The cosmic expansion history tests the dynamics of the global evolution of the universe
and its energy density contents, while the cosmic growth history tests the evolution of the
inhomogeneous part of the energy density. By comparing both histories, we can distinguish
the nature of the physics responsible of the acceleration of the universe: dark energy or modified gravity. Most of the observational evidence for the accelerating universe comes from
geometrical tests that measure directly H(z) = ˙ a/a, the expansion rate of the universe, such
as measurements of the luminosity distance using standard candles (Sn Ia) or measurements
of the angular distance using standard rulers as baryonic acoustic oscillations. Observations
of the cosmic expansion history alone can not distinguish dark energy from modified gravity,
since the expansion history H(z) can be reproduced by any modified gravity model, by changing the energy equation of state "w". The additional observational input that is required is the growth function delta(z) = (delta-ro / ro)(z) of the linear matter density contrast as a function of redshift (usually used as the normalized growth function D(z) = delta(z)/delta(0)).
In the first part of the thesis, we study the Integrated Sachs-Wolfe effect (ISW), through the
cross-correlation between large scale clustering, traced by galaxies (in our case from the catalog SDSS) and primordial temperature fluctuations from CMB (using the catalog WMAP).
Photons that come from the last scattering surface can be red or blue shifted by the time evolution of fluctuations in the gravitational potentials created by large scale structures, which are traced by the large scale galaxy distribution. The ISW effect gives us information about dark energy (DE), because DE modifies the evolution of dark matter gravitational potential.
In principle, the ISW effect can probe dark energy independently from other observations,
such as Supernovae Ia.
The correlation between galaxies in redshift space can also be used to study the evolution of
the dark matter gravitational potential in a way that is complementary to the cross-correlation
of galaxies with CMB photons. In the second part of the thesis, we will study this effect in the
luminous red galaxies of the SDSS. These galaxies trace very large volumes which is important to have more signal, and they have a known evolution which make easy to work with them.

KEY WORDS: cosmology, large scale structure, growth of perturbations, ISW effect, redshift
distortions, LRG.

RESUMEN CASTELLANO:

En la primera parte de la tesis, estudiamos el efecto Integrado Sachs-Wolfe (ISW), a través
de la correlaci´on cruzada entre la estructura a gran escala trazada por galaxias (aquí usamos
el catálogo SDSS) y las fluctuaciones primordiales de temperatura del fondo cósmico de microondas (catálogo WMAP). Los fotones que provienen de la superficie de última interacción
pueden ser movidos hacia el azul o rojo por la evolución en el tiempo de las fluctuaciones
en los potenciales gravitacionales, creados por la estructura a gran escala. El efecto ISW da
información de la energía oscura, porque esta modifica la evolución de los potenciales gravitacionales de materia oscura. En principio, el efecto ISW puede probar la energía oscura independientemente de otras observaciones, como Supernovas Ia.
La correlación entre galaxias en el espacio de velocidades también se puede utilizar en
el estudio de la evolución de los potenciales gravitacionales de forma complementaria a la
obtenida mediante el efecto ISW. En la segunda parte de la tesis, estudiamos las distorsiones
en el espacio de velocidades para las galaxias luminosas rojas del catálogo SDSS. Estas galaxias trazan volúmenes grandes, esencial para obtener una buena señal, y además tienen una evolución conocida, facilitando su estudio.