My research interests revolve broadly around quantum field theory, cosmology and string inspired higher dimensional theories including Kaluza-Klein theory, Large Extra Dimensions, and brane-world models. I am particularly interested in the Casimir Effect, and the manifestation of this phenomenon in extra dimensions was a main feature of my Ph.D research. Specifically, I am interested in the role of Casimir energy in dimensional stabilization and as a natural source for dark energy.
The Casimir Effect
The Casimir Effect is the most salient manifestation of the quantum vacuum fluctuations. One of the fundamental ideas behind quantum field theory is that the vacuum of spacetime can be considered a quantum harmonic oscillator. More precisely, every point in space is an oscillators and certain excitations represent the matter and energy we are familiar with. One of the principal foundations of quantum theory is the Heisenberg Uncertainty Principle which tells us that no field oscillator can ever be at rest, and that there will always be a residual 'zero point' fluctuation. When one sums over all modes of the zero point oscillations and performs appropriate renormalizations one can calculate the energy contained in a region of spacetime due to the vacuum fluctuations. Casimir predicted that if one placed two conducting parallel plates close together in a vacuum then the boundary conditions imposed on the vacuum would create a pressure asymetry on the anterior portion of the plates when compared to the interior region. This asymmetry leads to a force - the Casimir force. This effect has been verified in the laboratory for decades.
Randall Sundrum Model
An important issue in theoretical physics today is the hierarchy problem which questions why gravity is so much weaker than the other three fundamental forces of nature, electromagnetism and the two nuclear forces. The RS model proposes that we exist on a five dimensional membrane. The extra (or fifth) dimension connects us to another membrane. Only gravity is free to propagate in the fifth dimension which is highly 'warped' or curved. The main idea is that gravity is 'stuck' in the extra dimension and as such its quantum wavefunction decays to such an extent that by the time it reaches our universe it is strongly damped, making it appear weaker.
Cosmic Inflation
Recent experimental discoveries indicate the space and time is not only expanding, but that it is expanding at an ever increasing rate or 'inflating'. There is no currently accepted model for why this is the case although there are numerous proposals. One of the key ingredients for inflation is negative energy, which is just the ingredient that appears in caluclations of the Casimir effect.
