Hořava-Lifshitz theory of gravity and its applications to cosmology.

Abstract

In this dissertation, I studied Hořava-Lifshitz gravity and its applications to inflationary cosmology. After introducing the original proposal with the projectability and detailed balance conditions, I discussed its attracting features as well as the problems it faces. An extended model without the detailed balance condition was then studied and found to be stable in de Sitter spacetime, but still possess an extra scalar mode in the gravity sector. I then studied a model with an extra U(1) symmetry dubbed as the projectable general covariant HL gravity and showed that it has the same degree of freedom as general relativity, and is free of the stability problem. It was found that the FLRW universe is necessarily flat, given that the coupling with matter takes a specific form. I also studied the scalar perturbations around the FLRW metric and presented all the possible gauge choices. Applications of the general covariant model in inflationary cosmology were studied in the second part. After deriving the slow-roll conditions in this model, I showed that in the super-horizon regions the scalar perturbations become adiabatic, and the comoving curvature perturbation is constant, because of this slow-roll condition. By using the uniform approximation technique, power spectra and indices of primordial scalar and tensor perturbations under the slow-roll approximations were expressed explicitly in terms of the slow-roll parameters and the various coupling constants. I found that they are in general different from, but reducible to, the values in the class of simplest inflation models. Next I studied the non-Gaussianities of these perturbations. For scalar perturbations, by properly choosing the coupling constants, a large nonlinearity parameter fNL is possible. I also found that the bispectrum favors the equilateral shape as a result of the higher order spatial derivatives, and that folded shape is enhanced when the vacuum is from the Bunch-Davis vacuum. Both the squeezed and the equilateral shapes appear in the bispectrum for primordial gravitational waves. In addition, the polarization tensors of the tensor fields have strong effects on the shapes of the bispectrum.