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Much work on quantum gravity has focussed on short-distance problems such as non-renormalizability and singularities. However, quantization of gravity raises important long-distance issues, which may be more important guides to the conceptual advances required. These include the problems of black hole information and gauge invariant observables, and those of inflationary cosmology. An overview of aspects of these problems, and apparent connections, will be given.

I will argue that the dynamical renormalization group can be used to resum late time divergences appearing in loop computations in de Sitter. In the case of a scalar field with quartic interactions, the resummed propagator is the massive one. Standard mean field theory techniques can then be used to estimate the mass. This is analogous to the thermal field theory story but with some notable differences. We discuss whether a critical point can exist in dS where mean field methods fail.

We clarify the origin of IR divergence in single-field models of inflation and provide the correct way to calculate the observable fluctuations. First, we show the presence of gauge degrees of freedom in the frequently used gauges such as the comoving gauge and the flat gauge. These gauge degrees of freedom are responsible for the IR divergences that appear in loop corrections of primordial perturbations. We propose, in this talk, one simple but explicit example of gauge-invariant quantities. Then, we explicitly calculate such a quantity to find that the IR divergence is absent in the slow-roll approximation. In this formalism, we revisit the consistency relation that connects the three-point function in the squeezed limit with the spectral index.

General Relativity receives quantum corrections relevant at macroscopic distance scales and near event horizons. These arise from the conformal scalar degrees of freedom in the extended effective field theory of gravity generated by the trace anomaly of massless quantum fields in curved space. Linearized perturbations of the Bunch-Davies state in de Sitter space show that these new scalar degrees of freedom are associated with macroscopic changes of state on the cosmological horizon scale, with potentially large stress tensors that can lead to substantial backreaction effects in cosmology. In the extended effective theory the cosmological ``constant" is a state dependent condensate whose value is scale dependent and which possesses an infrared stable conformal fixed point at zero. These considerations suggest that the observed dark energy of our universe may be a macroscopic finite size effect whose value depends not upon Planck scale physics but upon extreme infrared physics on the cosmological horizon scale.

In this talk I will describe my recent work on the structure of entanglement in field theory from the point of view of mutual information. I will give some basic scaling intuition for the entanglement entropy and then describe how this intuition is better captured by the mutual information. I will also describe a proposal for twist operators that can be used to calculate the mutual information using the replica method. Finally, I will discuss the relevance of my results for holographic duality and entanglement based simulation methods for many body systems.

I introduce a general method for constraining the shape of the inflationary potential from Cosmic Microwave Background (CMB) temperature and polarization power spectra. This approach relates the CMB observables to the shape of the inflaton potential via a single source function that is responsible for the observable features in the initial curvature power spectrum. The source function is, to an excellent approximation, simply related to the slope and curvature of the inflaton potential, even in the presence of large or rapidly changing deviations from scale-free initial conditions. Oscillatory features in the WMAP temperature power spectrum have led to interest in exploring models with features in the inflationary potential, but such cases are typically studied on a case-by-case basis. This formalism generalizes previous studies by exploring the complete parameter space of inflationary models in a single analysis. I will present results from a Markov Chain Monte Carlo likelihood analysis of WMAP 7-year and other data sets that probe the inflationary potential both at large and small scales, and I will discuss constraints from upcoming high-sensitivity experiments.

Even though the security of quantum key distribution has been rigorously proven, most practical schemes can be attacked and broken. These attacks make use of imperfections of the physical devices used for their implementation. Since current security proofs assume that the physical devices' exact and complete specification is known, they do not hold for this scenario. The goal of device-independent quantum key distribution is to show security without making any assumptions about the internal working of the devices. In this talk, I will first explain the assumptions 'traditional' security proofs make and why they are problematic. Then, I will discuss how the violation of Bell inequalities can be used to show security even when a large part of the physical devices is untrusted.