Since cosmology is no longer "the data-starved science", the problem of how to best analyze large data sets has recently received considerable attention, and Karhunen-Loève eigenvalue methods have been applied to both galaxy redshift surveys and Cosmic Microwave Background (CMB) maps. We present a comprehensive discussion of methods for estimating cosmological parameters from large data sets, which includes the previously published techniques as special cases. We show that both the problem of estimating several parameters jointly and the problem of not knowing the parameters a priori can be readily solved by adding an extra singular value decomposition step.It has recently been argued that the information content in a sky map from a next generation CMB satellite is sufficient to measure key cosmological parameters (h, Ω, Λ, etc.) to an accuracy of a few percent or better -in principle. In practice, the data set is so large that both a brute force likelihood analysis and a direct expansion in signal-to-noise eigenmodes will be computationally unfeasible. We argue that it is likely that a Karhunen-Loève approach can nonetheless measure the parameters with close to maximal accuracy, if preceded by an appropriate form of quadratic "precompression".We also discuss practical issues regarding parameter estimation from present and future galaxy redshift surveys, and illustrate this with a generalized eigenmode analysis of the IRAS 1.2 Jy survey optimized for measuring β ≡ Ω 0.6 /b using redshift space distortions.

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

Euclid is a European Space Agency medium-class mission selected for launch in 2019 within the Cosmic Vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky.Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis.This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

Collisions between galaxy clusters provide a test of the non-gravitational forces acting on dark matter. Dark matter's lack of deceleration in the 'bullet cluster collision' constrained its self-interaction cross-section σ DM /m < 1.25 cm 2 /g (68% confidence limit) for long-ranged forces. Using the Chandra and Hubble Space Telescopes we have now observed 72 collisions, including both 'major'and 'minor' mergers. Combining these measurements statistically, we detect the existence of dark mass at 7.6σ significance. The position of the dark mass has remained closely aligned within 5.8±8.2 kpc of associated stars: implying a self-interaction cross-section σ DM /m < 0.47 cm 2 /g (95% CL) and disfavoring some proposed extensions to the standard model.Many independent lines of evidence now suggest that most of the matter in the Universe is in a form outside the standard model of particle physics. A phenomenological model for cold dark matter (1) has proved hugely successful on cosmological scales, where its gravitational influence dominates the formation and growth of cosmic structure. However, there are several 1 arXiv:1503.07675v2 [astro-ph.CO] 13 Apr 2015 challenges on smaller scales: the model incorrectly predicts individual galaxy clusters to have more centrally concentrated density profiles (2), larger amounts of substructure (3, 4), and the Milky Way to have more satellites able to produce stars (5) than are observed. These inconsistencies could be resolved through astrophysical processes (6), or if dark matter particles are either warm (7) or self-interact with cross-section 0.1 ≤ σ DM /m ≤ 1 cm 2 /g (8-10). Following (11), we define the momentum transfer per unit mass σ DM /m, integrating over all scattering angles and assuming that individual dark matter particles are indistinguishable.Self-interaction within a hidden dark sector is a generic consequence of some extensions to the standard model. For example, models of mirror dark matter (12) and hidden sector dark matter (12-16) all predict anisotropic scattering with σ DM /m ≈ 1 barn/GeV = 0.6 cm 2 /g, similar to nuclear cross-sections in the standard model. Note that couplings within the dark sector can be many orders of magnitude larger than those between dark matter and standard model particles, which is at most of order picobarns (17).In terrestrial collider experiments, the forces acting on particles can be inferred from the trajectory and quantity of emerging material. Collisions between galaxy clusters, which contain dark matter, provide similar tests for dark sector forces. If dark matter's particle interactions are frequent but exchange little momentum (via a light mediator particle that produces a longranged force and anisotropic scattering), the dark matter will be decelerated by an additional drag force. If the interactions are rare but exchange a lot of momentum (via a massive mediator that produces a short-ranged force and isotropic scattering), dark matter will tend to be scattered away and lost (11,18,19).The dynamics of colliding dark matter...