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 是欧洲航天局的一项中型任务，在 2015-2025 年宇宙愿景计划中选择于 2020 年发射。欧几里得的主要目标是了解宇宙加速膨胀的起源。欧几里得将通过测量星系的形状和红移以及星系团在大部分天空中的分布来探索宇宙的膨胀历史和宇宙结构的演化。尽管欧几里得的主要驱动力是暗能量的本质，但欧几里得科学涵盖了广泛的主题，从宇宙学到星系演化再到行星研究。在这篇评论中，我们关注宇宙学和基础物理学，特别强调当前标准模型之外的科学。我们讨论五个广泛的主题：暗能量和修正引力、暗物质、初始条件、基本假设和数据分析中的方法论问题。这次审查是在欧几里得理论工作组内计划和进行的，旨在为欧几里得任务准备期间该小组活动的科学主题提供指导。