Self-Protection of Massive Cosmological Gravitons

Relevant deformations of gravity present an exciting window of opportunity to probe the rigidity of gravity on cosmological scales. For a single-graviton theory, the leading relevant deformation constitutes a graviton mass term. In this paper, we investigate the classical and quantum stability of massive cosmological gravitons on generic Friedman backgrounds. For a Universe expanding towards a de Sitter epoch, we find that massive cosmological gravitons are self-protected against unitarity violations by a strong coupling phenomenon.Comment: 1+11 pages, v2: references adde

Brane Induced Gravity: From a No-Go to a No-Ghost Theorem

Numerous claims in the literature suggest that gravity induced on a higher co-dimensional surface violates unitarity in the weak coupling regime. However, it remained unclear, why a conserved source localized on this surface and giving rise to an induced gravity term at low energies would absorb and emit the associated ghost, given a consistent source-free theory. In this article it is shown that the appearance of the induced Einstein Hilbert term does not threaten the unitarity of the theory. The physics arguments behind this statement are presented in a semi-covariant language, but the detailed proof is given using Dirac's constraint analysis. It is shown that the would-be ghost highlighted in previous works is non-dynamical and therefore not associated with a state in the Hilbert space. As a result of these investigations, brane induced gravity goes without a ghost, opening an exciting window of opportunity for consistent deformations of gravity at the largest observable distances.Comment: 13 pages, v2: matches version published in Physical Review

Consistency of Relevant Cosmological Deformations on all Scales

Using cosmological perturbation theory we show that the most relevant defor- mation of gravity is consistent at the linear level. In particular, we prove the absence of uni- tarity violating negative norm states in the weak coupling regime from sub- to super-Hubble scales. This demonstrates that the recently proposed classical self-protection mechanism of deformed gravity extends to the entire kinematical domain.Comment: 22 pages, 4 figure

Island of Stability for Consistent Deformations of Einstein's Gravity

We construct explicitly deformations of Einstein's theory of gravity that are consistent and phenomenologically viable since they respect, in particular, cosmological backgrounds. We show that these deformations have unique symmetries in accordance with unitarity requirements, and give rise to a curvature induced self-stabilizing mechanism. As a consequence, any nonlinear completed deformation must incorporate self-stabilization on generic spacetimes already at lowest order in perturbation theory. Furthermore, our findings include the possibility of consistent and phenomenologically viable deformations of general relativity that are solely operative on curved spacetime geometries, reducing to Einstein's theory on the Minkowski background.Comment: 4 pages, 3 figures, v2: discussion of phenomenology and applications added, presentation optimize

Modified and condensed gravity

This doctoral thesis deals with both infrared modifications of gravity and with the recently proposed microscopic picture of black holes. The former subject, i.e. infrared modifications of gravity, denotes a class of theories that typically weaken Einsteins theory of gravity at very large (usually cosmological) distance scales while preserving its successes at smaller distances (in particular within the solar system). Infrared modified theories of gravity allow to make progress with the cosmological constant problem since the cosmological constant literally corresponds to a space-time source of infinite extent. The results presented in this thesis concern two representatives of infrared modified theories of gravity: Massive Gravity and Brane Induced Gravity. Massive Gravity has been extensively studied for graviton propagation on a flat Minkowski background. What we will do in this thesis, however, is to study Massive Gravity on curved backgrounds such as cosmologically relevant FRW backgrounds. It actually turns out that the physics associated with the propagation of gravitons on curved spaces is enormously rich. In particular, we were able to show that the linear theory is protected from potential unitarity violations by generically entering a strong coupling regime before the unitary violation of the linear theory could have occurred. We coined this mechanism the self-protection mechanism. In fact, the self-protection mechanism can be understood as a striking example of the recently proposed classicalization mechanism, where the classicalon plays the role of the new background geometry that forms when entering the non-linear regime. Even though that the self-protection mechanism is very appealing from a theoretical perspective, it goes hand in hand with the destruction of the FRW background as soon as we enter the non-linear regime. This is phenomenological unacceptable as this always happens for early times in the universe. This led us to the construction of a completely new theory of massive deformations, where we supple- mented the known ’hard mass’ term with a new ’soft mass’ term. This new theory is both stable and consistent on the whole Friedman manifold. A particular interesting special case can be obtained when we set the hard mass identically equal to zero, since in this case we obtain a modification that is solely operative on curved backgrounds, whereas we still have standard massless graviton propagation for regions where the background curvature is small. This modification is thus completely orthogonal to known massive gravity theories. The other infrared modified theory of gravity this thesis deals with, i.e. Brane Induced Gravity, has been thought to contain a ghost within its spectrum of physical particles if we consider two or more additional spatial dimensions (whereas for one spatial dimension we would obtain the consistent DGP model). However, this ghost degree of freedom is completely unexpected physically, as we can think of Brane Induced Gravity simply as a higher dimensional Einstein gravity theory with a specific, healthy four dimensional source. Therefore, we performed a complete Dirac constraint analysis that actually showed that the Hamiltonian on the constraint surface is positive definite, and thus that Brane Induced Gravity is consistent, contrary to prior claims in the literature. By studying the system as well in the covariant language, we were able to understand that these previous derivations of the ghost degree of freedom did not take the 00-Einstein equation into account properly. This equation actually is a constraint that renders the would-be ghost mode non-dynamical. The other subject of this thesis deals with the microscopic picture of black holes recently proposed by Gia Dvali and Cesar Gomez. To be concrete, we invented a novel non-relativistic scalar theory that is supposed to mimic properties of general relativity relevant for black hole physics but is simple enough to make extensive quantitative calculations. In a first step, we analyzed the system perturbatively. This allowed us to show that there is indeed indication that the system dynamically secures to stay at the point of quantum phase transition. However, only a thorough nonlinear numerical analysis that is currently under investigation will yield a definite answer

B-Spline Volumes for Time Dependent Bathymetry Modelling

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

An ensemble neural network model for real-time prediction of urban floods

The real-time forecasting of urban flooding is a challenging task for the following two reasons: (1) urban flooding is often characterized by short lead times, (2) the uncertainty in precipitation forecasting is usually high. Standard physically based numerical models are often too slow for the use in real-time forecasting systems. Data driven models have small computational costs and fast computation times and may be useful to overcome this problem. The present study presents an artificial neural network based model for the prediction of maximum water levels during a flash flood event. The challenge of finding a suitable structure for the neural network was solved with a new growing algorithm. The model is successfully tested for spatially uniformly distributed synthetic rain events in two real but slightly modified urban catchments with different surface slopes. The computation time of the model in the order of seconds and the accuracy of the results are convincing, which suggest that the method may be useful for real-time forecasts.Bundesministerium für Bildung und Forschung/Sonderprogramm GEOTECHNOLOGIEN/03G0846A/E