·Particle CosmologyCosmology offers particle physicists a method of testing models that is complementary to accelerator experiments. Particles that cannot be produced easily in accelerators can have drastic effects in the early universe. This can be seen in the new theories of gravity that involve submillimeter extra dimensions. My collaborators and I recently put severe constraints on a class of such theories. In these models, oscillations of the light field (the radion, a particular type of modulus field) that determines the size of the extra dimensions can over-close the universe. It had been proposed that a period of late inflation could solve this problem, however we found that the required inflaton scale is so low that it cannot successfully reheat the universe. We also found that in a five dimensional AdS scenario (the Randall-Sundrum model) for solving the hierarchy problem, the extra dimensional gravity can force the universe to collapse shortly after becoming matter dominated, thus such theories cannot describe our universe. We later found that when such models are stabilized by additional interactions, they are cosmologically viable and the radion must have Higgs-like interactions. We also used string theory techniques to analyze certain models where gravity is four dimensional at intermediate distances, but five dimensional at long distances.

Current observations of distant supernovae reveal that they are fainter than expected in a Universe with an expansion that is slowing down, or in other words the supernovae seem to be more distant that we expected. The standard explanation of this observation is that the expansion of the Universe has been accelerating rather than slowing down. We recently considered a model where the dimming of supernovae is based on photon-axion oscillations. This axion couples to photons, which allows a photon to transform into an axion in the presence of a magnetic field. So light traveling in intergalactic magnetic fields can in part turn into axions, and evade detection on Earth. A source would then appear fainter even if the Universe is not accelerating. We also found that axions may play a role in generating trans-GZK cosmic rays. It has been argued that a dark energy equation of state parameter w<-1 may be slightly favored by the data, although no consistent theory actually has so negative a w. We recently showed that the combination of a cosmological constant and axion effects can mimic w<-1.

Earlier on in my career I have studied the efficiency of monopole annihilation in the early universe. Using Big Bang nucleosynthesis constraints, I have also put limits on the strength of gauge interactions of right-handed neutrinos, concentrating on gauge bosons that couple to the tau-neutrinos. I found that the mass of such a gauge boson, divided by the gauge coupling, must be larger than roughly 2 TeV for it not to contribute excessively to the expansion rate of the universe at the time of nucleosynthesis.

Another emphasis of my research is an attempt to understand the pattern of fermion masses. An attractive possibility is that mass generation is dynamical, as happens in QCD. Such dynamical chiral symmetry breaking involves strong-coupling physics, so there are many open questions.

I have worked on the critical behavior of extended technicolor models. I derived an effective action for the low-energy degrees of freedom in a model in which a combination of gauge and four-fermion couplings is near a critical value for spontaneous chiral symmetry breaking. Previous work suggested that the resultant light scalar resonances can enhance fermion masses without violating bounds on flavor changing neutral currents. We estimated the width of these scalar resonances and found that they are extremely broad for realistic values of the gauge coupling.

In recent years, there has been a controversy over whether the chiral phase transition in 2+1 dimensional QED is first or second order. To resolve the issue, my collaborators and I calculated the fermion-antifermion scattering amplitude and located its poles. Since no pole goes to zero momentum at the transition point, we concluded that the transition is not second order. We have also extended our analysis to the zero temperature chiral phase transition in 3+1 dimensional

SU(N)gauge theories, like QCD, where we found that there is a critical number of fermion flavors (near 4N) above which there is no chiral symmetry breaking. Again the phase transition is not second order.