Talks

I will review some recent work on infrared issues for scalar fields in exact and quasi de Sitter space. Renewed interest in this topic has been driven by the observational potential for a more accurate determination of statistics of the primordial curvature perturbations, especially non-Gaussianity. Interestingly, the resulting questions are not only relevant for mapping inflationary models to observation but also link directly to more fundamental questions about the initial state, eternal inflation, and the long time dynamics of interacting quantum fields in curved space. Infrared questions provide a precisely calculable way to put pressure on inflation as a rigorous and consistent framework, ready to confront future observations.

We explore simple but novel solutions of general relativity which, classically, approximate cosmologies cycling through an infinite set of ``bounces." These solutions require curvature K=+1, and are supported by a negative cosmological term and matter with -1 < w < -1/3. They can be studied within the regime of validity of general relativity. We argue that quantum mechanically, particle production leads eventually to a departure from the regime of validity of semiclassical general relativity, likely yielding a singular crunch.

I provide a mathematical model of holographic cosmology whose coarse grained description is that of a homogeneous isotropic, flat universe, which makes a transitions from an FRW to an eternal de Sitter regime.&nbsp;Based on this model, I suggest some heuristic ideas which explain the low initial entropy of the universe and may provide a description of an inflationary era with small fluctuations.

I will argue that anthropic reasoning is unnecessary or misleading when the universe/multiverse is small enough that another observer with exactly your memories is unlikely to exist. Instead, one can evaluate theories or make predictions in the standard Bayesian way, based on the conditional probability of something unknown given all that you do know. Things are not so clear when the universe is large enough that all competing theories predict that an observer with your exact memories exists with probability close to one. I will discuss issues that arise in such large or infinite universes, such as "Boltzmann brains", and will argue that pending better understanding of these issues one should be hesitant to draw conclusions different from those that would apply to a small iverse.

We present a holographic framework for inflationary universes, in particular those that are either asymptotically de Sitter or asymptotically power-law. This framework reveals how cosmological observables, including the primordial power spectrum and non-Gaussianities, are encoded in the correlation functions of a three-dimensional non-gravitational quantum field theory. Introducing a simple yet general class of holographic models, we obtain distinctive observational predictions that are compatible with current observational data and may be either confirmed or excluded by Planck.

Problematic growths of curvature and anisotropy are found in nonsingular bouncing cosmologies that include both an ekpyrotic phase and a bouncing phase. Classically, initial curvature and anisotropy that are suppressed during the ekpyrotic phase will grow back exponentially during the nonsingular bouncing phase. Besides, curvature perturbations and anisotropy are generated by quantum fluctuations during the ekpyrotic phase. In the bouncing phase, an adiabatic curvature perturbation grows to dominate and gives rise to a blue spectrum that spoils the scale-invariance. Meanwhile, a scalar shear perturbation grows nonlinear and creates an overwhelming anisotropy that disrupts the nonsingular bounce altogether.

Einstein's theory of General Relativity and its couplings to matter in 3+1 dimensions can be slightly enlarged with the requirement of a local scale (conformal) symmetry and the corresponding gauge degrees of freedom. This form of the theory is a prediction from 2T-gravity in 4+2 dimensions. It has no dimensionful constants, not even the gravitational constant, and requires all scalar fields to be conformally coupled to gravity and to the rest of matter. The theory can be gauge fixed to the usual gravity theory in the Einstein frame, thus generating the gravitational constant. Other physically equivalent forms of gauge fixing lead to the complete set of exact analytic solutions of the usual Friedmann equations, including radiation, curvature, anisotropy and a special potential for a scalar field coupled minimally to gravity. These analytic cosmological solutions, which are geodesically complete at singularities, reveal many surprising properties that are not noticeable with approximate cosmological solutions. Some aspects of the exact solutions will be reviewed in this lecture. In particular, it is predicted that the universe is cyclic and furthermore is has a period of antigravity between every big crunch and the following big bang.

I will briefly review the predictions of the theory of the Selection of the Initial Conditions of the Universe from the Landscape Multiverse and focus on recent and upcoming evidence. In this theory, the wavefunction of the universe propagating on the landscape is localized via Anderson localization. Decoherence of the wavefunction is triggered by the backreaction of massive superhorizon fluctuations. Thus the selection of the initial conditions is determined by the quantum dynamics of gravitational (vacuum energy) vs. matter degrees of freedom. Dynamics selects only high energy universes as 'survivors' while low energy universe become 'terminal'. I will describe how the nonlocal quantum entanglement associated with decoherence provides a second source of perturbations and gives rise to a series of derived predictions. Three of the signatures of the theory predicted in 2006 (the giant void; a suppressed \sigma_8; and, the dark flow) were tested soon afterwards. The fourth prediction will be tested by LHC in a year.