The avalanche of data over the past 10-20 years has propelled cosmology into the “precision era”. The next challenge cosmology has to meet is to enter the era of accuracy. Because of the intrinsic nature of studying the Cosmos and the sheer amount of data available now and coming soon, the only way to meet this challenge is by developing suitable and specific statistical techniques. The road from precision Cosmology to accurate Cosmology goes through statistical Cosmology. I will outline some open challenges and discuss some specific examples.

Euclid is the next ESA mission devoted to cosmology. It aims at observing most of the extragalactic sky, studying both gravitational lensing and clustering over ~15,000 square degrees. The mission is expected to be launched in year 2020 and to last six years. The sheer amount of data of different kinds, the variety of (un)known systematic effects and the complexity of measures require efforts both in sophisticated simulations and techniques of data analysis. We review the mission main characteristics, some aspects of the the survey and highlight some of the areas of interest to this meeting.

The standard Bayesian model formalism comparison cannot be applied to most cosmological models as they lack well-motivated parameter priors. However, if the data-set being used is separable, then it is possible to use some of the data to obtain the necessary parameter distributions, the rest of the data being retained for model comparison. While such methods are not fully prescriptive, they provide a route to applying Bayesian model comparison in cosmological situations where it could not otherwise be used.

I conclude the SCCC21 conference highlighting some of the contrasts we heard about, some specific topics (the statistics of random fields), and discuss how some of these play out in the analysis of cosmic microwave background data. I conclude with a hopeful look at the efficacy of blind analyses in the CMB and elsewhere in cosmology.

A range of Bayesian tools has become widely used in cosmological data treatment and parameter inference (see Kunz et al.2007, Trotta 2008, Amendola et al.2013). With increasingly big datasets and higher precision, tools that enable us to further enhance the accuracy of our measurements gain importance. Here we present an approach based on internal robustness, introduced in Amendola et al. (2013) and adopted in Heneka et al. (2014), to identify biased subsets of data and hidden correlation in a model independent way.

Luminous Red Galaxies (LRGs) have old, red stellar populations often interpreted as evidence of a formation scenario in which these galaxies form in a single intense burst of star formation at high redshift. By measuring the average age of LRGs at two different redshifts, one can potentially measure the redshift interval corresponding to a time interval and thus measure the Hubble parameter H(z) ≈ −(1 + z)−1 Δ z/Δt (as in Jimenez & Loeb). The goal of this project is to measure directly the expansion rate of the universe at the redshift range 0.1 < z < 1.0 within 3% precision. We explore the age-dating of Sloan Digital Sky Survey LRGs using the stellar population models of Lick absorption line indices after stacking spectra in redshift bins to increase the signal-to-noise. We also use the method of full spectral fitting to measure the ages of LRGs observed with the Southern Africa Large Telescope (SALT).

The Hubble constant H0 describes not only the expansion of local space at redshift z ~ 0, but is also a fundamental parameter determining the evolution of the universe. Recent measurements of H0 anchored on Cepheid observations have reached a precision of several percent. However, this problem is so important that confirmation from several methods is needed to better constrain H0 and, with it, dark energy and the curvature of space. A particularly direct method involves the determination of distances to local galaxies far enough to be part of the Hubble flow through water vapor (H2O) masers orbiting nuclear supermassive black holes. The goal of this article is to describe the relevance of H0 with respect to fundamental cosmological questions and to summarize recent progress of the ‘Megamaser Cosmology Project’ (MCP) related to the Hubble constant.

We investigate the possibility of using Luminous Red Galaxies (LRGs) as “Cosmic chronometers” to measure the expansion rate of the universe to 3% over a redshift range 0.1 < z < 1.0. In this method, H(z) is directly measured by using the ages of passively evolving galaxies to determine dz/dt. We first present results from our study of LRGs in simulations Crawford et al. where we explore the impact of extended star formation histories on the measurements of the Hubble parameter. We then extract a carefully selected sample of LRGs taken from Sloan Digital Sky Survey (SDSS) Data Released Seven (DR7), stack spectra in redshift bins to increase the signal-to-noise, and use the Lick index modelling presented in Thomas et al. to age-date the sample. We discuss the implications for expansion rate measurements and outline a proposal to observe LRGs with the Southern African Large Telescope (SALT).

The cosmic abundance of the 3He isotope has important implications for many fields of astrophysics. We are using the 8.665 GHz hyperfine transition of 3He+ to determine the 3He/H abundance in Milky Way H ii regions and planetary nebulae. Here we review the 30 year history of our 3He program, report on its current status, and describe our future plans.

The ionization balances for HI, OI and DI being locked together by charge exchange, the deuterium-to-oxygen ratio is considered to be a good proxy for the deuterium-to-hydrogen ratio, in particular within the interstellar medium. As the DI and OI column densities are of similar orders of magnitude for a given sight line, comparisons of the two values are generally less subject to systematic errors than comparisons of DI and HI. Moreover, D/O is additionally sensitive to astration, because as stars destroy deuterium, they should produce oxygen. D/O measurements are now available for tens of lines of sight in the interstellar medium, most of them from FUSE observations. The D/H and D/O ratios show different pictures, D/H being clearly more dispersed than D/O. The low, homogeneous D/O ratio measured on distant lines of sight suggests a deuterium abundance representative of the present epoch that is about two times lower than this measured within the local interstellar medium.

Analyses of FUSE spacecraft spectra have provided measurements of D/H in the gas phase of the interstellar medium for many lines of sight extending to several kpc from the Sun. These measurements, together with the earlier Copernicus, HST, and IMAPS data, show a wide range of D/H values that have challenged both observers and chemical evolution modellers. I believe that the best explanation for the diverse D/H measurements is that deuterium can be sequestered on to carbonaceous grains and PAH molecules and thereby removed from the interstellar gas. Grain destruction can raise the gas phase D/H value to approximately the total D/H value. Supernovae and stellar winds, however, can decrease the total D/H value along lines of sight on time scales less than mixing time scales. I will summarize the theoretical and observational arguments for this model and estimate the most likely range for the total D/H in the local Galactic disk. This range in total D/H presents a constraint on realistic Galactic chemical evolution models or the primordial value of D/H or both.

For the last 25 years, the 21 cm line has been used productively to investigate the large–scale structure of the Universe, its peculiar velocity field and the measurement of cosmic parameters. In February 2005 a blind HI survey that will cover 7074 square degrees of the high latitude sky was started at Arecibo, using the 7-beam feed L-band feed array (ALFA). Known as the Arecibo Legacy Fast ALFA (ALFALFA) Survey, the program is producing a census of HI-bearing objects over a cosmologically significant volume of the local Universe. With respect to previous blind HI surveys, ALFALFA offers an improvement of about one order of magnitude in sensitivity, 4 times the angular resolution, 3 times the spectral resolution, and 1.6 times the total bandwidth of HIPASS. ALFALFA can detect 7×104D2M⊙ of HI, where D is the source distance in Mpc. As of mid 2007, 44% of the survey observations and 15% of the source extraction are completed. We discuss the status of the survey and present a few preliminary results, in particular with reference to the proposed “dark galaxy” VirgoHI21.