Research Interests: Quantum Gravity and Cosmology
The twentieth century brought into physics two revolutionary theories:
Einstein's theory of General Relativity (GR) and Quantum mechanics. They both changed our understanding of Nature dramatically and successfully passed numerous experimental tests but, at the same time, seemed to be contradictory to each other. Luckily the two never meet in everyday life, as the former describes gravity manifesting itself in interactions of large and heavy bodies, whereas the latter applies to tiny objects of atomic size and smaller.
However, under very general assumptions, GR predicts singularities inside Black Holes and in the very beginning of the Universe - the famous "Big Bang" singularity. There the physicists have to admit that the theory of GR breaks down. And that is exactly where the two theories meet and have to be reconciled.
My current research interests are in the field of Loop Quantum Gravity (LQG), a candidate for such a unifying theory. Modern astrophysical experiments indicate that, at least on large scales, the Universe appears very symmetric: homogeneous and isotropic. In fact, we have two sources of information from outer space: the distribution of galaxies and the Cosmic Microwave Background (CMB). The aforementioned symmetry simplifies the analysis enormously and makes cosmology a fruitful testing arena for existing theories of gravity.
Recent Research with Students
- ACURA project: "Asteroid Collisions" with Josh Fixelle (September 09 - present)
As has been widely discussed recently, our planet may become a probable target for asteroids. We investigate several scenarios proposed to prevent asteroid collisions with Earth. The asteroid 99942 Apophis is considered as a typical representative. Among others, the recent "gravitational tractor" scenario proposed in [1] is discussed. For a simplistic toy-model we obtain estimates for both the mass of the tractor and the amount of fuel required to tow a potentially dangerous asteroid off-course so as to avoid a collision with the Earth. In addition, we analyze two more scenarios titled "sling-shot" and "bumping", and comment on their relative efficiency compared to the "towing" scenario. Based on the analysis, the bumping scenario looks most promising.
- ACURA project: "Fysics is Phun" with Brian Drelling (September 09 - present) Fysics is Phun is a team-based game in which the competitors outwit each other by creating plausible false statements and by making their rivals fall for the fakes they created. The game process can be facilitated and made smoother with the help of networked computers and appropriate software. The purpose of this ACURA project is to design such software. It is expected that it would diminish the amount of time needed for a typical game by a factor of two, which would make it more dynamical and attractive for interested faculty.
- ACURA project: "Mathematical Modelling of Traffic Jams" with Artem Busorguin, Arpit Patel, Prashant Sharma, and Qi Zhang (September 08 - May 09). Abstract
Selected Publications (see also complete publication list)
(the order of authors is alphabetical)
- Bojowald, M., G. Hossain, M. Kagan, and S. Shankaranarayanan
"Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity" , Phys. Rev.79 043505 (2009) (available at arXiv) - Bojowald, M., G. Hossain, M. Kagan, and S. Shankaranarayanan
"Anomaly freedom in perturbative loop quantum gravity", Phys. Rev. D 78, 063547 (2008) (available at arXiv) - Bojowald, M., H. H. Hernandez, M. Kagan, and A. Skirzewski
"Effective constraints of loop quantum gravity", Phys. Rev. D 75, 64022 (2007)
(available at arXiv) - Bojowald, M., H. H. Hernandez, M. Kagan, P. Singh, and A. Skirzewski
"Formation and evolution of structure in Loop Cosmology", Phys. Rev. Lett. 98, 031301 (2007) (available at arXiv) - Bojowald, M., H. H. Hernandez, M. Kagan, P. Singh, and A. Skirzewski
"Hamiltonian cosmological perturbation theory with loop quantum gravity corrections", Phys. Rev. D 74, 123512 (2006) (available at arXiv) - Bojowald, M. and M. Kagan
"Loop cosmological implications of a non-minimally coupled scalar field", Phys. Rev. D 74, 044033 (2006) (available at arXiv) - Bojowald, M. and M. Kagan
"Singularities in Isotropic Non-Minimal Scalar Field Models", Class.Quant.Grav., 23, 4983 (2006) (available at arXiv) - Kagan M.
"Phenomenological implications of an alternative Hamiltonian constraint for quantum cosmology", Phys. Rev. D 72, 104044 (2005) (available at arXiv)