### Physics of the very early universe from Planck satellite observations

The very early universe is still poorly understood, but from observations made by the WMAP satellite we know that small oscillations in a hot primordial plasma can account for most of the structure we see. These small oscillations must be seeded from an earlier phase, often conjectured to be a period of inflation, during which the scale factor of the universe was accelerating. It has proved very hard to learn about the inflationary era. Fortunately, this situation is changing. The Planck Surveyor satellite was launched in May 2009 and will return data within a few years, from which we hope to discover more details about the physics which gave rise to the density fluctuation. Before this can be done, it will be necessary to have a map from the possible scenarios of particle physics to the parameters which Planck can observe. In the course of this project, you will develop and apply some of the details of this mapping.

The primordial density perturbation is the principal observational relic of the very early universe. Its properties encode many details about the era in which it was synthesized, but it is not yet understood how to unlock this information. The WMAP satellite returned its first data in 2003, and its analysis has been dominated by the two-point statistics of the density perturbation. From these we have learned that the primordial density fluctuation is very close to Gaussian, and although it is nearly scale invariant there is marginally more power on large scales than shorter ones. These facts already constrain the types of physics which could have produced such a fluctuation, but many possibilities remain and it is hard to discriminate between them.

The newly-launched Planck satellite has the power to discriminate among different scenarios to a much finer degree. Its power comes from a sensitivity to small non-linearities in the fluctuation, which characterize departures from exact Gaussianity. Over the last five years an enormous amount of theoretical effort has been expended to understand inflationary non-Gaussianities. It is known that any observation of non-linear effects will rule out the simplest, and theoretically-preferred, models. Nevertheless, many outstanding questions still remain. What causes non-linear effects to grow or decay? If we observe a large or small non-Gaussianity, which are the models which will remain viable? Are there combinations of the non-Gaussian fraction with other observables, such as the fraction of gravity waves, which cannot be produced in any model?

The aim of this project is to answer some of these questions. The study of inflationary density perturbations draws on a broad range of physics. To compute their properties at birth requires a version of quantum field theory adapted to curved spacetime, whereas their subsequent evolution is described by classical general relativity. Special properties of the inflationary phase mean that the general relativistic evolution can equally be described as a dynamical system of trajectories evolving in phase space, so that powerful techniques from non-linear optics or non-equilibrium statistical mechanics may be applied. The Astronomy Centre has a strong track record in this area. Many details of both the Gaussian and non-Gaussian theories were contributed by researchers at Sussex, and the department continues to work at the cutting edge of the field.

This project provides an opportunity to develop your skills in fundamental physics and apply them to a problem which intimately connects theory and observation. The project is flexible, depending on your interests. If you are primarily interested in applying quantum field theory to inflation, then many examples of inflationary models in string theory produce fluctations with special initial conditions. These must be calculated using the ``in--in'' or Schwinger--Keldysh formalism, which also applies to thermal and non-equilibrium field theory. On the other hand, if your interests lie in the comparison of inflationary models with observation, then the important task is to understand how an initial distribution of fluctuations evolves during the inflationary era, with growing or decaying non-linearities. The transport of the distribution is described by an effective Boltzmann equation, which can be solved using analytic or semianalytic techniques. From studying how the distribution evolves with the underlying phase space flow, we hope to determine model-independent conditions which cause non-linearities to become large.

The Astronomy Centre maintains links with researchers elsewhere in Europe and North America, and it is expected that opportunities for collaboration will occur during the course of the project.

For more information/to apply for this project, please contact Dr. David Seery (email: D.Seery [AT] sussex.ac.uk).