Conference

Tony Downes The geometry of space-time can only be determined by making measurements on physical systems. The ultimate accuracy achievable is then determined by quantum mechanics which fundamentally governs these systems. In this talk I will describe uncertainty principles constraining how well we can estimate the components of a metric tensor describing a gravitational field. I shall outline a number of examples which can be easily constructed with a minimum of mathematical complexity. I will also attempt to derive a general bound on the uncertainty in any attempt to determine the metric tensor which is expected to hold in an arbitrary globally hyperbolic space-time. I shall use tools developed within the algebraic approach to quantum field theory on a classical space-time background. I shall not consider limits on estimating space-time metrics that might arise from a quantisation of gravity itself.

I will present a recent result showing that general relativity admits a dual description in terms of a 3D scale invariant theory. The dual theory was discovered by starting with the basic observation that, fundamentally, all observations can be broken down into local comparisons of spatial configurations. Thus, absolute local spatial size is unobservable. Inspired by this principle of "relativity of size", I will motivate a procedure that allows the refoliation invariance of general relativity to be traded for 3D local scale invariance. This trade does away with "many fingered time" and offers a new possibility for dealing with the many technical and conceptual difficulties associated with the Wheeler-DeWitt equation.

Basic epistemological considerations suggest that the laws of nature should be scale invariant and no fundamental length scale should exist in nature. Indeed, the standard model action contains only two terms that break scale invariance: the Einstein-Hilbert term and the Higgs mass term. We give a simple introduction to Weyl's 1918 scale invariant gravity based on basic epistemology and discuss the three main objections put forth by Einstein: 1) the hydrogen spectrum depends on their previous history of the atom (something which is empirically ruled out to a high precision), 2) there is no account for proper time in Weyl's theory, and 3) fieldequations are 4th order leading to Ostrogradsky-type instabilities. We show that the first two objections can readily be answered. In particular the second objection is answered by developing a physical model of an ideal clock from which proper time is identified as the reading of the clock. We then outline an attempt to tackle the third objection by breaking foliation invariance and so introduce a preferred simultaneity. We show that Lorentz invariance can still be maintained if only the gravitational sector is sensitive to the preferred foliation. We impose the restrictions I) the new theory should contain general relativity in the limit of zero scale curvature, II) no fundamental length scales should appear, III) the field equations should be of second order.

Tamara Davis The last decade of astrophysics has shown more than ever before that cosmology can teach us about the nuts-and-bolts of basic physics. This has been driven by the discovery of the accelerating universe (dark energy) --- the theories being proposed to explain dark energy often invoke new physics such as brane-worlds arising from fledgling models of quantum-gravity. It has become evident that the large timescales and spatial-scales probed by cosmology allow us to learn about fundamental physics in a way inaccessible to any earth-bound experiment. This talk will review my work as part of the ESSENCE and SDSS supernova surveys, and the WiggleZ Baryon Acoustic Oscillation survey, to test new fundamental physics. I'll present the latest data and discuss how the cosmological constraints will be improved in the future with more data, different types of data, and improved analysis techniques.

We propose one way to regularize the fluctuations generated during inflation. We show that, as long as we consider the case that the non-linear interaction acts for a finite duration, observable fluctuations are free from IR divergences not only in the single field models but also in the multi field model. In contrast to the single field model, to discuss observables, we need to take into account the effects of quantum decoherence which pick up a unique history of the universe from various possibilities contained in initial quantum state set naturally in the early stage of the universe.

De Sitter space is a maximally symmetric space, and any (time dependent) backreaction necessarily breaks the symmetry. On the other hand, the backreaction in FLRW spaces (which, from the cosmological perspective, are more realistic spaces) respects the symmetries of the background space. One could therefore argue that it is more natural to study the backreaction on quasi-de Sitter spaces, and more generally on FLRW spaces. As examples, I will present our results on the one loop (Hubble) effective potential calculation, and the one loop stress energy calculation. We find that the backreaction from infrared modes can be important if a massless scalar couples nonminimally to the Ricci with a negative coupling, and if the Universe expands faster than exponentially.

A method is developed for dealing with ultraviolet divergences in calculations of cosmological correlations, which does not depend on dimensional regularization. An extended version of the WKB approximation is used to analyze the divergences in these calculations, and these divergences are controlled by the introduction of Pauli--Villars regulator fields. This approach is illustrated in the theory of a scalar field with arbitrary self-interactions in a fixed flat-space Robertson--Walker metric with arbitrary scale factor $a(t)$. Explicit formulas are given for the counterterms needed to cancel all dependence on the regulator properties, and an explicit prescription is given for calculating finite correlation functions.

I will present our work on loop corrections to the power spectrum of curvature fluctuations in single-field inflationary models. We consider both standard slow-roll (where the interactions between gravitons and the scalar are included for the first time) and non-canonical Lagrangians. We show that the tensor modes cannot be neglected since, in some models, they produce one loop contributions with an amplitude that is comparable to the one coming from the scalar sector. Our study of loop corrections in non-canonical theories characterized by a small speed of sound (c_s) provides quantitative bounds on c_s, to be compared with similar constraints derived from CMB observations.

I will discuss the emergence of anomalous scaling dimensions for superhorizon fluctuations and the main ideas and concepts of particle decay during inflation, via the resummation of secular terms with the dynamical renormalization group. There are loops, IR effects and (lots of...) issues.

In theories with light or massless fields, loop diagrams can develop infrared divergences. We demonstrate how these can be resolved for a theory of massless interacting scalar fields in Euclidean de Sitter space. We also comment on applications to the in-in formalism in Lorentzian de Sitter space.

Using simple semiclassical relations it is possible to show that the conventional cosmological correlation functions are affected by significant IR corrections in quasi de Sitter space-times when averaged over very large volumes (in the "large box"). The IR effects apparently imply a breakdown of perturbation theory in the large box on sufficiently long time scales, for example the time between self-reproduction and reheating in chaotic inflation. An interpretation of the apparent breakdown of the perturbative expansion of gravity will also be briefly discussed.