The Cosmic Microwave Background (CMB) contains the statistical information about the early seeds of the structure formation in our Universe. Its natural counterpart in the local universe is the distribution of galaxies that arises as a result of gravitational growth of those primordial and small density fluctuations. The characterization of the distribution of inhomogeneities at large-scale in the local Universe provides a powerful tool, complementary to the CMB, to determine the origin and the energy content of the Universe, the expansion rate of the Universe during the cosmic history, and the detailed process of formation of the large-scale structures (LSS). The study of the LSS in the coming years will attempt to address the following open questions in cosmology:

What is the dark matter, and which is its detailed contribution to the energy content of the Universe?

What is the dark energy, and how it affects the dynamics of the Universe?

What is the connection between large scale structure and galaxy formation?

Do fundamental constants vary along the history of the Universe?

Is there evidence for primordial non-Gaussianities giving information on the details of the inflationary expansion epoch of the Universe?

In order to contribute to the possible answer to those questions, in this project we will use several large scale structure probes:

The distribution and large-scale clustering of the galaxies, and its evolution with time. The matter power spectrum (P(k)) and the two-point correlation function (ξ(r)) contain certain geometric features associated to some characteristic length-scales in the Universe, as the horizon at matter-radiation equality, or the acoustic horizon at last scattering. In particular, the latter determines the Baryon Acoustic Oscillation (BAO) scale.

The higher order statistics: the three-point statistics characterizes the deviation from Gaussinity and therefore the structure formation through gravitational instability, the galaxy bias, and the primordial non-Gaussianities.

The distribution of the cosmic voids in the Universe. Both the statistics of big voids, as well as the characterization of the void expansion, provides a complementary tool to determine the matter density and the equation of state of the dark energy. Cosmic voids contain information of the higher order statistics of galaxies and can be used to further constrain the BAO scale.

The cosmic web can be used to characterize the formation of structures and relate the large scale structure with galaxy formation processes.

The distribution and abundance of galaxy clusters, as well as the evolution with time. Among other parameters, the cluster mass function depends both on the matter density as well as in the amplitude of the power spectrum. The time evolution of the mass function n(M,z) is also govern by the growth of structures in the Universe, thus being also sensitive to the equation of state of the dark energy.