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I present a simple exactly solveable model of eternal inflation.  The correlation functions have a discrete analogue of conformal symmetry, which can be compactly expressed using the machinery of p-adic numbers.  I comment on the implications for actual cosmology, and in particular for holographic descriptions of eternal inflation.

Supersymmetry plays a fundamental role in the radiative stability of many inflationary models.  I will explain how supersymmetry and naturalness require additional scalar degrees of freedom with masses on the order of the inflationary Hubble scale.  These fields lead to distinctive non-gaussian signatures that may be observable in both the CMB and large scale structure.

Hawking's discovery of black holes radiance along with Bekenstein's conjecture of the generalized second law of thermodynamics inspired a conceptually pleasing connection between gravity, thermodynamics and quantum theory. However, the discovery that the spectrum of the radiation is in fact thermal, together with the no-hair theorem, has brought along with it some undesirable consequences, most notably the information loss paradox. There have been many proposals to the resolution of this paradox, with the most natural resolution being that during the time of collapse the radiation given off is not completely thermal and can carry small amounts of information with it. In this talk, we will revisit the so-called pre-Hawking radiation given off during the scenario of gravitational collapse by utilizing the so-called functional Schroedinger equation (FSE) and quantum kinetic equation (QKE). Here we find that the spectrum never becomes thermal and discuss the reasons for this. Finally we will discuss the implications of this result, as well as previous results, toward the resolution of the information paradox.

In this talk I will describe how to calculate the exact partition function for free bosons on the plane with lacunae using world line effective field theory. It will be shown that the partition function for a plane with two spherical holes can be calculated by matching exactly for the infinite set of Wilson coefficients and then performing the ensuing Gaussian integration. This same partition function can also be calculated using conformal field theory technique and the equality of the two results will be shown. I will demonstrate that there is an exact correspondence between the Wilson coefficients (susceptabilities) in the effective field theory and the weights of the individual excitations of the closed string coherent state on the boundary. The partition function for the case of three holes, where CFT techniques necessitate a closed form for the map from the corresponding closed string pants diagram, is still calculable within the EFT. I will also show how conformal mappings can be used within the matching procedure to calculate the partition function for elliptically shaped boundaries. Finally I will show that the Wilson coefficients for the case of quartic and higher order kernels, where standard CFT techniques are no longer applicable, can also be completely determined.

Using an approach originally developed to study gravitational wave absorption in black hole binary systems, we generalize the EFT of single clock inflation to include dissipative effects. We restrict ourselves to situations where the degrees of freedom responsible for dissipation do no contribute to the density perturbations at late time, and moreover they are predominately sensitive to the field whose fluctuations control the end of inflation. The dynamics of the perturbations is then modified by the appearance of `friction' and noise terms, and assuming certain locality properties we show that there is a regime, characterized by a large friction coefficient \gamma >> H, in which the power spectrum is dominated by the noise and it is significantly modified with respect to the Bunch-Davies result. Furthermore, the non-linear realization of the symmetries implies non-gaussianties which are enhanced with respect to single clock models without dissipation by a factor of \gamma/H, and whose shape functions can in principle be distinguished from those obtained in the Bunch-Davies vacuum. We also discuss the matching of the EFT with a few key examples such as trapped and warm inflation.

The Effective Field Theory (EFT) approach can be employed to perform high PN order calculations of the Hamiltonian of a binary system. We show how we reproduced the 3PN dynamics by means of an algorithm implemented in Mathematica and our progress towards the computation of the 4PN Hamiltonian. We also show the EFT computation of the tail term affecting the conservative dynamics at 4PN order, first derived using traditional methods by Blanchet and Damour.

Based on tetrad-generalized canonical formalism by Arnowitt, Deser, and Misner most recent achievements in analytic calculations of higher order post-Newtonian Hamiltonians for spinning binary black holes and neutron stars are presented. The results of the generalized ADM formalism are put into mathematical relationship with those obtained within the Effective Field Theory approach.

The advent of large spectroscopic surveys of galaxies in the early 1980s has shown us that galaxies assemble in large scale structures. Recently, cosmic voids have received more attention through the availability wide and deep galaxy surveys. Voids have a simple phase space structure and thus are easier to model than cluster of galaxies. I will present two important applications of the precise analysis of voids in the context of constraining the equation of state of dark energy. First I will discuss how they could be used to have a much better determination of the expansion factor than using traditional methods, like Baryonic Acoustic Oscillations. Second, I will show that voids is maybe the only large-scale structure for which the dynamics can be finely modelled, notably through the use of the Monge-Ampere-Kantorovitch orbit reconstruction method. For the two above cases, I will present how we can mathematically define cosmic voids, the methods that have been developed to find them and some results based on N-body simulations for constraining the Dark Energy equation of state.

High-accuracy templates predicted by general relativity for the gravitational waves generated by inspiralling compact binaries (binary star systems composed of neutron stars and/or black holes) have been developed using a mixed multipolar and post-Newtonian (MPN) formalism. In this talk we shall review the foundations of this formalism and its main results, including the equations of motion and radiation from compact binaries up to 3.5PN order. We shall also present some recent work on the comparison between post-Newtonian approximations and black hole perturbations applied to compact binaries in the small mass ratio limit.