Kjell Rosquist

An exact quantification of backreaction in relativistic cosmology

An important open question in cosmology is the degree to which the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) solutions of Einsteins equations are able to model the large-scale behavior of the locally inhomogeneous observable universe. We investigate this problem by considering a range of exact n-body solutions of Einsteins constraint equations. These solutions contain discrete masses, and so allow arbitrarily large density contrasts to be modeled. We restrict our study to regularly arranged distributions of masses in topological 3-spheres. This has the benefit of allowing straightforward comparisons to be made with FLRW solutions, as both spacetimes admit a discrete group of symmetries. It also provides a time-symmetric hypersurface at the moment of maximum expansion that allows the constraint equations to be solved exactly. We find that when all the mass in the universe is condensed into a small number of objects (

A unified treatment of quartic invariants at fixed and arbitrary energy

\ensuremath{\lesssim}10

Variable jet properties in GRB 110721A: time resolved observations of the jet photosphere

) then the amount of back-reaction in dust models can be large, with

Spacetimes with a transitive similarity group

O(1)

Invariants at fixed and arbitrary energy. A unified geometric approach

deviations from the predictions of the corresponding FLRW solutions. When the number of masses is large (

INTEGRABLE HAMILTONIAN SYSTEMS WITH VECTOR POTENTIALS

\ensuremath{\gtrsim}100

Killing tensors in two‐dimensional space‐times with applications to cosmology

), however, then our measures of back-reaction become small (

Exact evolution of discrete relativistic cosmological models

\ensuremath{\lesssim}1%

Lax Pair Tensors and Integrable Spacetimes

). This result does not rely on any averaging procedures, which are notoriously hard to define uniquely in general relativity, and so provides (to the best of our knowledge) the first exact and unambiguous demonstration of back-reaction in general relativistic cosmological modelling. Discrete models such as these can therefore be used as laboratories to test ideas about back-reaction that could be applied in more complicated and realistic settings.

The magnetic part of the Weyl tensor, and the expansion of discrete universes

Two-dimensional Hamiltonian systems admitting second invariants which are quartic in the momenta are investigated using the Jacobi geometrization of the dynamics. This approach allows for a unified treatment of invariants at both arbitrary and fixed energy. In the differential geometric picture, the quartic invariant corresponds to the existence of a fourth rank Killing tensor. Expressing the Jacobi metric in terms of a Kahler potential, the integrability condition for the existence of the Killing tensor at fixed energy is a nonlinear equation involving the Kahler potential. At arbitrary energy, further conditions must be imposed which lead to an overdetermined system with isolated solutions. We obtain several new integrable and superintegrable systems in addition to all previously known examples.