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.