MULTIVERSE AND FUNDAMENTAL COSMOLOGY: Multicosmofun '12

PREFACE: Multiverse and Fundamental Cosmology
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 MULTIVERSE, VARYING CONSTANTS, SUPERSTRING THEORY


Global structure of the multiverse and the measure problem
View Description Hide DescriptionAn unresolved question in inflationary cosmology is the assignment of probabilities to different types of events that can occur in the eternally inflating multiverse. We explore the possibility that the resolution of this "measure problem" may rely on nonstandard dynamics in regions of high curvature. In particular, "big crunch" singularities that develop in bubbles with negative vacuum energy density may lead to bounces, where contraction is replaced by inflationary expansion. Similarly, singularities inside of black holes might be gateways to other inflating vacua. This would drastically affect the global structure of the multiverse. We consider a measure based on a probe geodesic which undergoes an infinite number of passages through crunches. This can be thought of as the worldline of an eternal "watcher", collecting data in an orderly fashion. This watcher's measure is independent of initial conditions and does not suffer from ambiguities associated with the choice of a cutoff surface.

Variation of fundamental constants on sub and superHubble scales: From the equivalence principle to the multiverse
View Description Hide DescriptionFundamental constants play a central role in many modern developments in gravitation and cosmology. Most extensions of general relativity lead to the conclusion that dimensionless constants are actually dynamical fields. Any detection of their variation on subHubble scales would signal a violation of the Einstein equivalence principle and hence a lead to gravity beyond general relativity. On superHubble scales, or maybe should we say on superuniverse scales, such variations are invoked as a solution to the finetuning problem, in connection with an anthropic approach.

A loop quantum multiverse?
View Description Hide DescriptionInhomogeneous spacetimes in loop quantum cosmology have come under better control with recent advances in effective methods. Even highly inhomogeneous situations, for which multiverse scenarios provide extreme examples, can now be considered at least qualitatively.

Entanglement in a multiverse with no common spacetime
View Description Hide DescriptionInteruniversal entanglement may even exist in a multiverse in which there is no common spacetime among the universes. In particular, the entanglement between the expanding and contracting branches of the universe might have observable consequences in the dynamical and thermodynamical properties of one single branch, making therefore testable the whole multiverse proposal, at least in principle.

Varying constant cosmologies and cosmic singularities
View Description Hide DescriptionWe review standard and nonstandard cosmological singularities paying special attention onto those which are of a weak type and do not necessarily exhibit geodesic incompletness. Then, we discuss how these singularities can be weakened, strengthened, or avoided due to the timevariation of the physical constants such as the speed of light c and the gravitational constant G.

Cosmic strings in Brane World models
View Description Hide DescriptionOn a warped 5dimensional axially symmetric space time an exact solution is found of a bulk scalar field with a cosmological constant. It turns out that from the effective field equations on the brane, where a U(1) scalargauge field is present, no signs of the features of a cosmic string with an asymptotically conical space time is found as in the 4D counterpart model. This is caused by the projection of the bulk Weyl tensor on the brane. This could explain why we do not observe cosmic strings.

Phantom collapse of electrically charged scalar field in dilaton gravity
View Description Hide DescriptionOur research focus on gravitational collapse of electrically charged scalar field in dilaton gravity and in the presence of phantom coupling. We examine dynamical behaviour of the scalar field coupled to Maxwell field when gravitational interactions have form consistent with the lowenergy limit of the string theory. Moreover, we allow the evolving fields to have negative sign in front of the respective kinetic term of the Lagrangian. The main aim of our studies is to investigate in what manner does the phantom nature of either Maxwell or dilaton fields (or both of them) affect the outcomes of the collapse. It turns out that the influence is crucial to the obtained spacetime structures. Negative kinetic energy of one (or both) of the fields delays, changes the course or even prevents the collapse.

Universe with closed timelike curves in a bounded region in Tdual ppwaves backgrounds
View Description Hide DescriptionIn the 10dimensional ppwaves background we have found using Tduality a 4dimensional universe with the closed timelike curves (CTC's) which appear in the region bounded by two coaxial elliptic cylinders. This 4dimensional universe is similar to the Gödeltype spacetime only in this region. Outside of this region the causal pathology does not appear.

Fate of YangMills black hole in early Universe
View Description Hide DescriptionAccording to the Big Bang Theory as we go back in time the Universe becomes progressively hotter and denser. This leads us to believe that the early Universe was filled with hot plasma of elementary particles. Among many questions concerning this phase of history of the Universe there are questions of existence and fate of magnetic monopoles and primordial black holes. Static solution of EinsteinYangMills system may be used as a toy model for such a black hole. Using methods of field theory we will show that its existence and regularity depend crucially on the presence of fermions around it.

 SPACETIME GEOMETRY, QUANTUM GRAVITY AND COSMOLOGY


At the limits of spacetime
View Description Hide DescriptionOne of the main challenges of the present search for quantum gravity theory is a conviction that such a theory should be "background independent". What does this mean? Points in a space loose their individuality if the Hausdorff axiom is not satisfied. Let C be a differential structure on a space M (i.e. C is a suitable functional algebra on M. The Hausdorff relation ρ_{H} is defined as ). It is clearly an equivalence relation. As it is well known, with each equivalence relation a groupoid is associated. A groupoid associated with any nonHausdorff situation allows us to "resolve" such a situation and subject it to the geometric investigation. This naturally leads to the methods of noncommutative geometry. Surprisingly, one obtains in this way a probabilistic description (in a generalized sense) of nonHausdorff domains. This strategy is applied to the analysis of "malicious singularities" in general relativity.

Quantum spacetime, from a practitioner's point of view
View Description Hide DescriptionWe argue that theories of quantum gravity constructed with the help of (Causal) Dynamical Triangulations have given us the most informative, quantitative models to date of quantum spacetime. Most importantly, these are derived dynamically from nonperturbative and backgroundindependent quantum theories of geometry. In the physically relevant case of four spacetime dimensions, the ansatz of Causal Dynamical Triangulations produces  from a fairly minimal set of quantum fieldtheoretic inputs  an emergent spacetime which macroscopically looks like a de Sitter universe, and on Planckian scales possesses unexpected quantum properties. Important in deriving these results are a regularized version of the theory, in which the quantum dynamics is well defined, can be studied with the help of numerical Monte Carlo methods and extrapolated to infinite lattice volumes.

The transfer matrix in four dimensional causal dynamical triangulations
View Description Hide DescriptionThe Causal Dynamical Triangulation model of quantum gravity (CDT) is a proposition to regularize the path integral over spacetime geometries using lattice regularization with discrete time and geometries realized as simplicial manifolds. The model admits a Wick rotation to imaginary time for each spacetime configuration. Using computer simulations we determined the phase structure of the model and discovered that it predicts a de Sitter phase with a fourdimensional spherical semiclassical background geometry. The model has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) times. The transfer matrix uniquely determines the theory. We show that the measurements of the scale factor of the (CDT) universe are well described by an effective transfer matrix where the matrix elements are labelled only by the scale factor. Using computer simulations we determine the effective transfer matrix elements and show how they relate to an effective minisuperspace action at all scales.

On precanonical quantization of gravity in spin connection variables
View Description Hide DescriptionThe basics of precanonical quantization and its relation to the functional Schrödinger picture in QFT are briefly outlined. The approach is then applied to quantization of Einstein's gravity in vielbein and spin connection variables and leads to a quantum dynamics described by the covariant Schrödinger equation for the transition amplitudes on the bundle of spin connection coefficients over spacetime, that yields a novel quantum description of spacetime geometry. A toy model of precanonical quantum cosmology based on the example of flat FLRW universe is considered.

A canonical approach to the classical and quantum massive cosmology
View Description Hide DescriptionWe study the classical and quantum dynamics of an open FRW cosmological model in the framework of the nonlinear massive gravity theory. It is shown that the classical solutions consist of two distinguishable branches: One is a contacting universe which tends to a future singularity with zero size, while another is an expanding universe having a past singularity from which it begins its evolution. We then employ the canonical quantization procedure in the given cosmological setting to £nd the cosmological wave functions. We use the resulting wave function to investigate the possibility of the avoidance of classical singularities due to quantum effects.

Asymptotic silence in loop quantum cosmology
View Description Hide DescriptionThe state of asymptotic silence, characterized by causal disconnection of the space points, emerges from various approaches aiming to describe gravitational phenomena in the limit of large curvatures. In particular, such behavior was anticipated by Belinsky, Khalatnikov and Lifshitz (BKL) in their famous conjecture put forward in the early seventies of the last century. While the BKL conjecture is based on purely classical considerations, one can expect that asymptotic silence should have its quantum counterpart at the level of a more fundamental theory of quantum gravity, which is the relevant description of gravitational phenomena in the limit of large energy densities. Here, we summarize some recent results which give support to such a possibility. More precisely, we discuss occurrence of the asymptotic silence due to polymerization of space at the Planck scale, in the framework of loop quantum cosmology. In the discussed model, the state of asymptotic silence is realized at the energy density ρ = ρ_{c}/2, where ρ_{c} is the maximal allowed energy density, being of the order of the Planck energy density. At energy densities ρ>ρ_{c}/2, the universe becomes 4D Euclidean space without causal structure. Therefore, the asymptotic silence appears to be an intermediate state of space between the Lorentzian and Euclidean phases.

Anisotropic refinement in loop quantum cosmology
View Description Hide DescriptionIn this work we present how an anisotropic scenario can be implemented in Loop Quantum Cosmology, considering specifically a perturbative approach and a latter refinement. The original perturbative dynamics acquires corrections by introducing lattice refinements in the original loop formulation. Some insights on how such refinements can be obtained are shown.

Euclidean quantum gravity and stochastic approach: Physical reality of complexvalued instantons
View Description Hide DescriptionIn this talk, we compare two states: the stationary state in stochastic inflation and the ground state wave function of the universe. We already know that, for the potential with a static field, two pictures give the same probability distribution. Here, we go beyond this limit and assert that two pictures indeed have deeper relations. We illustrate a simple example so that there is a corresponding instanton if a certain field value has a nonzero probability in the statistical side. This instanton should be complexvalued. Furthermore, the compact manifold in the Euclidean side can be interpreted as a coarsegraining grid size in the stochastic universe. Finally, we summarize the recent status and possible applications.

Natural cutoffs and Hilbert space representation of quantum mechanics
View Description Hide DescriptionWe construct a Hilbert space representation of quantum mechanics in the presence of all natural cutoffs encoded in a generalized uncertainty principle (GUP) that admits a minimal measurable length, a minimal measurable momentum and a maximal momentum.
