The IR stability of de Sitter QFT: Physical initial conditions

This work uses Lorentz-signature in-in perturbation theory to analyze the late-time behavior of correlators in time-dependent interacting massive scalar field theory in de Sitter space. We study a scenario recently considered by Krotov and Polyakov in which the coupling $g$ turns on smoothly at finite time, starting from $g=0$ in the far past where the state is taken to be the (free) Bunch-Davies vacuum. Our main result is that the resulting correlators (which we compute at the one-loop level) approach those of the interacting Hartle-Hawking state at late times. We argue that similar results should hold for other physically-motivated choices of initial conditions. This behavior is to be expected from recent quantum "no hair" theorems for interacting massive scalar field theory in de Sitter space which established similar results to all orders in perturbation theory for a dense set of states in the Hilbert space. Our current work i) indicates that physically motivated initial conditions lie in this dense set, ii) provides a Lorentz-signature counter-part to the Euclidean techniques used to prove such theorems, and iii) provides an explicit example of the relevant renormalization techniques.Comment: 32 pages, 3 figure

The IR stability of de Sitter QFT: results at all orders

We show that the Hartle-Hawking vacuum for theories of interacting massive scalars in de Sitter space is both perturbatively well-defined and stable in the IR. Correlation functions in this state may be computed on the Euclidean section and Wick-rotated to Lorentz-signature. The results are manifestly de Sitter-invariant and contain only the familiar UV singularities. More importantly, the connected parts of all Lorentz-signature correlators decay at large separations of their arguments. Our results apply to all cases in which the free Euclidean vacuum is well defined, including scalars with masses belonging to both the complementary and principal series of $SO(D,1)$. This suggests that interacting QFTs in de Sitter -- including higher spin fields -- are perturbatively IR-stable at least when i) the Euclidean vacuum of the zero-coupling theory exists and ii) corresponding Lorentz-signature zero-coupling correlators decay at large separations. This work has significant overlap with a paper by Stefan Hollands, which is being released simultaneously.Comment: 30 pp., 4 figures. Small typos fixed, refs adde

Modular Frobenius manifolds and their invariant flows

The space of Frobenius manifolds has a natural involutive symmetry on it: there exists a map $I$ which send a Frobenius manifold to another Frobenius manifold. Also, from a Frobenius manifold one may construct a so-called almost dual Frobenius manifold which satisfies almost all of the axioms of a Frobenius manifold. The action of $I$ on the almost dual manifolds is studied, and the action of $I$ on objects such as periods, twisted periods and flows is studied. A distinguished class of Frobenius manifolds sit at the fixed point of this involutive symmetry, and this is made manifest in certain modular properties of the various structures. In particular, up to a simple reciprocal transformation, for this class of modular Frobenius manifolds, the flows are invariant under the action of $I\,.

Western European radiocarbon dates and holocene marine changes, with special reference to concepts involving Scottish archaeological material

The concept of a single "25 foot raised beach" has dominated opinion on the relationship between Scottish archaeological material and sea level change for most of the present century. Recent work has however demonstrated that Holocene coastal changes were much more complicated than this concept suggested. These complexities have not yet been fully resolved, either in Scotland or elsewhere. Doubt exists as to how far sequences of changes observed in one area are likely also to be represented on other stretches of coastline. At present, Scottish geomorphological and archaeological evidence does not in itself appear adequate for a reliable evaluation of this. The seaboard of Western Europe between north Norway and Biscay contains a substantially wider range of Holocene land movement regimes and coastal environments than is represented in Scotland, and thus offers a basis for assessing the relative importance of ocean level variations and more local factors. The evaluation of this type of interplay and the isolation of the eustatic(ocean wide) component has long been a matter of controversy in the literature. During the past decade, however, almost a thousand radiocarbon dates relevant to Holocene coastal changes have become available in Western Europe. These permitted the development of a new type of approach to the problem, based on a detailed analysis of the timing of episodes of transgression and regression. From this it became apparent that despite the diversity of conditions on the European seaboard, the ubiquitous influence of ocean level variations had dominated the timing of shoreline changes throughout the Holocene. The only major exception was the Baltic, when cut off from the ocean during periods such as the "Ancylus Lake" stage, but it proved possible to define these phases closely in terms of C¹⁴ chronology. None of the published Holocene eustatic curves appears to be based on more than about 10% of the number of radiocarbon dates included in the present survey. Accordingly, a new curve taking these dates into account was derived. The eustatic and other data from the survey were then compared with the Scottish evidence, using detailed information now available for the Forth-Tay area as a control. It was found that the Scottish data could be interpreted . in a way consistent with the results from the remainder of Western Europe. A model of relative sea level change was constructed, and discussed in terms of the available archaeological material. It was concluded that although necessarily provisional, this model appeared to offer a hypothesis for future investigation that seemed potentially more profitable than that provided by the "25 foot raised beach" concept

Places to Swim: Perspectives Report

People love to recreate around, on and in the water. As part of the Department of Planning and Open Spaces Program, Places to Swim provides an opportunity to improve access to natural waterways for recreation across NSW. This report investigates the issues, barriers and benefits associated with opening waterways for recreation. NSW is enriched with a range of beautiful and healthy waterways providing opportunities for people to swim and recreate safely, create places that people can visit, and help build better communities. A key attribute for all swimming sites is ensuring they are safe to use. Recreation involving waterways inherently involves risks, including exposure to waterborne contaminants and the risk of injury and drowning. As new swimming sites are opened the risks need to be identified, monitored, and managed