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In this talk, I will outline a quantum generalization of causal networks that are used to analyze complex probabilistic inference problems involving large numbers of correlated random variables. I will review the framework of classical causal networks and the graph theoretical constructions that are abstracted from them, including entailed conditional independence, d-separation and Markov equivalence. I will show how to generalize the definition of causal networks to the quantum case, such that the same graph theoretic constructions apply, and give an explicit representation of the states supported on the graph as the Gibbs states of certain classes of Hamiltonians.

Not only general relativity but also quantum theory plays important roles in current cosmology. Quantum fluctuations of matter fields are supposed to have provided the initial seeds of all the structure of the current universe, and quantum gravity is assumed to have been essential in the earliest stages. Both issues are not fully understood, although several heuristic effects have been discussed. In this talk, implications of an effective framework taking into account the coupling of matter and gravity are discussed. This touches on interpretational issues of quantum mechanics, cosmological observations and properties of quantum gravity.

In this talk I will discuss some aspects of graviton production by moving branes. After a brief introduction to braneworld cosmology I will focus on braneworlds in a five-dimensional bulk, where cosmological expansion is mimicked by motion through AdS_5. The moving brane acts naturally as a time-dependent boundary for the five-dimensional graviton (five-dimensional tensor perturbations) leading to graviton production out of quantum vacuum fluctuations. This effect is related to the so-called dynamical Casimir effect, i.e. the generation of real photons out of vacuum fluctuations of the quantized electromagnetic field in dynamical cavities. By applying the formalism used to study the dynamical Casimir effect I will show explicitly that the five-dimensional graviton reduces to the four-dimensional one in the late time approximation of such braneworlds. In the last part of the talk I will study a (toy) model where two branes approach each other in a radiation dominated phase, bounce off and move apart from each other afterwards. Thereby generation of massive gravitons takes place caused by the coupling of the Kaluza-Klein modes to the gravitational zero mode which exhibits a blue spectrum. At the end I will discuss possible applications of the formalism to more interesting scenarios (braneworld inflation etc).

The laws of physics are usually meant to be set in stone; variability is not usually part of physics. Yet contradicting Einstein\'s tenet of the constancy of the speed of light raises nothing less than that possibility. I will discuss some of the more dramatic implications of a varying speed of light. João Magueijo is Professor of Physics at Imperial College London. He is currently visiting Perimeter Institute and the Canadian Institute for Theoretical Astrophysics in Toronto. He received his doctorate in theoretical physics at Cambridge University, and has been a visiting scientist at the University of California at Berkeley and Princeton University. Joao Magueijo, Theory of Relativity, speed of light, VSL, varying speed of light, Dirac, cosmology, geometry, dimensional, dimensionless, Bekenstein, Brans-Dicke, varying constant, Einstein, time dilation, length contraction, horizons, Big Bang, grand-unified theory, Planck length, Planck time, gravity, space, time, quantum gravity, varying alpha, Kelvin, quasar, laws of physics