We will review the DFR approach to Quantum Space- Time and discuss the state of the art and the open issues. The DFR model is a fully covariant model of flat quantum spacetime generated by selfadjoint coordinates, where covariance is unitarily implemented, and the commutation relations among the coordinates are derived from a stability condition of spacetime under localisation alone. It must be regarded as a sort of analogue of semiclassical quantisation, providing the noncommutative geometric background for the quantum theory of fields at an intermediate regime, where few processes take place at very high energy; attempts to construct dynamical models also will be shortly reviewed and discussed. The stability condition is enforced through uncertainty relations which should prevent the purely kynematical black-hole formation. The quantum geometry arising from the interplay of the universal differential calculus with the specific algebra of the model provides a precise framework for discussing bounds to measurements of position,length, and n-volumes operators. We will conclude with an outlook. References: [arXiv:hep-th/0303037], [arXiv:1005.2130], [arXiv:hep-th/0301100],[arXiv:1201.2519], [arXiv:1206.3067]. See also the review [arXiv:1004.5261v3].

We introduce the basic physical ideas and mathematical methods underlying Loop Quantum Gravity (LQG).

The theory of cosmological perturbations makes the link between quantum gravity theories of the very early universe and current cosmological observations. In this lecture, I will present the basics of this theory and its application to inflationary cosmology.

I will present the motivation for a generalization of geometry due to gravity. I will then describe the standard examples of noncommutative geometries and in particular Connes framework.

We discuss brane solutions in matrix models, focusing on the IKKT model. The effective geometry of the branes is described, and the significance of fluctuations is clarified. This leads to nonabelian gauge fields, scalar fields and fermions propagating on the brane, governed by an effective metric. The emphasis is to demonstrate how all degrees of freedom required for physics may arise from the matrix model. The quantization of the IKKT model is briefly discussed

A free wheel discussion on our prejudices on how we would like the creator to shape geometry at the beginning of the universe, confronting how the geometry at Planck length appears in various theories and models (strings, Loop Quantum gravity, noncommutative geometry...)

My morning lecture will consist of a (reasonably self- contained) introduction to Causal Dynamical Triangulations, a non-perturbative path integral method to constructing a fundamental theory of quantum gravity, including its motivation, ingredients, computational implementation and an overview of results in the dimensions the theory has been studied (1+1, 2+1 and the physically relevant case of 3+1 dimensions).

The aim of this lecture is to give a intuitive introduction to noncommutative geometry and explain how it allows to unify general relativity with the SU(2)xU(1)xSU(3) model of electro-weak and strong forces. We will review the phenomenological constraints resulting from this unification, in particular on the Higgs mass.

A relativistic version of the cosmological principle is presented where maximal symmetry is not postulated on surfaces of `simultaneity', but rather on past light-cones. This principle is then confronted with observational data: the Hubble diagram of supernovae, weak lensing, CMB and BAO. (joint work with Andre Tilquin)

Several Models of gravitational Leptogenesis, that is a lepton over antilepton asymmetry at early epochs of the Universe, do exist in the literature and involve coupling of fermions with non trivial curvatures of the early Universe space-time, leading to different dispersion relations between particles and antiparticles. Such differences in the Lepton sector can then be communicated in the baryon sector via baryon plus (or minus) Lepton conserving processes, such as sphalerons (or grand unified models). One can thus obtain phenomenologically correct values for the so-induced baryon asymmetry in the Universe, without the need for extra sources of CP violation, such as Supersymmetry and/or Sterile Neutrinos, for which at present we have no (concrete) experimental evidence. Nevertheless, such models suffer from fine tuning problems, which I will outline during the lecture. To avoid such problems, I will discuss an alternative way of obtaining such differences in the dispersion relation between matter and antimatter, and in particular neutrinos, by coupling the latter to space-time defects in early epochs of our Universe. The defects can be provided by certain compactified brane structures in brane/string-inspired Cosmologies. I will explain carefully why there is a preferential role of neutrinos, compared to other charged leptons and quarks in the Standard Model, in interacting with the ``medium'' of the brane defects, and how such a coupling leads to different dispersion relations between neutrinos and antineutrinos, when the latter propagate in dense media of these brane defects. I will also discuss how in such models overclosure of the early universe can be avoided, despite the presence of a dense medium of massive defects, with masses of order up to Planck mass. This stems from specific properties of the stringy/brane model, and requires an extra bulk space, onto which the brane Universe is embedded and moves. Phenomenologically correct values of the baryon asymmetry and matter over antimatter dominance can be obtained in this model without the aforementioned fine tuning problems that characterise other models of gravitational leptogenesis. As a spin off of this model, which is also a topic appropriate for further discussion in this workshop, I will discuss such CPT Violating issues in Finsler Cosmologies, that is cosmological space-times, in which the metric tensor depends on phase-space variables, instead of only coordinates.

Discussion on the phenomenology of quantum gravity.

Cosmological perturbations are said to be seeded by quantum vacuum fluctuations of the inflaton and metric field. Yet, they are used successfully in numerical simulations as classical sources since squeezing and decoherence render their quantum distribution undistinguishable from a classical stochastic distribution. However, an actual realization did take place at some stage, from which large scale structure subsequently developed. I will discuss two extensions of quantum mechanics, hidden variables and dynamical collapse, in the framework of which the measurement problem is naturally solved (and the Born rule recovered) and apply those to cosmological perturbation theory.

The effects that quantum gravity-motivated natural UV cutoffs at the Planck scale have on inflationary predictions for the CMB have garnered much interest in the literature. These studies have so far been mostly confined to UV cutoffs that are locally Lorentz symmetry- breaking. Here, we propose a locally Lorentz covariant approach which takes the form of a cutoff on the local density of dynamical degrees of freedom of the field theory. This cutoff thus has an intuitive information theoretic interpretation. We are studying the type and magnitude of possible signatures that this covariant cutoff would have in the CMB. The techniques we employ tie in naturally with recent results in spectral geometry that showed that spacetime could be simultaneously continuous and discrete in the same way that information can be.

TBA

In the framework of the algebraic approach to quantum field theory, the existence of Hadamard states allows for a thorough discussion of the regularization and renormalization freedoms of all observables. As a by- product, we can analyse rigorously the semiclassical Einstein?s equations showing that the renormalisation of the stress-energy tensor plays a crucial role. Furthermore, if we consider free scalar matter as well as homogeneous and isotropic solutions of the semiclassical Einstein?s equations, the system displays a de Sitter type behaviour even without a cosmological constant introduced a priori. We will show that, contrary to what often advocated, these solutions turn out to be stable and a comparison with experimental data is possible.

I start by giving a general introduction to the motivation for and the problems of a theory of quantum gravity. I then briefly describe the main approaches - quantum general relativity (including loop quantum gravity) and string theory - and some of their applications. I then give a general introduction to quantum cosmology, in which I mainly deal with geometrodynamics, but make also remarks on loop quantum cosmology.

My idea here is to give a short introduction myself (at most half an hour), followed by short presentations of participants and a general discussion. As for the topics of the short presentations, I suggest: "The no-boundary condition", "The tunnelling condition", "Boundary conditions in loop quantum cosmology", as well as other suggestions by participants.

In addition to simple scale invariance, a universe dominated by dark energy naturally gives rise to correlation functions possessing full conformal invariance. This is due to the mathematical isomorphism between the conformal group of certain three dimensional slices of de Sitter space and the de Sitter isometry group SO(4,1). In the standard homogeneous, isotropic cosmological model in which primordial density perturbations are generated during a long vacuum energy dominated de Sitter phase, the embedding of flat spatial 3-dim sections in de Sitter space induces a conformal invariant perturbation spectrum and definite prediction for the shape of the non-Gaussian CMB bispectrum. This form for the bispectrum is intrinsic to the symmetries of de Sitter space, and in that sense, independent of specific model assumptions. It is different from the predictions of single field slow roll inflation models, which rely on the breaking of de Sitter invariance. We propose a quantum origin for the CMB fluctuations in the scalar gravitational sector from the conformal anomaly that could give rise to these non-Gaussianities without a slow roll inflation field. Moreover we argue that conformal invariance also leads to the expectation for the relation $n_S - 1 = n_T$ between the spectral indices of the scalar and tensor power spectrum. Confirmation of this prediction or detection of non-Gaussian correlations in the CMB of the bispectral shape function predicted by conformal invariance can be used to establish the physical origin of primordial density fluctuations, and distinguish between different dynamical models of cosmological vacuum dark energy. [JCAP09(2012)024, arXiv:1103.4164]

I will describe the theory for the dynamic selection of the initial conditions of the universe from the landscape and its observational predictions. This theory allows for the wavefunction of the universe to propagate through the landscape while including decoherence, thereby unifying the many worlds interpretation of quantum mechanics with the landscape of string theory into a single mutliverse. Four of its predictions have been recently succesfully tested.

We review a recent proposal where spacetime is characterized by a multifractal geometry where dimension changes with the scale. This "anomalous" type of spacetime texture improves the UV behaviour of perturbative quantum field theories, including gravity. After introducing the basic ingredients, we discuss properties of quantum mechanics and field theories living thereon, with applications to gravity and cosmology. The formalism has also connections with noncommutative geometry and other theories of quantum gravity based upon the renormalization group flow.

After giving an overview of the basic features of Horava gravity, I will focus on the latest developments and argue that, at least for the most general and complete version of the theory, the infrared phenomenology is by now relatively well understood and pathologies have been tamed. This implies that time has come for the theory to face a new series of intriguing challenges, related to quantization, ultraviolet phenomenology, black holes and cosmological singularities etc. I will present some ideas and first results in some of these directions.

TBA

I discuss the curvature perturbation and the delta-N formalism, with focus on observationally relevant non-gaussianities, which may be generated either during inflation or at the end of inflation. Modelling attempts involve both inflatons and spectators. I emphasize the importance of understanding the decay mechanisms of the inflaton; examples are modulated reheating and preheating. I also discuss briefly isocurvature perturbations.

Group field theories are a class of models that are designed to define a sum over histories approach to quantum gravity. After a brief presentation of the relevant points and features of the theory, I will describe a preliminary attempt to give an effective description of homogeneous cosmologies and their effective dynamics, within an approximation of the full group field theory dynamics that matches closely the Bogoliubov approximation to the dynamics of Bose-Einstein condensates.

Two uncertainties define the prevailing attitude toward the LHC: uncertainty about what new physics it may find (if any); together with dissatisfaction with the "technical naturalness" arguments which (when applied to the hierarchy problem) help suggest what it should be looking for. The dissatisfaction arises because of a wide- spread despair about finding a technically natural solution to the cosmological constant problem, despite much effort spent seeking it. In this talk I describe a mechanism within supersymmetric extra-dimensional theories that allows the low-energy effective cosmological constant naturally to be of order the Kaluza-Klein scale. If this is the solution to the cosmological constant problem, then it requires extra dimensions that are both very supersymmetric and large enough to be relevant to the LHC. It in particular implies there must be modifications to gravity on micron distances as well as on cosmological scales. For the LHC it implies in particular three predictions. (1) the (so far - successful) prediction that no supersymmetric partners will be discovered, despite the low-energy supersymmetry; (2) many missing energy channels, with a gravity scale of 10 TeV; and (3) the existence of string excitations of standard model particles, likely below 10 TeV.