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Vikman, Alexander (2007): K-essence: cosmology: causality and emergent geometry. Dissertation, LMU München: Faculty of Physics
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Abstract

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.