3 research outputs found
Gradient flows and instantons at a Lifshitz point
I provide a broad framework to embed gradient flow equations in
non-relativistic field theory models that exhibit anisotropic scaling. The
prime example is the heat equation arising from a Lifshitz scalar field theory;
other examples include the Allen-Cahn equation that models the evolution of
phase boundaries. Then, I review recent results reported in arXiv:1002.0062
describing instantons of Horava-Lifshitz gravity as eternal solutions of
certain geometric flow equations on 3-manifolds. These instanton solutions are
in general chiral when the anisotropic scaling exponent is z=3. Some general
connections with the Onsager-Machlup theory of non-equilibrium processes are
also briefly discussed in this context. Thus, theories of Lifshitz type in d+1
dimensions can be used as off-shell toy models for dynamical vacuum selection
of relativistic field theories in d dimensions.Comment: 19 pages, 1 figure, contribution to conference proceedings (NEB14);
minor typos corrected in v
Topologically Massive Gravity and Ricci-Cotton Flow
We consider Topologically Massive Gravity (TMG), which is three dimensional
general relativity with a cosmological constant and a gravitational
Chern-Simons term. When the cosmological constant is negative the theory has
two potential vacuum solutions: Anti-de Sitter space and Warped Anti-de Sitter
space. The theory also contains a massive graviton state which renders these
solutions unstable for certain values of the parameters and boundary
conditions. We study the decay of these solutions due to the condensation of
the massive graviton mode using Ricci-Cotton flow, which is the appropriate
generalization of Ricci flow to TMG. When the Chern-Simons coupling is small
the AdS solution flows to warped AdS by the condensation of the massive
graviton mode. When the coupling is large the situation is reversed, and warped
AdS flows to AdS. Minisuperspace models are constructed where these flows are
studied explicitly
Mixmaster universe in Horava-Lifshitz gravity
We consider spatially homogeneous (but generally non-isotropic) cosmologies
in the recently proposed Horava-Lifshitz gravity and compare them to those of
general relativity using Hamiltonian methods. In all cases, the problem is
described by an effective point particle moving in a potential well with
exponentially steep walls. Focusing on the closed-space cosmological model
(Bianchi type IX), the mixmaster dynamics is now completely dominated by the
quadratic Cotton tensor potential term for very small volume of the universe.
Unlike general relativity, where the evolution towards the initial singularity
always exhibits chaotic behavior with alternating Kasner epochs, the
anisotropic universe in Horava-Lifshitz gravity (with parameter lambda > 1/3)
is described by a particle moving in a frozen potential well with fixed (but
arbitrary) energy E. Alternating Kasner epochs still provide a good description
of the early universe for very large E, but the evolution appears to be
non-ergodic. For very small E there are harmonic oscillations around the fully
isotropic model. The question of chaos remains open for intermediate energy
levels.Comment: 1+35 pages, 4 figure