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Unformatted text preview: Living Rev Relativ (2018) 21:2 REVIEW ARTICLE Cosmology and fundamental physics with the Euclid satellite Luca Amendola1 · Stephen Appleby2 · Anastasios Avgoustidis3 · David Bacon4 · Tessa Baker5 · Marco Baldi6,7,8 · Nicola Bartolo9,10,11 · Alain Blanchard12 · Camille Bonvin13 · Stefano Borgani14,15,16 · Enzo Branchini17,18,19 · Clare Burrage3 · Stefano Camera20,21,22,23 · Carmelita Carbone24,25,26 · Luciano Casarini27,28 · Mark Cropper29 · Claudia de Rham30 · Jörg P. Dietrich31 · Cinzia Di Porto32 · Ruth Durrer13 · Anne Ealet33 · Pedro G. Ferreira34 · Fabio Finelli35,36 · Juan García-Bellido37 · Tommaso Giannantonio38 · Luigi Guzzo39,40 · Alan Heavens30 · Lavinia Heisenberg41 · Catherine Heymans42 · Henk Hoekstra43 · Lukas Hollenstein44 · Rory Holmes45 · Zhiqi Hwang46 · Knud Jahnke47 · Thomas D. Kitching48 · Tomi Koivisto49 · Martin Kunz13 · Giuseppe La Vacca50 · Eric Linder51 · Marisa March52 · Valerio Marra53 · Carlos Martins54 · Elisabetta Majerotto55 · Dida Markovic56 · David Marsh57 · Federico Marulli7,36,58 · Richard Massey59 · Yannick Mellier60,61 · Francesco Montanari62 · David F. Mota63 · Nelson J. Nunes64 · Will Percival65 · Valeria Pettorino66,67 · Cristiano Porciani68 · Claudia Quercellini32 · Justin Read69 · Massimiliano Rinaldi70 · Domenico Sapone71 · Ignacy Sawicki72 · Roberto Scaramella73 · Constantinos Skordis74,75 · Fergus Simpson76 · Andy Taylor77 · Shaun Thomas78 · Roberto Trotta79 · Licia Verde80,81 · Filippo Vernizzi82 · Adrian Vollmer83 · Yun Wang84 · Jochen Weller38 · Tom Zlosnik85 · (The Euclid Theory Working Group)* Received: 3 November 2016 / Accepted: 13 November 2017 / Published online: 12 April 2018 © The Author(s) 2018 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 This article is a revised version of . Change summary: Major revision, updated and expanded. Forecasts are not updated in this version, with respect to 2012. Change details: The main changes are in Part I, where Sect. 1.4 was merged in parts with Sect. 1.5, some text reordered and updated; a couple of subsections are new. There are smaller updates in the other parts. Seven new figures were added. About 300 new references have been cited. DISCLAIMER: This is not an official Euclid document and its content reflects solely the views of the contributing authors. B (The Euclid Theory Working Group) [email protected] * Extended author information available at the end of the article. 123 2 Page 2 of 345 L. Amendola et al. (The Euclid Theory Working Group) 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. Keywords Dark energy · Cosmology · Galaxy evolution Abbreviations AGN ALP BAO BBKS BOSS BPol BigBOSS CAMB CDE CDM CDMS CL CLASS CMB COMBO-17 COSMOS CPL CQ CRESST DE DES DETF DGP DM EBI EDE EMT EROS 123 Active galactic nucleus Axio-like particle Baryonic acoustic oscillations Bardeen–Bond–Kaiser–Szalay Baryon oscillation spectroscopic survey B-polarization satellite Baryon oscillation spectroskopic survey Code for anisotropies in the microwave background Coupled dark energy Cold dark matter Cryogenic dark matter search Confidence level Cosmic linear anisotropy solving system Cosmic microwave background Classifying objects by medium-band observations Cosmological evolution survey Chevallier–Polarski–Linder Coupled quintessence Cryogenic rare event search with superconducting thermometers Dark energy Dark energy survey Dark energy task force Dvali–Gabadadze–Porrati Dark matter Eddington–Born–Infeld Early dark energy Energy–momentum tensor Expérience pour la recherche d’objets Sombres Cosmology and fundamental physics with the Euclid satellite eROSITA FCDM FFT FLRW FoM FoG GEA GR HETDEX ICM IH IR ISW KL LCDM LHC LRG LSB LSS LSST LTB MACHO MCMC MCP MF MG MOND MaVaNs NFW NH PCA PDF PGB PKDGRAV PPF PPN PPOD PSF QCD RDS RG SD SDSS SIDM SN TeVeS Page 3 of 345 2 Extended ROentgen survey with an imaging telescope array Fuzzy cold dark matter Fast Fourier transform Friedmann–Lemaître–Robertson–Walker Figure of merit Fingers of god Generalized Einstein-aether General relativity Hobby–Eberly telescope dark energy experiment Intracluster medium Inverted hierarchy Infrared Integrated Sachs–Wolfe Kullback–Leibler divergence Lambda cold dark matter Large hadron collider Luminous red galaxy Low surface brightness Large scale structure Large synoptic survey telescope Lemaître–Tolman–Bondi Massive compact halo object Markov Chain Monte Carlo Mini-charged particles Mass function Modified gravity Modified Newtonian dynamics Mass varying neutrinos Navarro–Frenk–White Normal hierarchy Principal component analysis Probability distribution function Pseudo-Goldstein Boson Parallel K–D tree GRAVity code Parameterized post-Friedmann Parameterized post-Newtonian Predictive posterior odds distribution Point spread function Quantum chromodynamics Redshift space distortions Renormalization group Savage–Dickey Sloan digital sky survey Self interacting dark matter Supernova Tensor vector scalar 123 2 Page 4 of 345 UDM UV WDM WFXT WIMP WKB WL WLS WMAP XMM-Newton vDVZ L. Amendola et al. (The Euclid Theory Working Group) Unified dark matter Ultra Violett Warm dark matter Wide-field X-ray telescope Weakly interacting massive particle Wentzel–Kramers–Brillouin Weak lensing Weak lensing survey Wilkinson microwave anisotropy probe X-ray multi-mirror mission van Dam–Veltman–Zakharov List of symbols ca D A (z) ∂/ Π ij σ Bo b BΦ (k1 , k2 , k3 ) g(X ) ζ r (z) H η, τ κ t Λ  rc  F θ μ π η(a, k) ρ Tμν w Fαβ σ8 uμ Ωm f sky 123 Adiabatic sound speed Angular diameter distance Angular spin raising operator Anisotropic stress perturbation tensor Uncertainty Bayes factor Bias (ratio of galaxy to total matter perturbations) Bispectrum of the Bardeen’s potential Born–Infeld kinetic term Comoving curvature perturbation Comoving distance Conformal Hubble parameter, H = a H Conformal time Convergence Cosmic time Cosmological constant Cosmological parameters Cross over scale d’Alembertian,  = ∇ 2 Derivative of f (R) Divergence of velocity field Direction cosine Effective anisotropic stress Effective anisotropic stress parameterization Energy density Energy momentum tensor Equation of state Fisher information matrix Fluctuation amplitude at 8 km/s/Mpc Four-velocity Fractional matter density Fraction of sky observed Cosmology and fundamental physics with the Euclid satellite ΔM τ (z)  G(a) γ fg beff h H (z) ξi δi j f (R) Pl (μ) L() β(z) D L (z) Q(a, k) δm gμν μ C G N P(k) p δp χ (z) z R φ A Ψ, Φ ns a fa  cs Σ ij HT T (k) Bi k Page 5 of 345 2 Gauge invariant comoving density contrast Generic opacity parameter Gravitational slip parameter Growth function/growth factor Growth index/shear Growth rate Halo effective linear bias factor Hubble constant in units of 100 km/s/Mpc Hubble parameter Killing field Kronecker delta Lagrangian in modified gravity Legendre polynomials Likelihood function Linear redshift-space distortion parameter Luminosity distance Mass screening effect Matter density perturbation Metric tensor Modified gravity function: μ = Q/η Multipole power spectrum Newton’s gravitational constant Number of e-folds, N = ln a Matter power spectrum Pressure Pressure perturbation Radial, dimensionless comoving distance Redshift Ricci scalar Scalar field Scalar potential Scalar potentials Scalar spectral index Scale factor Scale of Peccei–Quinn symmetry breaking Spherical harmonic multipoles Sound speed Total neutrino mass/inverse covariance matrix/PPN parameter Trace-free distortion Transfer function Vector shift Wavenumber 123 2 Page 6 of 345 L. Amendola et al. (The Euclid Theory Working Group) Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part I Dark energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.2 Background evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.2.1 Parametrization of the background evolution . . . . . . . . . . . . . . . I.3 Perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.3.1 Cosmological perturbation theory . . . . . . . . . . . . . . . . . . . . . I.3.2 Modified growth parameters . . . . . . . . . . . . . . . . . . . . . . . . I.3.3 Phantom crossing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.4 Generic properties of dark energy and modified gravity models . . . . . . . . . I.4.1 Dark energy as a degree of freedom . . . . . . . . . . . . . . . . . . . . I.4.2 A definition of modified gravity . . . . . . . . . . . . . . . . . . . . . . I.4.3 The background: to what precision should we measure w? . . . . . . . . I.4.4 Dark-energy: linear perturbations and growth rate . . . . . . . . . . . . I.4.5 Parameterized frameworks for theories of modified gravity . . . . . . . I.5 Models of dark energy and modified gravity . . . . . . . . . . . . . . . . . . . I.5.1 Quintessence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.5.2 K-essence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.5.3 Coupled dark-energy models . . . . . . . . . . . . . . . . . . . . . . . I.5.4 f(R) gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.5.5 Massive gravity and higher-dimensional models . . . . . . . . . . . . . I.5.6 Beyond massive gravity: non-local models and multigravity . . . . . . . I.5.7 Effective field theory of dark energy . . . . . . . . . . . . . . . . . . . I.5.8 Observations and screening mechanisms . . . . . . . . . . . . . . . . . I.5.9 Einstein Aether and its generalizations . . . . . . . . . . . . . . . . . . I.5.10 The tensor–vector–scalar theory of gravity . . . . . . . . . . . . . . . . I.5.11 Other models of interest . . . . . . . . . . . . . . . . . . . . . . . . . . I.6 Nonlinear aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.6.1 N-body simulations of dark energy and modified gravity . . . . . . . . . I.6.2 The spherical collapse model . . . . . . . . . . . . . . . . . . . . . . . I.7 Observational properties of dark energy and modified gravity . . . . . . . . . . I.7.1 General remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.7.2 Observing modified gravity with weak lensing . . . . . . . . . . . . . . I.7.3 Observing modified gravity with redshift surveys . . . . . . . . . . . . I.7.4 Constraining modified gravity with galaxy–CMB correlations . . . . . . I.7.5 Cosmological bulk flows . . . . . . . . . . . . . . . . . . . . . . . . . I.7.6 Model independent observations . . . . . . . . . . . . . . . . . . . . . I.8 Forecasts for Euclid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.8.1 A review of forecasts for parametrized modified gravity with Euclid . . I.8.2 Euclid surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.8.3 Forecasts for the growth rate from the redshift survey . . . . . . . . . . I.8.4 Weak lensing non-parametric measurement of expansion and growth rate I.8.5 Testing the non-linear corrections for weak lensing forecasts . . . . . . I.8.6 Forecasts for the dark-energy sound speed . . . . . . . . . . . . . . . . I.8.7 Weak lensing constraints on f(R) gravity . . . . . . . . . . . . . . . . . I.8.8 Forecast constraints on coupled quintessence cosmologies . . . . . . . . I.8.9 Forecasts for the anisotropic stress parameter η . . . . . . . . . . . . . . I.8.10 Extra-Euclidean data and priors . . . . . . . . . . . . . . . . . . . . . . I.8.11 Forecasts for model independent observations . . . . . . . . . . . . . . I.9 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part II Dark matter and neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.2 Dark matter halo properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.2.1 The halo mass function as a function of redshift . . . . . . . . . . . . . II.2.2 The dark matter density profile . . . . . . . . . . . . . . . . . . . . . . 123 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 10 10 12 13 15 15 18 23 27 27 29 30 38 42 45 46 49 50 55 61 68 71 74 77 80 83 84 84 92 101 101 103 108 113 114 116 120 120 122 124 136 138 142 147 149 152 153 160 161 163 163 165 166 169 Cosmology and fundamental physics with the Euclid satellite Page 7 of 345 2 II.3 Euclid dark matter studies: wide-field X-ray complementarity . . . . . . . . . . . . II.4 Dark matter mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.4.1 Charting the universe in 3D . . . . . . . . . . . . . . . . . . . . . . . . . . II.4.2 Mapping large-scale structure filaments . . . . . . . . . . . . . . . . . . . . II.5 Constraints on dark matter interaction cross sections . . . . . . . . . . . . . . . . . II.5.1 Dark matter–dark matter interactions . . . . . . . . . . . . . . . . . . . . . II.5.2 Dark matter–baryonic interactions . . . . . . . . . . . . . . . . . . . . . . II.5.3 Dark matter–dark energy interactions . . . . . . . . . . . . . . . . . . . . . II.6 Constraints on warm dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . II.6.1 Warm dark matter particle candidates . . . . . . . . . . . . . . . . . . . . . II.6.2 Dark matter free-streaming . . . . . . . . . . . . . . . . . . . . . . . . . . II.6.3 Current constraints on the WDM particle from large-scale structure . . . . . II.6.4 Nonlinear structure in WDM . . . . . . . . . . . . . . . . . . . . . . . . . II.7 Neutrino properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.7.1 Evidence of relic neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . II.7.2 Neutrino mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.7.3 Hierarchy and the nature of neutrinos . . . . . . . . . . . . . . . . . . . . . II.7.4 Number of neutrino species . . . . . . . . . . . . . . . . . . . . . . . . . . II.7.5 Model dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.7.6 Σ forecasted error bars and degeneracies . . . . . . . . . . . . . . . . . . . II.7.7 Neff forecasted errors and degeneracies . . . . . . . . . . . . . . . . . . . . II.7.8 Nonlinear effects of massive cosmological neutrinos on bias, P(k) and RSD II.8 Coupling between dark energy and neutrinos . . . . . . . . . . . . . . . . . . . . . II.9 Unified dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.9.1 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.9.2 Euclid observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.10 Dark energy and dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.11 Ultra-light scalar fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.11.1 Phenomenology and motivation . . . . . . . . . . . . . . . . . . . . . . . . II.11.2 Particle physics and string theory models . . . . . . . . . . . . . . . . . . . II.11.3 Constraints from large scale structure . . . . . . . . . . . . . . . . . . . . . II.12 Dark-matter surrogates in theories of modified gravity . . . . . . . . . . . . . . . . II.12.1 Extra fields in modified gravity . . . . . . . . . . . . . . . . . . . . . . . . II.12.2 Vector dark matter in Einstein-Aether models . . . . . . . . . . . . . . . . II.12.3 Scalar and tensors in TeVeS . . . . . . . . . . . . . . . . . . . . . . . . . . II.12.4 Tensor dark matter in models of bigravity . . . . . . . . . . . . . . . . . . . II.13 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part III Initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III.2 Constraining inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III.2.1 Primordial perturbations from inflation . . . . . . . . . . . . . . . . . . . . III.2.2 Forecast constraints on the power spectrum . . . . . . . . . . . . . . . . . . III.3 Probing the early universe with non-Gaussianities . . . . . . . . . . . . . . . . . . III.3.1 Local non-Gaussianity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III.3.2 Shapes: what do they tell us? . . . . . . . . . . . . . . . . . . . . . . . . . III.3.3 Beyond shapes: scale dependence and the squeezed limit . . . . . . . . . . III.3.4 Beyond inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III.4 Primordial non-Gaussianity and large-scale structure . . . . . . . . . . . . . . . . III.4.1 Constraining primordial non-Gaussianity and gravity from 3-point statistics III.4.2 Non-Gaussian halo bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . III.4.3 Number counts of nonlinear structures . . . . . . . . . . . . . . . . . . . . III.4.4 Forecasts for Euclid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III.4.5 Complementarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III.5 Isocurvature modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III.5.1 The origin of isocurvature perturbations . . . . . . . . . . . . . . . . . . . III.5.2 Constraining isocurvature perturbations . . . . . . . . . . . . . . . . . . . . III.6 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 171 171 172 173 174 177 177 178 178 178 179 179 180 182 182 183 185 185 186 187 189 193 196 197 198 198 200 200 202 203 206 206 206 208 208 209 210 210 211 212 214 218 218 220 222 223 224 225 227 228 229 232 232 232 235 236 123 2 Page 8 of 345 L. Amendola et al. (The Euclid Theory Working Group) Part IV Testing the basic cosmological hypotheses . . . . . . . ....
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