Scientific Series

Inflation, a postulated epoch of accelerated expansion in the early universe, has become a principal component of the standard model of cosmology. From a wide variety of initial conditions, inflation produces a nearly homogeneous universe populated by density fluctuations that seed large-scale structure. However, inflation is such a good homogenizer that, once unleashed, in many cases it becomes eternal, ending only within spontaneously nucleated bubbles. In this scenario, our observable universe resides inside one such bubble. Surprisingly, it is possible to perform direct observational tests of eternal inflation. The most dramatic and detectable signatures of eternal inflation arise from the collision between bubbles in the very early universe, which leave an imprint on the cosmic microwave background (CMB) radiation. In this talk, I will motivate and describe the eternal inflation scenario and present the results of a search for the signatures of eternal inflation in CMB data from the Wilkinson Microwave Anisotropy Probe.

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is still an open problem. We address this issue by relating the quaternionic-Kähler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instantons are captured by contact transformations between different patches. We derive those by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electro-magnetic duality, and using mirror symmetry. As a result, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions.

The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In particular the spectral dimension, which measures the return probability of a fictitious diffusion process on space-time, provides a valuable probe which is easily accessible both in the continuum functional renormalization group and discrete Monte Carlo simulations of the gravitational action. In this talk, I will give a detailed exposition of the fractal properties associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). Comparing these continuum results to three-dimensional Monte Carlo simulations, we demonstrate that the resulting spectral dimensions are in very good agreement. This comparison also provides a natural explanation for the apparent conflicts between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.

Black holes lead a double life, simultaneously the dark, enigmatic, hairless consequence of general relativity and the powerful engines lurking at the hearts of galaxies with cosmological consequences.

In this talk we discuss a proposed dual matrix formulation of N = 4 Super Yang-Mills on R^4 coupled to 4D Einstein supergravity. We review the evidence accumulated so far in favor of this proposal, which includes a successful match of the symmetries of the continuum theory, and the computation of MHV gluon and graviton scattering amplitudes in terms of matrix model correlators. We also discuss some avenues of ongoing investigation.

First part: The research group in Yaounde (Cameroon), working on Mathematical Modelling and Applications is introduced. Second part: Global existence of solutions to the spatially homogeneous Einstein-Maxwell-Boltzmann system on a Bianchi type 1 space-time is proved.

Three-dimensional fluids with nontrivial vorticity can be described holographically. It is well-known that the Kerr-AdS geometry gives rise to a 'cyclonic' flow. Lorentzian Taub--NUT--AdS_4 geometries give rise to a rotating fluid with vortex flow.

The boundary conditions of general black holes in asymptotically flat spacetimes can be modified such that a conformal symmetry emerges. The black holes with asymptotic geometry modified in this manner satisfy the equations of motion of minimal supergravity in one dimension more. Their symmetry suggests that a dual conformal field theory description exists that can account for the black hole entropy even in the case of black holes that are far from extremality.

Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations as arise in relativistic FLRW cosmology, and it also is known that a correspondence between Newtonian and relativistic dust cosmologies continues to hold in linearized perturbation theory in the marginally bound/spatially flat case. Nevertheless, it is far from obvious that Newtonian gravity can provide a good global description of an inhomogeneous cosmology when there is significant nonlinear dynamical behavior at small scales. We investigate this issue in the light of a perturbative framework that we have recently developed, which allows for such nonlinearity at small scales. We propose a relatively straightforward "dictionary"---which is exact at the linearized level---that maps Newtonian dust cosmologies into general relativistic dust cosmologies, and we use our "ordering scheme" to determine the degree to which the resulting metric and matter distribution solve Einstein's equation. We find that Einstein's equation fails to hold at "order 1" at small scales and at "order $\epsilon$" at large scales. We then find the additional corrections to the metric and matter distribution needed to satisfy Einstein's equation to these orders. While these corrections are of some interest in their own right, our main purpose in calculating them is that their smallness should provide a criterion for the validity of the original dictionary (as well as simplified versions of this dictionary). We expect that, in realistic Newtonian cosmologies, these additional corrections will be very small; if so, this should provide strong justification for the use of Newtonian simulations to describe relativistic cosmologies, even on scales larger than the Hubble radius.