The cosmological large-scale structure encodes a wealth of information about the origin and evolution of our Universe. Galaxy redshift surveys provide a 3-dimensional picture of the luminous sources in the Universe. These are however biased tracers of the underlying dark matter field. I will discuss the different components which are relevant to model galaxy bias, ranging from deterministic nonlinear, over non-local, to stochastic components. These effective bias ingredients permit us to save computational time and memory requirements, to efficiently produce mock galaxy catalogues. These are useful to study systematics of survey, test analysis tools, and compute covariance matrices to perform a robust analysis of the data. Moreover, this description permits us to implement them in inference analysis methods to recover the dark matter field and its peculiar velocity field. I will show some examples based on the largest sample of luminous red galaxies to date based on the final BOSS SDSS-III data release.

Almost all cosmologists accept nowadays that the redshift of the galaxies is due to the expansion of the Universe (cosmological redshift), plus some Doppler effect of peculiar motions, but can we be sure of this fact by means of some other independent cosmological test? Here I will review some recent tests: CMBR temperature versus redshift, time dilation, the Hubble diagram, the Tolman or surface brightness test, the angular size test, the UV surface brightness limit and the Alcock-Paczynski test. Some tests favour expansion and others favour a static Universe. Almost all the cosmological tests are susceptible to the evolution of galaxies and/or other effects. Tolman or angular size tests need to assume very strong evolution of galaxy sizes to fit the data with the standard cosmology, whereas the Alcock-Paczynski test, an evaluation of the ratio of observed angular size to radial/redshift size, is independent of it.

Driven by the potential of large-scale structure (LSS) observations to shed light on the physics behind the accelerated expansion of the Universe, several ground-breaking galaxy surveys are currently under way. These surveys will measure the LSS of the Universe with unprecedented precision, providing new insights not only on the origin of cosmic acceleration, but also on many other important physical parameters. The ongoing Baryon Oscillation Spectroscopic Survey (BOSS) is an example of these new surveys. In this talk I review our theoretical understanding of LSS and the details of the analysis of these measurements. I also describe the cosmological implications of the latest clustering measurements from BOSS, with an emphasis on the problem of understanding cosmic acceleration.

Any viable theory of the formation and evolution of galaxies should be able to broadly account for the emergent properties of the galaxy population, and their evolution with time, in terms of fundamental physical quantities. Yet, when citing the key processes we believe to be central to the story, we often find ourselves listing from a vast and confusing melee of modelling strategies & numerical simulations, rather than appealing to traditional analytic derivations where the connections to the underlying physics are more tangible. By re-examining both complex models and recent observational surveys in the spirit of the classic theories, we will investigate to what extent the trends in the galaxy population can still be seen as an elegant fingerprint of cosmology and fundamental physics.

The first galaxies are thought to have started the reionization of the Universe, that is the transformation of the cosmic hydrogen from its initial neutral to its present ionized state that occurred during the first few hundred million years after the Big Bang. I will review the key physics of reionization by the first galaxies and highlight the computational challenges of simulating the relevant processes, primarily the transport of ionizing photons. I will introduce the radiative transfer method TRAPHIC that we have developed to address these challenges. I will discuss the application of TRAPHIC in zoomed cosmological simulations of the first galaxies and evaluate the prospects for observing these galaxies with the upcoming James Webb Space Telescope. I will conclude by presenting first results from Aurora, a new suite of simulations to investigate reionization and galaxy formation across a large range of scales.

I revisit the claim of Dark Energy detection after stacking CMB data on the angular position of voids and superclusters in Sloan Data. I examine the theoretically expected amplitude for the ISW-induced signal and explore its scale dependence. I next confront these predictions with results obtained from real WMAP data, and evaluate the degree of agreement and the possible presence of contaminants. In a more general context, I address the possibility of unveiling the signature of Dark Energy on the CMB by looking at isolated regions on the sky hosting high-threshold projected under/over-densities: this constitutes a novel approach since it is less sensitive to large angle systematics commonly present in large scale structure surveys.

In this talk I will review the subject of cosmological inflation, a period of early accelerated expansion. I will discuss Friedmann-Robertson-Walker cosmology and the horizon and flatness problems, and introduce inflation as a solution to those problems. I will also discuss the generation of  the primordial (scalar and tensor) spectrum of perturbations which provides the seeds for the large scale structure in the Universe. I will review quickly the status of observations in relation to the inflationary parameters, and then the implications for model building.

I will review some theoretical ideas in Cosmology different to the standard "Big Bang": the Quasi-steady State model, Plasma Cosmology model, non-cosmological redshifts, alternatives to non-baryonic dark matter and/or dark energy, and others. Some open problems of Cosmology within the standard model will also be summarized.

In the first part of this talk I will present a historical review of the CMB observations, one of the most powerful cosmological probes. Following the first talk of this series, where Jose Alberto described the basic parameters that define the standard cosmological model, I will here summarize the constraints to these parameters that have been derived from these observations. I will also describe the current challenges in this field, in particular the detection of the inflation's B-mode signal through CMB polarization observations, as well as the experiments that have been developed worldwide to this aim, including IAC's QUIJOTE. In the second part, I will focus on the so-called ``missing baryon problem'', i.e. the fact that the half of the expected baryon content of the local universe remains yet undetected. I will describe the theoretical studies that provide hints on where these baryons could be located, and the observational efforts that have been undertaken in this regard.