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.