K-essence: cosmology

In this work we consider different aspects of k-essence theories,
which are scalar field theories described by the generally
covariant and Lorentz invariant action with non-canonical kinetic
terms. It is shown that, because of the intrinsic nonlinearity,
these theories can have rather unexpected and unusual physical
properties. As in the usual relativistic field theories, any
nontrivial dynamical solution of the k-essence equation of motion
spontaneously breaks the Lorentz invariance. Thus the perturbations
around such solutions propagate in a "new aether". In contrast to
the usual relativistic field theories, these perturbations
propagate in an "effective" metric which is different from the
usual gravitational metric. This effective metric can be
interpreted as the so-called "emergent spacetime". In this thesis
we show that the dynamics of the perturbations can be described by
the action which is generally covariant with respect to the
reparameterization of this "emergent spacetime". The most
interesting manifestation of this "emergent spacetime" is that
perturbations can propagate faster than light. We show that despite
the superluminal propagation the causal paradoxes do not arise in
these theories, and in this respect these theories are not less
safe than General Relativity. This superluminal propagation of
perturbations has interesting consequences for cosmology and black
hole physics. In particular, it is possible to construct models of
inflation with an enhanced production of gravitational waves. This
in turn can be verified in the nearest future by the observations
of the B-mode polarization of the Cosmic Microwave Background
Radiation (CMBR). Moreover, we have shown that there exist
k-essence models which in principle allow to obtain information
from the region beyond the black hole horizon. This information is
encoded in the perturbations around the solution describing the
stationary accretion of the k-essence onto the black hole. In
addition, we discuss the possible dynamical violation of the Null
Energy Condition (NEC) in the k-essence models. The violation of
NEC by the dynamical Dark Energy (DE) is not excluded and even
slightly preferred by observations Moreover, the violation of NEC
plays a crucial role in the pre-Big-Bang scenarios. We have shown
that in the framework of general k-essence the dynamical violation
of NEC is physically implausible.