Conference

How can we rule out whole classes of dark energy models? And what quantities, at what redshift, and with what accuracy, should be measured in order to rule out these classes of models? I present answers to these questions by discussing an approach that utilizes the principal component parametrization of dark energy. I show results based on current data, and future forecasted data from SNAP and Planck.

We show that the existence of the bullet cluster, 1E0657-56, is incompatible with the prediction of the standard Lambda CDM cosmology. The probability of finding the large infall velocity (3000 km/s) necessary for explaining the X-ray and weak lensing data of 1E0657-56 is between 3.3x10^{-11} and 3.6x10^{-9}. The existence of the bullet cluster poses a serious challenge to LCDM cosmology, unless a lower infall velocity solution for 1E0657-56 with <1800 km/s is found.

The Atacama Cosmology Telescope (ACT) has recently measured the CMB angular power spectrum from maps with arcminute resolution at 148 GHz. By fitting to a template for the SZ angular power spectrum, we constrain the model's amplitude A_SZ < 1.63 (95% confidence level) and the amplitude of matter perturbations sigma_8 < 0.86 (95% CL). In this talk, we review the fiducial template and present additional templates for the SZ angular power spectrum based on different models for the hot gas in dark matter halos. We also discuss how the TSZ, KSZ, and SZ power spectra scale with sigma_8.

X-ray surveys and deep Chandra observations recently provided ~10% accurate measurements of the total mass in nearly 100 galaxy clusters at z=0-0.9. These data clearly show the effect of Dark Energy on slow-down of the structure growth at z<1. THe combination of the structure growth measurements with other cosmological observations substantially improves the constraints on the Dark Energy equation of state parameter. More advanced applications include constraints on the deviations from General Relativity on 10-100 Mpc scales. Will the situation improve in the future when samples of 10^3-10^5 clusters are available? I will review the current ''bottlenecks'', and discuss possible strategies for using future cluster data for ''precision cosmology''.

Observations are opening new windows to test general relativity at cosmological scales. In this talk, I will discuss how gravity determines the expansion and structure formation of the universe, what smoking guns of gravity in the cosmos we are expecting, what difficulties we are facing to perform unambiguous tests of gravity and what are possible ways to overcome these difficulties.

Non-linear structures in the universe leave characteristic imprints in the cosmic microwave background. These include Compton scattering (Sunyaev-Zeldovich effects) and gravitational lensing. The South Pole Telescope now has a catalog of massive galaxy clusters that were discovered this way, along with a measure of the background fluctuations generated by smaller clusters, that can be used to chart the growth of structure in the universe.

We point out and explicitly demonstrate a close connection that exists between featureless Mott insulators and fractional quantum Hall liquids. Using magnetic Wannier states as the single-particle basis in the lowest Landau level (LLL), we demonstrate that the Hamiltonian of interacting bosons in the LLL maps onto a Hamiltonian of a featureless Mott insulator on triangular lattice, formed by the magnetic Wannier states. The Hamiltonian is remarkably simple and consists only of short-range repulsion and ring-exchange terms.

The heavy fermion URu2Si2 boasts a 25 year old mystery. Its ''hidden order'' phase transition at Tc=17.5K has eluded the onslaught of theory and experiment to describe the complex underlying mechanism. Whether the transition is due to conventional ordering of k-space heavy electrons or to a change in hybridization of the r-space states at each magnetic-moment-contributing U atom is unknown. Addressing the problem requires a probe which can simultaneously measure the real space and momentum space structure, making spectroscopic imaging STM (SI-STM) the natural choice. SI-STM studies of URu2Si2 above Tc reveal the first images of the Fano lattice electronic structure, the real-space spectroscopic manifestation of a periodic array of localized Kondo resonances at the U sites. Below Tc, however, a hybridization gap opens in the density of states. Quasiparticle interference imaging reveals a concurrent rapid splitting of a light symmetric k-space band to form two new heavy bands exhibiting momentum space anisotropy. Thus, the ''hidden order'' state emerges directly from the Fano lattice electronic structure and exhibits characteristics of alterations in the hybridization of states at each U atom.