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.

We study the gravitational field equations in the presence of a coupling between the derivative of a massless scalar field and the Einstein tensor. This configuration is motivated by Galileon gravity as it preserves shift invariance in the scalar sector. We analytically obtain solutions with static and spherically symmetric geometry, which also include black holes with a single regular horizon. We examine the thermodynamical properties of these solutions, and we reveal the non-perturbative nature of the coupling constant. We also find a phase transition, similar to the one described by Hawking and Page, which occurs at a critical temperature determined by both the black hole mass and by the strength of the coupling.

Despite its continued observational successes, there is a persistent (and growing) interest in extending cosmology beyond the standard model, ΛCDM. This is motivated by a range of apparently serious theoretical issues, involving such questions as the cosmological constant problem, the particle nature of dark matter, the validity of general relativity on large scales, the existence of anomalies in the CMB and on small scales, and the predictivity and testability of the inflationary paradigm. In this paper, we summarize the current status of ΛCDM as a physical theory, and review investigations into possible alternatives along a number of different lines, with a particular focus on highlighting the most promising directions. While the fundamental problems are proving reluctant to yield, the study of alternative cosmologies has led to considerable progress, with much more to come if hopes about forthcoming high-precision observations and new theoretical ideas are fulfilled.Keywords: cosmology -dark energy -cosmological constant problem -modified gravitydark matter -early universe Cosmology has been both blessed and cursed by the establishment of a standard model: ΛCDM. On the one hand, the model has turned out to be extremely predictive, explanatory, and observationally robust, providing us with a substantial understanding of the formation of large-scale structure, the state of the early Universe, and the cosmic abundance of different types of matter and energy. It has also survived an impressive battery of precision observational tests -anomalies are few and far between, and their significance is contentious where they do arise -and its predictions are continually being vindicated through the discovery of new effects (B-mode polarization [1] and lensing [2,3] of the cosmic microwave background (CMB), and the kinetic Sunyaev-Zel'dovich effect [4] being some recent examples). These are the hallmarks of a good and valuable physical theory.On the other hand, the model suffers from profound theoretical difficulties. The two largest contributions to the energy content at late times -cold dark matter (CDM) and the cosmological constant (Λ) -have entirely mysterious physical origins. CDM has so far evaded direct detection by laboratory experiments, and so the particle field responsible for it -presumably a manifestation of "beyond the standard model" particle physics -is unknown. Curious discrepancies also appear to exist between the predicted clustering properties of CDM on small scales and observations. The cosmological constant is even more puzzling, giving rise to quite simply the biggest problem in all of fundamental physics: the question of why Λ appears to take such an unnatural value [5,6,7]. Inflation, the theory of the very early Universe, has also been criticized for being fine-tuned and under-predictive [8], and appears to leave many problems either unsolved or fundamentally unresolvable. These problems are indicative of a crisis.From January 14th-17th 2015, we held a conference in Oslo, Norway to surve...

We consider the sector of Horndeski's gravity characterized by the coupling between the kinetic scalar field term and the Einstein tensor. We numerically construct neutron star configurations where the external geometry is identical to the Schwarzschild metric but the interior structure is considerably different from standard general relativity. We constrain the only parameter of this model from the requirement that compact configurations exist, and we argue that solutions less compact than neutron stars, such as white dwarfs, are also supported. Therefore, our model provides an explicit modification of general relativity that is astrophysically viable and does not conflict with Solar System tests.