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.

/pdf/cosmology-and-fundamental-physics-with-the-euclid-satellite-1pi37a138r.pdf

Cosmology and Fundamental Physics with the Euclid Satellite

Cosmic shear is the distortion of images of distant galaxies due to weak gravitational lensing by the large-scale structure in the Universe. Such images are coherently deformed by the tidal field of matter inhomogeneities along the line of sight. By measuring galaxy shape correlations, we can study the properties and evolution of structure on large scales as well as the geometry of the Universe. Thus, cosmic shear has become a powerful probe into the nature of dark matter and the origin of the current accelerated expansion of the Universe. Over the last years, cosmic shear has evolved into a reliable and robust cosmological probe, providing measurements of the expansion history of the Universe and the growth of its structure. We review here the principles of weak gravitational lensing and show how cosmic shear is interpreted in a cosmological context. Then we give an overview of weak-lensing measurements, and present the main observational cosmic-shear results since it was discovered 15 years ago, as well as the implications for cosmology. We then conclude with an outlook on the various future surveys and missions, for which cosmic shear is one of the main science drivers, and discuss promising new weak cosmological lensing techniques for future observations.

https://iopscience.iop.org/article/10.1088/0034-4885/78/8/086901/pdf

Cosmology with cosmic shear observations: a review

Cosmic shear is the distortion of images of distant galaxies due to weak gravitational lensing by the large-scale structure in the Universe. Such images are coherently deformed by the tidal field of matter inhomogeneities along the line of sight. By measuring galaxy shape correlations, we can study the properties and evolution of structure on large scales as well as the geometry of the Universe. Thus, cosmic shear has become a powerful probe into the nature of dark matter and the origin of the current accelerated expansion of the Universe. Over the last years, cosmic shear has evolved into a reliable and robust cosmological probe, providing measurements of the expansion history of the Universe and the growth of its structure. 
We review here the principles of weak gravitational lensing and show how cosmic shear is interpreted in a cosmological context. Then we give an overview of weak-lensing measurements, and present the main observational cosmic-shear results since it was discovered 15 years ago, as well as the implications for cosmology. We then conclude with an outlook on the various future surveys and missions, for which cosmic shear is one of the main science drivers, and discuss promising new weak cosmological lensing techniques for future observations.

The core structure of galaxy clusters is fundamentally important. Even though self-gravitating systems have no stable equilibrium state due to their negative heat capacity, numerical simulations find density profiles which are universal in the sense that they are fairly flat within a scale radius and gradually steepen farther outward, asymptotically approaching a logarithmic slope of ≈−3 near the virial radius. We argue that the reason for the formation of this profile is not satisfactorily understood. The ratio between the virial radius and the scale radius, the so-called concentration, is found in simulations to be closely related to the mass and the redshift and low for cluster-sized haloes, but observed to be substantially higher at least in a subset of observed clusters. Haloes formed from cold dark matter should furthermore be richly substructured. We review theoretical and observational aspects of cluster cores here, discuss modifications by baryonic physics and observables that can provide better insight into the internal structure of clusters.

Internal Cluster Structure

We examine the cosmological constraining power of future large-scale weak lensing surveys on the model of \emph{Euclid}, with particular reference to primordial non-Gaussianity. Our analysis considers several different estimators of the projected matter power spectrum, based on both shear and flexion, for which we review the covariances and Fisher matrices. The bounds provided by cosmic shear alone for the local bispectrum shape, marginalized over $\sigma_8$, are at the level of $\Delta f_\mathrm{NL} \sim 100$. We consider three additional bispectrum shapes, for which the cosmic shear constraints range from $\Delta f_\mathrm{NL}\sim 340$ (equilateral shape) up to $\Delta f_\mathrm{NL}\sim 500$ (orthogonal shape). The competitiveness of cosmic flexion constraints against cosmic shear ones depends on the galaxy intrinsic flexion noise, that is still virtually unconstrained. Adopting the very high value that has been occasionally used in the literature results in the flexion contribution being basically negligible with respect to the shear one, and for realistic configurations the former does not improve significantly the constraining power of the latter. Since the flexion noise decreases with decreasing scale, by extending the analysis up to $\ell_\mathrm{max} = 20,000$ cosmic flexion, while being still subdominant, improves the shear constraints by $\sim 10%$ when added. However on such small scales the highly non-linear clustering of matter and the impact of baryonic physics make any error estimation uncertain. By considering lower, and possibly more realistic, values of the flexion intrinsic shape noise results in flexion constraining power being a factor of $\sim 2$ better than that of shear, and the bounds on $\sigma_8$ and $f_\mathrm{NL}$ being improved by a factor of $\sim 3$ upon their combination. (abridged)

Constraining primordial non-Gaussianity with cosmological weak lensing: shear and flexion

Weak gravitational lensing has proven to be a powerful tool to map directly the distribution of dark matter in the Universe. The technique, currently used, relies on the accurate measurement of the gravitational shear that corresponds to the first-order distortion of the background galaxy images. More recently, a new technique has been introduced that relies on the accurate measurement of the gravitational flexion that corresponds to the second-order distortion of the background galaxy images. This technique should probe structures on smaller scales than that of a shear analysis. The goal of this paper is to compare the ability of shear and flexion to reconstruct the dark matter distribution by taking into account the dispersion in shear and flexion measurements. Our results show that the flexion is less sensitive than shear for constructing the convergence maps on scales that are physically feasible for mapping, meaning that flexion alone not be used to do convergence map reconstruction, even on small scales.

Weak Lensing Mass Reconstruction: Flexion vs Shear

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Weak Lensing Mass Reconstruction: Flexion vs Shear