Large Scale Structure:  Theories of the origin and the evolution of the universe predict the statistical properties of the dark matter distribution on the largest scales.  So if we could measure the dark matter clustering we could learn about the Universe composition, its evolution and even about inflation. In particular the shape of the power spectrum contains information about  cosmological parameters such as matter density , baryon density,  n,  dn/d lnk.  Higher-order correlations can be used to test the nature of the initial conditions such as non gaussianity.  While we cannot easily observe the dark matter distribution directly   and the galaxy distribution could be  a biased  tracer of the dark matter distribution, higher-order correlations can be used to measure this bias. I have developed the bispectrum technique and  I have applied it to the 2 degree field (2dF) galaxy redshift  survey to constrain the bias parameter: 2dF galaxies are faithful tracers of the dark matter distribution.  I have used galaxy surveys data (2dF and SDSS) in combination with other data sets to constrain cosmological parameters. I have also investigated the potential of large scale structures to constrain the nature of the initial conditions. I am now member of the LSST large scale structure working group; membership of the Sloan Digital Sky Survey III and of the Euclid Near Infrared Spectrograph consortium under way.
 
Cosmic Microwave Background: The big bang theory predicts that the early universe was hot and dense and an almost perfect blackbody. Thus the universe should be filled by this radiation called the cosmic microwave background (CMB). The CMB was emitted 130000 years after the big bang, thus by looking at the CMB we  see the very early universe.  The statistical properties of the small  CMB  temperature fluctuations can tell us about the early universe, the universe age,  geometry  and composition. I was involved with the analysis of WMAP data. These data confirmed the standard cosmological model: the universe is made by 4% baryonic matter, 23% dark matter, 73% dark energy, and it is consistent with being spatially flat. The age of the Universe is 13.7Gyr, the Hubble constant is 73 km/s/Mpc. The dark matter is cold and collisionless, the sum of  neutrino masses has to be  less than 1.8 eV. The dark energy is consistent with being a cosmological constant. The primordial power spectrum has a spectral slope slightly red (ns ~0.96), as predicted in the simplest inflationary scenarios. The data allow one to put some  constraints on specific inflationary models. Intriguingly the data seems to favor models with a slightly negative running of the spectral index. The CMB light is also polarized. Polarization is the next frontier for CMB experiments.  So far WMAP has detected the polarization signature of the  reionization of the universe (due to the first generation of stars), and has imposed upper limits on primordial gravity waves. The next generation CMB experiments such as ACT will use the CMB as a back illumination for cosmological structure formation.  
NON TECHNICAL
 
The study of dark energy is interesting, to me, for two reasons. An accelerated expansion (similar to the present day one but much much faster) might have happened shortly after the big bang (a theory known as inflation) and generated the primordial perturbations. Can the two accelerations be driven by the same physics? The other reason is that in both inflation and dark energy I think the breakthrough will come from a close collaboration with theoretical particle physicists.  
 
Learn more here about the project of studying the expansion history of the Universe by looking at “cosmic clocks”.
Primordial non-Gaussianity: what is the nature of the initial conditions? knowledge of  their detailed statistical properties will  help explain the mechanism that originates them.
Dark energy: Recent observations seems to indicate that something is making the expansion of the Universe accelerate. What is it?   A cosmological constant seems to fit the data well so far, but it is important to explore other options such as slowly rolling scalar fields (quintessence) and possible modifications of the law of gravity on very large scales, tricking us into thinking that the Universe is accelerating. We should devise new observations and ways to interpret current observations to learn more about the nature of dark energy.