theoretical cosmology
the standard model
inhomogeneous cosmologies
The standard model of cosmology assumes a homogeneous and isotropic universe, and as a description of the bulk properties of the universe, it has served us well. But the real universe is distinctly non-homogeneous on all scales except possibly the largest, so it is important to study the behaviour of inhomogeneities. Inhomogeneous cosmology uses exact solutions of the Einstein field equations to explore the full non-linear evolution of inhomogeneous structures.
The Metric of the Cosmos. This is the ultimate application of Einstein’s field equations – determining the relation between matter and geometry in the real universe. The idea of reducing observed cosmological data to a metric was first explicitly discussed by Kristian & Sachs in 1966. Though a fair bit of theoretical development has been done, the methods have never been implemented, and therefore key questions such as choosing appropriate numerical methods, anaylysing uncertainties, and how to handle the intricacies of real observational data, etc, have not been addressed. A numerical reduction scheme is being developed and tested with fake data.
The large amounts of cosmological data generated by current and future redshift surveys will make this project practicable in the near future. This data will allow us to move beyond the assumption of homogeneity, and instead quantify the degree of homogeneity or lumpiness on a metric level. More importantly, as the data becomes increasingly accurate, the proper reduction and interpretation of the high redshift data will require knowledge of the cosmic geometry that is traveled through by the light rays we observe.
Properties and Behaviour of Inhomogeneous Cosmological Models. Inhomogeneous solutions of Einstein’s field equations provide models of both small and large structures that are fully non-linear. This project focuses on models that are physically reasonable, avoiding those for which the matter behaviour cannot be justified. By determining their evolution, causaliy, horizons, topology, etc, we better understand the origin and nature of observed cosmic structure, especially those aspects that perturbation theory and the Newtonian approximation don’t address.
The Lemaitre-Tolman (LT) and Szekeres (S) metrics are probably the most physically realistic inhomogeneous cosmological models. Recent work has shown how to construct LT metrics with specified density or velocity profiles at chosen times, reproducing e.g. the formation of an Abel cluster, a galaxy with a central black hole, and more recently a void. This has made it much easier to model specific properties or behaviours.
The Szekeres metric is a lot more general than the LT metric, having no simple symmetries. This makes it even more realistic as a model for cosmic structure, and very useful for establishing which behaviours found in the LT model are a result of spherical symmetry and which aren’t. Recent work has established physical regularity conditions, investigated possible topologies, studied horizons and singularities, and analysed the possible density evolution patterns.
Junction Conditions and the Exit from Inflation. Exact solutions of Einstein’s field equations can also be constructed by joining two metrics at a (possibly moving) boundary, and applying the junction conditions for GR, which are much trickier than in flat spacetime. The exit from inflation may create regions of the universe that are not inflating as bubbles in an inflating background. The formation and growth of these bubbles is therefore a question that can be modeled using junctions conditions, and a recent result - that the boundary approaches light speed in finite time - requires further investigation. This would establish the viability (or otherwise) of chaotic inflation.
magnetic fields in cosmology
Despite the widespread presence of magnetic fields in the universe, the origin of cosmic magnetism is still a matter of considerable debate. Work is currently underway to develop a second order gauge-invariant approach to describe the generating large-scale cosmological magnetic fields. In this approach, magnetic fields are generated via the non-linear coupling between weak electric fields which may be produced for example by charge separation induced by fluctuations in the relative number densities of the species that make up the plasma, and gravitational waves during the low conductivity epoch of reheating. The appealing features of this mechanism are (i) the generic nature of the gravito-electromagnetic interaction; (ii) the unbiased and natural way in which the whole process comes to a halt; (iii) the asymptotic decay of the accompanying electric field, which leaves the cosmic medium permeated by a large scale seed magnetic field with strength well within the galactic dynamo requirements.
Magnetic fields also have an important effect on the polarization of the CMB via Faraday rotation. Scalar perturbations can only generate E type polarization, while tensor perturbations generate both E and B type polarization. A magnetic field also generates both polarizations, but in addition, it induces a correlation via Faraday rotation. This results in a correlation between B type polarization and the temperature anisotropies. Such a correlation does not arise in the context of statistical isotropy, but a large-scale magnetic field breaks the isotropy and produces an novel signature, which may be more accessible to observation.
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