
Abstract 

Credits 

List of acronyms 

List of symbols 

Introduction 
1 
Dark
Energy 
1.1 
Introduction 
1.2 
Background evolution 

1.2.1 
Parametrization of
the background evolution 
1.3 
Perturbations 

1.3.1 
Cosmological perturbation
theory 

1.3.2 
Modified growth parameters 
1.4 
Models of dark energy and
modified gravity 

1.4.1 
Quintessence 

1.4.2 
Kessence 

1.4.3 
A definition of modified
gravity 

1.4.4 
Coupled darkenergy models 

1.4.5 
Phantom crossing 

1.4.6 
f(R)
gravity 

1.4.7 
Massive gravity and higherdimensional models 

1.4.8 
Einstein
Aether and its generalizations 

1.4.9 
The TensorVectorScalar theory
of gravity 
1.5 
Generic properties of dark energy and modified gravity
models 

1.5.1 
To which precision should we measure w? 

1.5.2 
The effective
anisotropic stress as evidence for modified gravity 

1.5.3 
Parameterized
frameworks for theories of modified gravity 
1.6 
Nonlinear aspects 

1.6.1 
Nbody
simulations of dark energy and modified gravity 

1.6.2 
The spherical
collapse model 
1.7 
Observational properties of dark energy and modified
gravity 

1.7.1 
General remarks 

1.7.2 
Observing modified gravity with weak
lensing 

1.7.3 
Observing modified gravity with redshift surveys 

1.7.4 
Cosmological
bulk flows 
1.8 
Forecasts for Euclid 

1.8.1 
A review of forecasts for parametrized
modified gravity with Euclid 

1.8.2 
Euclid surveys 

1.8.3 
Forecasts for the growth
rate from the redshift survey 

1.8.4 
Weak lensing nonparametric measurement
of expansion and growth rate 

1.8.5 
Testing the nonlinear corrections for weak
lensing forecasts 

1.8.6 
Forecasts for the darkenergy sound speed 

1.8.7 
Weak
lensing constraints on gravity 

1.8.8 
Forecast constraints on coupled
quintessence cosmologies 

1.8.9 
ExtraEuclidean data and priors 
1.9 
Summary
and outlook 
2 
Dark Matter and Neutrinos 
2.1 
Introduction 
2.2 
Dark
matter halo properties 

2.2.1 
The halo mass function as a function of
redshift 

2.2.2 
The dark matter density profile 
2.3 
Euclid dark matter studies:
widefield Xray complementarity 
2.4 
Dark matter mapping 

2.4.1 
Charting
the universe in 3D 
2.5 
Scattering cross sections 

2.5.1 
Dark matter–dark
matter interactions 

2.5.2 
Dark matter–baryonic interactions 

2.5.3 
Dark
matter–dark energy interactions 
2.6 
Crosssection constraints from galaxy
clusters 

2.6.1 
Bulleticity 
2.7 
Constraints on warm dark matter 

2.7.1 
Warm dark
matter particle candidates 

2.7.2 
Dark matter freestreaming 

2.7.3 
Current
constraints on the WDM particle from largescale structure 
2.8 
Neutrino
properties 

2.8.1 
Evidence of relic neutrinos 

2.8.2 
Neutrino mass 

2.8.3 
Hierarchy
and the nature of neutrinos 

2.8.4 
Number of neutrino species 

2.8.5 
Model
dependence 

2.8.6 
forecasted error bars and degeneracies 

2.8.7 
forecasted errors and degeneracies 

2.8.8 
Nonlinear effects of massive
cosmological neutrinos on bias and RSD 
2.9 
Coupling between dark
energy and neutrinos 
2.10 
Unified Dark Matter 

2.10.1 
Theoretical
background 

2.10.2 
Euclid Observables 
2.11 
Dark energy and dark
matter 
2.12 
Ultralight scalar fields 

2.12.1 
Requirements 
2.13 
Darkmatter
surrogates in theories of modified gravity 

2.13.1 
Extra fields in modified
gravity 

2.13.2 
Vector dark matter in EinsteinAether models 

2.13.3 
Scalar
and tensors in TeVeS 

2.13.4 
Tensor dark matter in models of
bigravity 
2.14 
Outlook 
3 
Initial Conditions 
3.1 
Introduction 
3.2 
Constraining
inflation 

3.2.1 
Primordial perturbations from inflation 

3.2.2 
Forecast
constraints on the power spectrum 
3.3 
Probing the early universe with
nonGaussianities 

3.3.1 
Local nonGaussianity 

3.3.2 
Shapes: what do
they tell us? 

3.3.3 
Beyond shapes: scale dependence and the squeezed
limit 

3.3.4 
Beyond inflation 
3.4 
Primordial NonGaussianity and LargeScale
Structure 

3.4.1 
Constraining primordial nonGaussianity and gravity from
3point statistics 

3.4.2 
NonGaussian halo bias 

3.4.3 
Number counts of nonlinear
structures 

3.4.4 
Forecasts for Euclid 

3.4.5 
Complementarity 
3.5 
Isocurvature
modes 

3.5.1 
The origin of isocurvature perturbations 

3.5.2 
Constraining
isocurvature perturbations 
3.6 
Summary and outlook 
4 
Testing the
Basic Cosmological Hypotheses 
4.1 
Introduction 
4.2 
Transparency and
Etherington Relation 

4.2.1 
Violation of photon conservation 

4.2.2 
Axionlike
particles 

4.2.3 
Minicharged particles 
4.3 
Beyond
homogeneity and isotropy 

4.3.1 
Anisotropic models 

4.3.2 
Latetime
inhomogeneity 

4.3.3 
Inhomogeneous models: Large voids 

4.3.4 
Inhomogeneous
models: Backreaction 
4.4 
Reconstructing the global curvature at
different redshifts 
4.5 
Speculative avenues: nonstandard models of
primordial fluctuations 

4.5.1 
Probing the quantum origin of primordial
fluctuations 

4.5.2 
Earlytime anisotropy 

4.5.3 
Current and future constraints
from CMB and LSS on an anisotropic power spectrum 
5 
Statistical
Methods for Performance Forecasts 
5.1 
Introduction 
5.2 
Predicting
the science return of a future experiment 

5.2.1 
The Gaussian linear
model 

5.2.2 
Fishermatrix error forecast 

5.2.3 
Figure of merits 

5.2.4 
The
Bayesian approach 
5.3 
Survey design and optimization 
5.4 
Future
activities and open challenges 

Acknowledgments 

References 

Footnotes 

Figures 

Tables 