly breaks the de Sitter invariance of the background fields. We derive a simple expression for J(E), showing that both ``upward" and ``downward" tunneling contribute to the build-up of the current. For heavy fields, with m2 ≫ eE,H2, the current is exponentially suppressed, in agreement with the results of semiclassical instanton methods. Here, H is the inverse de Sitter radius. On the other hand, light fields with m ≪ H lead to a phenomenon of infrared hyperconductivity, where a very small electric field mH≲eE ≪ H2 leads to a very large current J ∼ H3/E. We also show that all Hadamard states for ϕ necessarily break de Sitter invariance. Finally, we comment on the role of initial conditions, and ``persistence of memory" effects.

We make a proposal for gauge-invariant observables in perturbative quantum gravity in cosmological spacetimes, building on the recent work of Brunetti et al. [JHEP 08 (2016) 032]. These observables are relational, and are obtained by evaluating the field operator in a field-dependent coordinate system. We show that it is possible to define this coordinate system such that the non-localities inherent in any higher-order observable in quantum gravity are causal, i.e., the value of the gaugeinvariant observable at a point x only depends on the metric and inflation perturbations in the past light cone of x. We then construct propagators for the metric and inflaton perturbations in a gauge adapted to that coordinate system, which simplifies the calculation of loop corrections, and give explicit expressions for relevant cases: matterand radiation-dominated eras and slow-roll inflation.

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.

We give a complete, self-contained, and mathematically rigorous proof that Euclidean Yang-Mills theories are perturbatively renormalisable, in the sense that all correlation functions of arbitrary composite local operators fulfil suitable Ward identities. Our proof treats rigorously both all ultraviolet and infrared problems of the theory and provides, in the end, detailed analytical bounds on the correlation functions of an arbitrary number of composite local operators. These bounds are formulated in terms of certain weighted spanning trees extending between the insertion points of these operators. Our proofs are obtained within the framework of the Wilson-Wegner-Polchinski-Wetterich renormalisation group flow equations, combined with estimation techniques based on tree structures. Compared with previous mathematical treatments of massless theories without local gauge invariance [R. Guida and Ch. Kopper, arXiv:1103.5692; J. Holland, S. Hollands, and Ch. Kopper, Commun. Math. Phys. 342 (2016) 385] our constructions require several technical advances; in particular, we need to fully control the BRST invariance of our correlation functions.

Abstract.We investigate the gauge-invariant observables constructed by smearing the graviton and inflaton fields by compactly supported tensors at linear order in general single-field inflation. These observables correspond to gauge-invariant quantities that can be measured locally. In particular, we show that these observables are equivalent to (smeared) local gaugeinvariant observables such as the linearised Weyl tensor, which have better infrared properties than the graviton and inflaton fields. Special cases include the equivalence between the compactly supported gauge-invariant graviton observable and the smeared linearised Weyl tensor in Minkowski and de Sitter spaces. Our results indicate that the infrared divergences in the tensor and scalar perturbations in single-field inflation have the same status as in de Sitter space and are both a gauge artefact, in a certain technical sense, at tree level.