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The general relativity has been tested from mm scales to solar system scales. The discovery of cosmic acceleration motivates the study of infrared modification of gravity at horizon scales. The cosmic expansion can be accelerated by dark energy without any correction to GR, but alternatively it can be explained by the modified gravity at large scales without introducing the unknown exotic energy. We introduce the linear structure formation theory of DGP and f(R) gravity, and present what it the strategy to test general relativity at cosmological scales.

Current measurements from WMAP and other cosmological probes are consistent with a simple inflationary model. Such models predict a background of gravitational waves which may soon be observable in the polarized component of the Cosmic Microwave Background. However, WMAP has observed significant levels of polarized radiation from our galaxy, due to both synchrotron radiation and thermal dust emission. A better understanding of this radiation will be vital if we are to correctly remove it and confidently detect an inflationary signal. As well as discussing the observational case for inflation, I will review the physical origins of the polarized galactic emission, present a simple model for the galactic magnetic field, and discuss current and future directions for improving upon our galactic models.

I first summarize how the recent avalanche of precision measurements involving the cosmic microwave background, galaxy clustering, the Lyman alpha forest, gravitational lensing, supernovae Ia and other tools probes has transformed our understanding of our universe. I then discuss key open problems such as the nature of dark matter, dark energy and the early universe.

With a cosmic flight simulator, we'll take a scenic journey through space and time. After exploring our local Galactic neighborhood, we'll travel back 13.7 billion years to explore the Big Bang itself and how state-of-the-art measurements are transforming our understanding of our cosmic origin and ultimate fate. We then turn to the question of whether this can all be described purely mathematically, and discuss implications ranging from standard physics topics like symmetries, irreducible representations, units, free parameters and initial conditions to broader issues like parallel universes, simulations and and Goedel incompleteness.

Cosmology ultimately aims to explain the initial conditions at the beginning of time and the entire subsequent evolution of the universe. The "beginning of time" can be understood in the Wheeler-DeWitt approach to quantum gravity, where homogeneous universes are described by a Schroedinger equation with a potential barrier. Quantum tunneling through the barrier is interpreted as a spontaneous creation of a small (Planck-size) closed universe, which then enters the regime of cosmological inflation and reaches an extremely large size. After sufficient growth, the universe can be adequately described as a classical spacetime with quantum matter. The initial quantum state of matter in the created universe can be determined by solving the Schroedinger equation with appropriate boundary conditions. I show that the most likely initial state is close to the vacuum state. This is the initial condition for inflation favored both by observational data and theoretical considerations.

During multi-field Inflation, the curvature perturbation can evovlve on superhorizon scales and will develop non-gaussianity due to non-linear interactions. In this talk I will discuss the calculation of this effect for models of inflation with two scalar fields.

A number of mechanisms have been introduced in previous literature that might be responsible for transitions between metastable minima in a scalar field theory coupled to gravity. The connection between these transition mechanisms has remained unclear, and current formulations of eternal inflation only include a subset of the allowed processes. In the first part of this talk, I will discuss how a number of transition mechanisms can be unified in the thin-wall limit, with interesting consequences for quantum cosmology and eternal inflation. I will then discuss making predictions in an eternally inflating universe, and introduce a measure for eternal inflation that is based on transitions rather than vacua.

Non-Gaussianities are a generic prediction of multi-field inflationary models and within reach of upcoming experiments. After reviewing current observational limits and the physical origin of a non-zero three point correlation function, I will discuss the possibility of detectable non-Gaussian signatures in a certain class of multi-field inflationary models, upon which assisted inflation/N-flation lies. Using the delta-N formalism within the slow roll approximation and focusing on N-flation (quadratic potentials without cross-coupling), we will see that said signatures are suppressed as the number of e-foldings grows, and that this suppression is increased in models with a broad spectrum of masses. We thus conclude that the production of a large non-Gaussian signal in models of this type is very unlikely.

At large scales the CMB spectrum measured by WMAP appears to have an anomalously low power of the quadrupole and an asymmetry of power at l < 40. We show that with an initial stage of fast roll of the inflation and a gradient in the initial conditions a simple chaotic inflation model may be capable of explaining both anomalies.

I consider a six dimensional space-time, in which two of the dimensions are compactified by a flux. Matter can be localized on a codimension one brane coupled to the bulk gauge field and wrapped around an axis of symmetry of the internal space. By studying the linear perturbations around this background, I show that the gravitational interaction between sources on the brane is described by Einstein 4d gravity at large distances. This is one of the first complete study of gravity in a realistic brane model with two extra dimensions, in which the mechanism of stabilization of the extra space is fully taken into account.

I discuss two instances in which nonlinear perturbations in cosmological models are important. First, in de Sitter space-time, the bare necessity that the perturbations should be part of a consistent Taylor expansion of the field equations leads to the requirement, using the 'linearization stability' arguments of the '70's, that the quantum field theory of a scalar field on de Sitter space-time is manifestly de Sitter invariant (not covariant). Second, the concern that in slow-roll inflation the effect of second order perturbations on the long wavelength (super Hubble) perturbations could be much stronger than that of the first order perturbations, for a wide range of slow-roll conditions, is explored in the context of a linear inflation potential and chaotic inflation.