Conference

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. 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.

I will discuss a novel framework of the very early universe which addresses the traditional horizon and flatness problems of big bang cosmology and predicts a scale invariant spectrum of perturbations. Unlike inflation, this scenario requires no exponential superluminal expansion of space-time. Instead, the early universe is described by a conformal field theory minimally coupled to gravity. The conformal fields develop a time-dependent expectation value which breaks the flat space so(4,2) conformal symmetry down to so(4,1), the symmetries of de Sitter, giving perturbations a scale invariant spectrum. The solution is an attractor, at least in the case of a single time-dependent field. Meanwhile, the metric background remains approximately flat but slowly contracts, which makes the universe increasingly flat, homogeneous and isotropic. The essential features of the scenario depend only on the symmetry breaking pattern and not on the details of the underlying lagrangian.

I analyze the various roles of infinity in current thinking about cosmology. Topics include initial conditions, attractor behavior, inflation and the precision and meaning of quantum measurements. I review the de Sitter equilibrium cosmology as an example of a finite cosmology, and present some new predictions that permit observable tests.