My research is focused on modifications of gravity and non-standard cosmological models. I also maintain an interest in analytical and numerical studies of General Relativity.
Modifications of Newtonian gravity and the consequences for galaxies and cosmology
Our Universe is apparently composed of ~25% dark matter and ~70% dark energy, with the visible material comprising only ~5% of the total matter/energy content. This conclusion is reached by applying General Relativity (and therefore Newtonian gravity in the weak-field limit) to cosmology and galactic astrophysics. In doing so, it becomes clear that several issues arise: galaxies rotate too quickly for their visible material; the required evolution of structure in the Universe proceeds too slowly given the Universe's age and the amount of visible matter, and the expansion of the Universe appears to be currently accelerating. The first two "problems" are resolved by postulating the presence of particles that interact almost entirely gravitationally, and have non-relativistic velocities, known as cold dark matter. The accelerated expansion of the Universe is accounted for by the inclusion of a cosmological constant (often called Lambda) in Einstein's equations.
Given the (current) total lack of direct experimental evidence for the existence of dark matter, or any indication at all about the nature of Lambda, many researchers have explored alternative ideas, including a modification of gravity in the very weak field regime known as MOND. A lot more information (at an introductory level) about this idea can be found at Stacy McGaugh's webpage here. A detailed academic review of the subject may be found here. The basic idea is that gravity may be stronger than Newtonian in situations where the mass density becomes extremely low (such as in the outskirts of galaxies).
To understand what the possible observational consequences of such a modification of gravity might be, I have used the MOND N-body/hydro patch of RAMSES referred to as RAyMOND (for details see my page about codes) to study the effects of modifying the Newtonian gravitational force for very weak accelerations on cosmological structure formation and, in very recent work, galaxies infalling into galaxy clusters. These studies suggest potentially large differences between a MOND Universe and a Universe dominated by dark matter, suggesting potential means of testing the MOND hypothesis.
Couplings between dark matter and dark energy
I am currently in the process of developing simulations to explore the effects on structure formation of including a coupling between dark matter and dark energy. As opposed to Lambda (a pure cosmological constant), dark energy typically refers to dynamical field(s) that are responsible for the late-time acceleration of the Universe. The simplest example is a single scalar field (quintessence). Given that there is no a priori reason for dark matter particles and dark energy to not interact, it is worthwhile exploring the potential consequences. With N-body simulations we can explore non-linear gravitational clustering of dark matter when this coupling is present. Many studies exist in the literature regarding this interesting possibility.
In previous work I have studied several aspects of analytic black hole solutions in General Relativity in 5 or more dimensions, and as such I maintain an interest in this area. Currently I am interested in using numerical methods to study gravitational collapse in modified gravity theories.