Since 2002 Perimeter Institute has been recording seminars, conference talks, and public outreach events using video cameras installed in our lecture theatres. Perimeter now has 7 formal presentation spaces for its many scientific conferences, seminars, workshops and educational outreach activities, all with advanced audio-visual technical capabilities. Recordings of events in these areas are all available On-Demand from this Video Library and on Perimeter Institute Recorded Seminar Archive (PIRSA). PIRSA is a permanent, free, searchable, and citable archive of recorded seminars from relevant bodies in physics. This resource has been partially modelled after Cornell University's arXiv.org.
Continuous-variable SICPOVMS seem unlikely to exist, for a variety of reasons. But that doesn't rule out the possibility of other 2-designs for the continuous-variable Hilbert space L2(R). In particular, it would be nice if the coherent states -- which form a rather nice 1-design -- could be generalized in some way to get a 2-design comprising *Gaussian* states. So the question is: "Can we build a 2-design out of Gaussian states?". The answer is "No, but in a very surprising way!" Like coherent states, Gaussian states have a natural transitive symmetry group.
If we imagine that the universe is truly eternal, special challenges arise for attempts to solve cosmological fine-tuning problems, especially the low entropy of the early universe. If the space of states is finite, the universe should spend most of its time near equilibrium. If the space of states is infinite, it becomes difficult to understand why our universe was in a particular low-entropy state.
I will discuss approaches to addressing this problem in a model-independent fashion.
"A positive cosmological constant allows arbitrarily many different quantum states, but apparently only if there can be big bangs and/or big crunches. Without any big bang or big crunch, the entropy may be limited by the Gibbons-Hawking entropy of pure deSitter, and the matter entropy might even more limited by a value roughly the three-fourths power of the Gibbons-Hawking entropy. A classical analogue of an upper limit on the entropy is the finite canonical measure for nonsingular cosmologies.
Closed systems never evolve to lower entropy states -- except when they do, which is if one waits a time that is exponential in the entropy change. Thus macroscopic decreases in entropy are 'never' observed. Yet in cosmology there are eternal systems in which downward entropy fluctuations of any magnitude eventually happen. What is the nature of such fluctuations?
Our universe may have formed via bubble nucleation in an eternally-inflating background. Furthermore, the background may have a compact dimension---the modulus of which tunnels out of a metastable minimum during bubble nucleation---which subsequently grows to become one of our three large spatial dimensions. We discuss some potential observational signatures of this scenario.
We propose a novel cosmological scenario, in which standard inflation is replaced by an expanding phase with a drastic violation of the Null Energy Condition (NEC): \dot H >> H^2. The model is based on the recently introduced Galileon theories, which allow NEC violating solutions without instabilities. The unperturbed solution describes a Universe that is asymptotically Minkowski in the past, expands with increasing energy density until it exits the regime of validity of the effective field theory and reheats.
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.
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. 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.
Check back for details on the next lecture in Perimeter's Public Lectures Series