Simulating the early universe in a laboratory

The very early universe was incredibly hot, at a temperature of 1032 Kelvin only 10-43 seconds after the Big Bang. Just as water freezes to ice on a cold day, the universe underwent many phase transitions on its 14 billion year journey to its present - comparatively frosty - 3-Kelvin state. Around one nano-second after the Big Bang, by which time the universe had already cooled enormously to around 1015 Kelvin, the universe underwent the electroweak phase transition.
This phase transition can be attributed to the deformation of the Higgs potential as the universe cooled. Above the transition temperature, Tc, the Higgs potential takes the form of a bowl shape, with a single minimum point at its centre. We say that this form is symmetric, since from the perspective of a person standing at its minimum point, the potential looks the same in every direction. The physical consequence of this symmetry is that prior to the electroweak phase transition, photons (which carry the electromagnetic force) and the W,W+ and Z bosons (which carry the weak nuclear force) were massless. Thus, at such times, the electromagnetic and weak forces were indistinguishable from one another. Below Tc, the Higgs potential takes the shape of a mexican hat. The centre point is no longer the minimum point of the potential; instead the potential possesses a ring of minimum points about its centre. Regardless of where you stand on this ring, the potential looks different in different directions. Hence, the electroweak phase transition broke the symmetry of the Higgs potential, giving mass to W, W+ and Z bosons, but not to photons. Consequently, the electromagnetic and weak forces differentiated, adopting the distinct properties that they still exhibit today.
We refer to regions of the universe that have and have not undergone the electroweak phase transition as true and false vacuums respectively. It has been postulated that the electroweak phase transition was first order, by which we mean that the universe was converted from false vacuum to true via rapidly expanding bubbles of true vacuum. The aim of my project is to model this electroweak phase transition using an anologue cold atom system. I am currently considering a one dimensional system, comprising of two atomic states, with the aim of considering higher dimensional systems with more atomic states in the future. I will be modelling such systems using the Stochastic-Projected Gross Pitaevskii Equation (SPGPE) - a stochastic equation that is commonly used to model phase transitions in finite temperature systems.
Some questions that my project aims to answer include:
* When and how did bubbles of true vacuum form in the early universe?
* How did they evolve?
* How did they interact with one another?
* How do our findings change when we consider systems with different dimensions and/or different numbers of atomic states?
* How do our results compare to those generated using different approaches?
Answering such questions may provide an insight into other mysteries of the early universe, such as the baryon assymetry problem or the processes by which gravitational waves and magnetic fields were generated.