Matter Induced Bimetric Actions for Gravity

The gravitational effective average action is studied in a bimetric truncation with a nontrivial background field dependence, and its renormalization group flow due to a scalar multiplet coupled to gravity is derived. Neglecting the metric contributions to the corresponding beta functions, the analysis of its fixed points reveals that, even on the new enlarged theory space which includes bimetric action functionals, the theory is asymptotically safe in the large $N$ expansion.Comment: 34 pages, no figures

Bimetric Renormalization Group Flows in Quantum Einstein Gravity

The formulation of an exact functional renormalization group equation for Quantum Einstein Gravity necessitates that the underlying effective average action depends on two metrics, a dynamical metric giving the vacuum expectation value of the quantum field, and a background metric supplying the coarse graining scale. The central requirement of "background independence" is met by leaving the background metric completely arbitrary. This bimetric structure entails that the effective average action may contain three classes of interactions: those built from the dynamical metric only, terms which are purely background, and those involving a mixture of both metrics. This work initiates the first study of the full-fledged gravitational RG flow, which explicitly accounts for this bimetric structure, by considering an ansatz for the effective average action which includes all three classes of interactions. It is shown that the non-trivial gravitational RG fixed point central to the Asymptotic Safety program persists upon disentangling the dynamical and background terms. Moreover, upon including the mixed terms, a second non-trivial fixed point emerges, which may control the theory's IR behavior.Comment: 35 pages, 3 figure

The Inclusive Classroom: Implementing Universal Design for Learning in the College Classroom

Students are entering higher education classrooms today with a variety of differences related to their learning, culture, background and language. A diversified classroom brings its own unique challenges. How can a professor effectively meet the unique learning needs of students in the classroom? This workshop focuses on the concept of Universal Design for Learning (UDL). Come and learn new strategies and methods to meet the needs of all learners in your classroom. UDL provides a blueprint for creating instructional goals, methods, materials and assessments that work for everyone — not a single, one-size-fits-all solution but rather flexible approaches that can be customized and adjusted for individual needs

Asymptotically Safe Lorentzian Gravity

The gravitational asymptotic safety program strives for a consistent and predictive quantum theory of gravity based on a non-trivial ultraviolet fixed point of the renormalization group (RG) flow. We investigate this scenario by employing a novel functional renormalization group equation which takes the causal structure of space-time into account and connects the RG flows for Euclidean and Lorentzian signature by a Wick-rotation. Within the Einstein-Hilbert approximation, the $\beta$-functions of both signatures exhibit ultraviolet fixed points in agreement with asymptotic safety. Surprisingly, the two fixed points have strikingly similar characteristics, suggesting that Euclidean and Lorentzian quantum gravity belong to the same universality class at high energies.Comment: 4 pages, 2 figure

Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data

The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In this work we carry out a detailed renormalization group study of the spectral dimension $d_s$ and walk dimension $d_w$ associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). We discover three scaling regimes where these generalized dimensions are approximately constant for an extended range of length scales: a classical regime where $d_s = d, d_w = 2$, a semi-classical regime where $d_s = 2d/(2+d), d_w = 2+d$, and the UV-fixed point regime where $d_s = d/2, d_w = 4$. On the length scales covered by three-dimensional Monte Carlo simulations, the resulting spectral dimension is shown to be in very good agreement with the data. This comparison also provides a natural explanation for the apparent puzzle between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.Comment: 26 pages, 6 figure

An automated, geometry-based method for hippocampal shape and thickness analysis

The hippocampus is one of the most studied neuroanatomical structures due to its involvement in attention, learning, and memory as well as its atrophy in ageing, neurological, and psychiatric diseases. Hippocampal shape changes, however, are complex and cannot be fully characterized by a single summary metric such as hippocampal volume as determined from MR images. In this work, we propose an automated, geometry-based approach for the unfolding, point-wise correspondence, and local analysis of hippocampal shape features such as thickness and curvature. Starting from an automated segmentation of hippocampal subfields, we create a 3D tetrahedral mesh model as well as a 3D intrinsic coordinate system of the hippocampal body. From this coordinate system, we derive local curvature and thickness estimates as well as a 2D sheet for hippocampal unfolding. We evaluate the performance of our algorithm with a series of experiments to quantify neurodegenerative changes in Mild Cognitive Impairment and Alzheimer's disease dementia. We find that hippocampal thickness estimates detect known differences between clinical groups and can determine the location of these effects on the hippocampal sheet. Further, thickness estimates improve classification of clinical groups and cognitively unimpaired controls when added as an additional predictor. Comparable results are obtained with different datasets and segmentation algorithms. Taken together, we replicate canonical findings on hippocampal volume/shape changes in dementia, extend them by gaining insight into their spatial localization on the hippocampal sheet, and provide additional, complementary information beyond traditional measures. We provide a new set of sensitive processing and analysis tools for the analysis of hippocampal geometry that allows comparisons across studies without relying on image registration or requiring manual intervention

Quantum Einstein Gravity

We give a pedagogical introduction to the basic ideas and concepts of the Asymptotic Safety program in Quantum Einstein Gravity. Using the continuum approach based upon the effective average action, we summarize the state of the art of the field with a particular focus on the evidence supporting the existence of the non-trivial renormalization group fixed point at the heart of the construction. As an application, the multifractal structure of the emerging space-times is discussed in detail. In particular, we compare the continuum prediction for their spectral dimension with Monte Carlo data from the Causal Dynamical Triangulation approach.Comment: 87 pages, 13 figures, review article prepared for the New Journal of Physics focus issue on Quantum Einstein Gravit