February 10, 2006

Hawking and no boundary initial conditions in the landscape

As if the authors knew of each other, the previous post was about Hartle, and today it is Hawking together with Hertog! The title is Populating the Landscape: A Top Down Approach. The paper is very clearly written. The top-down approach is compared to bottom-up way. Predictivity of the approach is discussed. Being not able to write anything of it better, I give a few quotes:

From their abstract: "We put forward a framework for cosmology that combines the string landscape with no boundary initial conditions. In this framework, amplitudes for alternative histories for the universe are calculated with final boundary conditions only. This leads to a top down approach to cosmology, in which the histories of the universe depend on the precise question asked."

Later " ... the quantum state of the universe at late times is likely to be independent of the state on the initial surface. This is because there are geometries in which the initial surface is in one universe and the final surface in a separate disconnected universe. Such metrics exist in the Euclidean regime, and correspond to the quantum annihilation of one universe and the quantum creation of another. Moreover, because there are so many different possible universes, these geometries dominate the path integral. Therefore even if the path integral had an initial boundary in the infinite past, the state on a surface S at late times would be independent of the state on the initial surface. It would be given by a path integral over all metric and matter field configurations whose only boundary is the final surface S. But this is precisely the no boundary quantum state."

"In the bottom-up picture it is thought that the universe begins with a grand unified symmetry, such as E8 ×E8. As the universe expands and cools the symmetry breaks to the Standard Model, perhaps through intermediate stages. The idea is that string theory predicts the pattern of breaking, and the masses, couplings and mixing angles of the Standard Model. However, as with the dimension of space, there seems to be no particular reason why the universe should evolve precisely to the internal space that gives the Standard Model. It is therefore more useful to compute no boundary amplitudes for a spacelike surface S with a given internal space. This is the top down approach, where one sums only over the subclass of histories which end up on S with the internal space for the Standard Model."

From conclusions: "A central idea that underlies the top down approach is the interplay between the fundamental laws of nature and the operation of chance in a quantum universe. In top down cosmology, the structure and complexity of alternative universes in the landscape is predictable from first principles to some extent, but also determined by the outcome of quantum accidents over the course of their histories."