Abstract: We review the recent literature on modified theories of gravity in the Palatini approach. After discussing the motivations that lead to consider alternatives to Einstein's theory and to treat the metric and the connection as independent objects, we review several topics that have been recently studied within this framework. In particular, we provide an in-depth analysis of the cosmic speed-up problem, laboratory and solar system tests, the structure of stellar objects, the Cauchy problem, and bouncing cosmologies. We also discuss the importance of going beyond the f(R) models to capture other phenomenological aspects related with dark matter/energy and quantum gravity.

Abstract: In this article we investigate the properties of the FLRW flat cosmological models in which the cosmic expansion of the Universe is affected by a dilaton dark energy (Liouville scenario). In particular, we perform a detailed study of these models in the light of the latest cosmological data, which serves to illustrate the phenomenological viability of the new dark energy paradigm as a serious alternative to the traditional scalar field approaches. By performing a joint likelihood analysis of the recent supernovae type la data (SNIa), the differential ages of passively evolving galaxies, and the baryonic acoustic oscillations (BAOs) traced by the Sloan Digital Sky Survey (SDSS), we put tight constraints on the main cosmological parameters. Furthermore, we study the linear matter fluctuation field of the above Liouville cosmological models. In this framework, we compare the observed growth rate of clustering measured from the optical galaxies with those predicted by the current Liouville models. Performing various statistical tests we show that the Liouville cosmological model provides growth rates that match well with the observed growth rate. To further test the viability of the models under study, we use the Press-Schechter formalism to derive their expected redshift distribution of cluster-size halos that will be provided by future X-ray and Sunyaev-Zeldovich cluster surveys. We find that the Hubble flow differences between the Liouville and the LambdaCDM models provide a significantly different halo redshift distribution, suggesting that the models can be observationally distinguished.

Abstract: The Sloan Digital Sky Survey (SDSS) surveyed 14,555 deg(2), and delivered over a trillion pixels of imaging data. We present a study of galaxy clustering using 900,000 luminous galaxies with photometric redshifts, spanning between z = 0.45 and z = 0.65, constructed from the SDSS using methods described in Ross et al. This data set spans 11,000 deg(2) and probes a volume of 3 h(-3) Gpc(3), making it the largest volume ever used for galaxy clustering measurements. We describe in detail the construction of the survey window function and various systematics affecting our measurement. With such a large volume, high-precision cosmological constraints can be obtained given careful control and understanding of the observational systematics. We present a novel treatment of the observational systematics and its applications to the clustering signals from the data set. In this paper, we measure the angular clustering using an optimal quadratic estimator at four redshift slices with an accuracy of similar to 15%, with a bin size of delta(l) = 10 on scales of the baryon acoustic oscillations (BAOs; at l similar to 40-400). We also apply corrections to the power spectra due to systematics and derive cosmological constraints using the full shape of the power spectra. For a flat Lambda CDM model, when combined with cosmic microwave background Wilkinson Microwave Anisotropy Probe 7 (WMAP7) and H-0 constraints from using 600 Cepheids observed by Wide Field Camera 3 (WFC3; HST), we find Omega(Lambda) = 0.73 +/- 0.019 and H-0 to be 70.5 +/- 1.6 s(-1) Mpc(-1) km. For an open Lambda CDM model, when combined with WMAP7 + HST, we find Omega(K) = 0.0035 +/- 0.0054, improved over WMAP7+HST alone by 40%. For a wCDM model, when combined with WMAP7+HST+ SN, we find w = -1.071 +/- 0.078, and H-0 to be 71.3 +/- 1.7 s(-1) Mpc(-1) km, which is competitive with the latest large-scale structure constraints from large spectroscopic surveys such as the SDSS Data Release 7 (DR7) and WiggleZ. We also find that systematic-corrected power spectra give consistent constraints on cosmological models when compared with pre-systematic correction power spectra in the angular scales of interest. The SDSS-III Data Release 8 (SDSS-III DR8) Angular Clustering Data allow a wide range of investigations into the cosmological model, cosmic expansion (via BAO), Gaussianity of initial conditions, and neutrino masses. Here, we refer to our companion papers for further investigations using the clustering data. Our calculation of the survey selection function, systematics maps, and likelihood function for the COSMOMC package will be released at http://portal.nersc.gov/project/boss/galaxy/photoz/.