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Berkhahn, Felix (2013): Modified and condensed gravity. Dissertation, LMU München: Faculty of Physics



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.