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Cosmology and Fundamental Physics with the Euclid Satellite

Luca Amendola, Stephen Appleby, Anastasios Avgoustidis, David Bacon, Tessa Baker, Marco Baldi, Nicola Bartolo, Alain Blanchard, Camille Bonvin, Stefano Borgani, Enzo Branchini, Clare Burrage, Stefano Camera, Carmelita Carbone, Luciano Casarini, Mark Cropper, Claudia de Rham, Joerg P. Dietrich, Cinzia Di Porto, Ruth Durrer, Anne Ealet, Pedro G. Ferreira, Fabio Finelli, Juan Garcia-Bellido, Tommaso Giannantonio, Luigi Guzzo, Alan Heavens, Lavinia Heisenberg, Catherine Heymans, Henk Hoekstra, Lukas Hollenstein, Rory Holmes, Ole Horst, Zhiqi Hwang, Knud Jahnke, Thomas D. Kitching, Tomi Koivisto, Martin Kunz, Giuseppe La Vacca, Eric Linder, Marisa March, Valerio Marra, Carlos Martins, Elisabetta Majerotto, Dida Markovic, David Marsh, Federico Marulli, Richard Massey, Yannick Mellier, Francesco Montanari, David F. Mota, Nelson J. Nunes, Will Percival, Valeria Pettorino, Cristiano Porciani, Claudia Quercellini, Justin Read, Massimiliano Rinaldi, Domenico Sapone, Ignacy Sawicki, Roberto Scaramella, Constantinos Skordis, Fergus Simpson, Andy Taylor, Shaun Thomas, Roberto Trotta, Licia Verde, Filippo Vernizzi, Adrian Vollmer, Yun Wang, Jochen Weller, Tom Zlosnik

TL;DR

<3-5 sentence high-level summary>Euclid aims to unravel the origin of cosmic acceleration by jointly exploiting weak lensing, galaxy clustering, cluster counts, and cross-correlations to test dark energy and modified gravity theories. The paper surveys background evolution, linear and nonlinear perturbations, and a broad landscape of dynamical dark-energy and gravity models, introducing practical parameterizations (e.g., Q, eta, mu, Sigma) and model-comparison strategies to forecast Euclid’s constraints. It emphasizes the importance of combining expansion-history measurements with growth-data, and highlights how Euclid will probe neutrino properties and warm dark matter, offering high-precision tests of the standard cosmological model and potential new physics. The results indicate that Euclid can constrain key growth and gravity parameters to percent-level precision, distinguish MG from standard DE, and significantly advance our understanding of the dark sector through complementary probes and cross-survey synergy.

Abstract

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 redshifts 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.

Cosmology and Fundamental Physics with the Euclid Satellite

TL;DR

<3-5 sentence high-level summary>Euclid aims to unravel the origin of cosmic acceleration by jointly exploiting weak lensing, galaxy clustering, cluster counts, and cross-correlations to test dark energy and modified gravity theories. The paper surveys background evolution, linear and nonlinear perturbations, and a broad landscape of dynamical dark-energy and gravity models, introducing practical parameterizations (e.g., Q, eta, mu, Sigma) and model-comparison strategies to forecast Euclid’s constraints. It emphasizes the importance of combining expansion-history measurements with growth-data, and highlights how Euclid will probe neutrino properties and warm dark matter, offering high-precision tests of the standard cosmological model and potential new physics. The results indicate that Euclid can constrain key growth and gravity parameters to percent-level precision, distinguish MG from standard DE, and significantly advance our understanding of the dark sector through complementary probes and cross-survey synergy.

Abstract

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 redshifts 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.

Paper Structure

This paper contains 180 sections, 343 equations, 63 figures, 25 tables.

Table of Contents

  1. Dark Energy
  2. Introduction
  3. Background evolution
  4. Parametrization of the background evolution
  5. Perturbations
  6. Cosmological perturbation theory
  7. Modified growth parameters
  8. Two new degrees of freedom
  9. Parameterizations and non-parametric approaches
  10. Trigger relations
  11. Phantom crossing
  12. Parameterizing the pressure perturbation
  13. Regularizing the divergences
  14. A word on perturbations when $w=-1$
  15. Generic properties of dark energy and modified gravity models
  16. ...and 165 more sections

Figures (63)

  • Figure 1: The evolution of $w$ as a function of the comoving scale $k$, using only the 5-year WMAP CMB data. Red and yellow are the 95% and 68% confidence regions for the LV formalism. Blue and purple are the same for the flow-equation formalism. From the outside inward, the colored regions are red, yellow, blue, and purple. Image reproduced by permission from Ilic:2010zp; copyright by APS.
  • Figure 2: The complete evolution of $w(N)$, from the flow-equation results accepted by the CMB likelihood. Inflation is made to end at $N=0$ where $w(N=0)=-1/3$ corresponding to $\epsilon_H(N=0)=1$. For our choice of priors on the slow-roll parameters at $N=0$, we find that $w$ decreases rapidly towards $-1$ (see inset) and stays close to it during the period when the observable scales leave the horizon ($N\approx 40\hbox{,--,}60$). Image reproduced by permission from Ilic:2010zp; copyright by APS.
  • Figure 3: Required accuracy on $w_{\mathrm{eff}} = -1$ to obtain strong evidence against a model where $-1 - \Delta_{-} \leq w_{\mathrm{eff}} \leq -1+\Delta_+$ as compared to a cosmological constant model, $w=-1$. For a given $\sigma$, models to the right and above the contour are disfavored with odds of more than 20:1.
  • Figure 4: Left: the cosmic microwave background angular power spectrum $l(l+1)C_l/(2\pi)$ for TeVeS (solid) and $\Lambda$CDM (dotted) with WMAP 5-year data NoltaEtAl2008. Right: the matter power spectrum $P(k)$ for TeVeS (solid) and $\Lambda$CDM (dotted) plotted with SDSS data.
  • Figure 5: Ratio of the total mass functions, which include the quintessence contribution, for $c_s=0$ and $c_s=1$ at $z=0$ (above) and $z=1$ (below). Image reproduced by permission from Creminelli-etal:2010; copyright by IOP and SISSA.
  • ...and 58 more figures