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% Masters/Doctoral Thesis
% LaTeX Template
% Version 2.5 (27/8/17)
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% Version 2.x major modifications by:
% Vel ([email protected])
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% This template is based on a template by:
% Steve Gunn (http://users.ecs.soton.ac.uk/srg/softwaretools/document/templates/)
% Sunil Patel (http://www.sunilpatel.co.uk/thesis-template/)
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% Template license:
% CC BY-NC-SA 3.0 (http://creativecommons.org/licenses/by-nc-sa/3.0/)
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%	PACKAGES AND OTHER DOCUMENT CONFIGURATIONS
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headsepline, % Uncomment to get a line under the header
%chapterinoneline, % Uncomment to place the chapter title next to the number on one line
%consistentlayout, % Uncomment to change the layout of the declaration, abstract and acknowledgements pages to match the default layout
]{MastersDoctoralThesis} % The class file specifying the document structure

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\usepackage{imakeidx}
%\usepackage{hyperref}
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\usepackage[backend=bibtex,style=authoryear,natbib=true]{biblatex} % Use the bibtex backend with the authoryear citation style (which resembles APA)

\addbibresource{example.bib} % The filename of the bibliography

\usepackage[autostyle=true]{csquotes} % Required to generate language-dependent quotes in the bibliography

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                                % for UPS
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%	MARGIN SETTINGS
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%----------------------------------------------------------------------------------------
%	THESIS INFORMATION
%----------------------------------------------------------------------------------------

\thesistitle{Théories de Gravité modifiée confrontées aux futures données du survey Euclid} % Your thesis title, this is used in the title and abstract,
          % print it elsewhere with \ttitle
\title{Théories de Gravité modifiée confrontées aux futures données du survey Euclid}
  % Your thesis title, this is used in the title and abstract,
          % print it elsewhere with \ttitle
\defencedate{20 Mai 2024}
\lab{Institut de Recherche en Astrophysique et Plan\'{e}tologie (UMR 5277)}
\nboss{2}
\nreferee{2}
\njudge{8}

\makesomeone{boss}{1}{Prof. Alain \textsc{Blanchard}}{}{Directeur de thèse}
\makesomeone{boss}{2}{Dr. Brahim \textsc{Lamine}}{}{Co-directeur de thèse}
\makesomeone{referee}{1}{Dr. Sophie \textsc{Henrot-Versill\'{e}}}{}{Rapporteuse}
\makesomeone{referee}{2}{Prof. Martin \textsc{Kunz}}{}{Rapporteur}
\makesomeone{judge}{1}{\small Prof. A. \textsc{Blanchard}}{\small Professeur des universités}{\small UPS/IRAP (France)}
\makesomeone{judge}{7}{\small Dr. B. \textsc{Lamine}}{\small Ma\^{i}tre de conférences}{\small UPS/IRAP (France)}
\makesomeone{judge}{2}{\small Dr. A. \textsc{Ealet}}{\small Directeur de recherche}{\small IPNL (France)}
\makesomeone{judge}{6}{\small Prof. M. \textsc{Kunz}}{\small Professeur associ\'{e}}{\small UNIGE (Suisse)}
\makesomeone{judge}{5}{\small Dr. T. \textsc{Kitching}}{\small{\it Reader}}{\small MSSL/UCL (Royaume-Uni)}
\makesomeone{judge}{4}{\small Dr. S. \textsc{Henrot-Versill\'{e}}}{\small Directeur de recherche}{\small LAL (France)}
\makesomeone{judge}{3}{\small Dr. P. \textsc{Fosalba}}{\small {\it Cient\'{i}fico titular}}{\small ICE, IEEC-CSIC (Espagne)}
%\makesomeone{judge}{8}{\small Dr. Y. \textsc{Mellier}}{\small Astronome}{\small IAP/IRFU (France)}

%\supervisor{Dr. James \textsc{Smith}} % Your supervisor's name, this is used in the title page, print it elsewhere with \supname
%\examiner{} % Your examiner's name, this is not currently used anywhere in the template, print it elsewhere with \examname
%\degree{Doctor of Philosophy} % Your degree name, this is used in the title page and abstract, print it elsewhere with \degreename
%\author{Antoine \textsc{DUPONT}} % Your name, this is used in the title page and abstract, print it elsewhere with \authorname


\makeatletter
\renewcommand{\authorname}{Antoine \textsc{DUPONT}}
\renewcommand{\@author}{Antoine \textsc{DUPONT}}
\makeatother



%\addresses{} % Your address, this is not currently used anywhere in the template, print it elsewhere with \addressname

%\subject{Biological Sciences} % Your subject area, this is not currently used anywhere in the template, print it elsewhere with \subjectname
%\keywords{} % Keywords for your thesis, this is not currently used anywhere in the template, print it elsewhere with \keywordnames
\university{\href{http://www.univ-tlse3.fr}{Universit\'{e} Toulouse 3
    Paul Sabatier}} % Your university's name and URL, this is used in the title page and abstract, print it elsewhere with \univname
%\department{\href{http://department.university.com}{Department or School Name}} % Your department's name and URL, this is used in the title page and abstract, print it elsewhere with \deptname
%\group{\href{http://researchgroup.university.com}{Research Group Name}} % Your research group's name and URL, this is used in the title page, print it elsewhere with \groupname
%\faculty{\href{http://faculty.university.com}{Faculty Name}} % Your faculty's name and URL, this is used in the title page and abstract, print it elsewhere with \facname

\AtBeginDocument{
\hypersetup{pdftitle=\ttitle} % Set the PDF's title to your title
\hypersetup{pdfauthor=\authorname} % Set the PDF's author to your name
%\hypersetup{pdfkeywords=\keywordnames} % Set the PDF's keywords to your keywords
}

\setstretch{1.175}

\begin{document}

\frontmatter % Use roman page numbering style (i, ii, iii, iv...) for the pre-content pages

\pagestyle{plain} % Default to the plain heading style until the thesis style is called for the body content

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%	TITLE PAGE
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%\begin{titlepage}
%\begin{center}

%\vspace*{.06\textheight}
%{\scshape\LARGE \univname\par}\vspace{1.5cm} % University name
%\textsc{\Large Doctoral Thesis}\\[0.5cm] % Thesis type

%\HRule \\[0.4cm] % Horizontal line
%{\huge \bfseries \ttitle\par}\vspace{0.4cm} % Thesis title
%\HRule \\[1.5cm] % Horizontal line

%\begin{minipage}[t]{0.4\textwidth}
%\begin{flushleft} \large
%\emph{Author:}\\
%\href{http://www.johnsmith.com}{\authorname} % Author name - remove the \href bracket to remove the link
%\end{flushleft}
%\end{minipage}
%\begin{minipage}[t]{0.4\textwidth}
%\begin{flushright} \large
%\emph{Supervisor:} \\
%\href{http://www.jamessmith.com}{\supname} % Supervisor name - remove the \href bracket to remove the link
%\end{flushright}
%\end{minipage}\\[3cm]

%\vfill

%\large \textit{A thesis submitted in fulfillment of the requirements\\ for the degree of \degreename}\\[0.3cm] % University requirement text
%\textit{in the}\\[0.4cm]
%\groupname\\\deptname\\[2cm] % Research group name and department name

%\vfill

%{\large \today}\\[4cm] % Date
%\includegraphics{Logo} % University/department logo - uncomment to place it

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%\end{center}
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%	DECLARATION PAGE
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%\begin{declaration}
%\addchaptertocentry{\authorshipname} % Add the declaration to the table of contents
%\noindent I, Isaac Tutusaus Lleixa, declare that this thesis titled, \enquote{\ttitle} and the work presented in it are my own. I confirm that:
%
%\begin{itemize}
%\item This work was done wholly or mainly while in candidature for a research degree at this University.
%\item Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated.
%\item Where I have consulted the published work of others, this is always clearly attributed.
%\item Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work.
%\item I have acknowledged all main sources of help.
%\item Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.\\
%\end{itemize}
%
%\noindent Signed:\\
%\rule[0.5em]{25em}{0.5pt} % This prints a line for the signature
%
%\noindent Date:\\
%\rule[0.5em]{25em}{0.5pt} % This prints a line to write the date
%\end{declaration}

\cleardoublepage

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%	QUOTATION PAGE
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\vspace*{0.2\textheight}

\noindent\enquote{\itshape La lutte elle-même vers les sommets suffit à remplir un coeur d'homme. Il faut imaginer Sisyphe heureux.
  }\bigbreak

\hfill Albert Camus, 1942

%----------------------------------------------------------------------------------------
%	ABSTRACT PAGE
%----------------------------------------------------------------------------------------

\begin{abstract_french}
\addchaptertocentry{R\'{e}sum\'{e}} % Add the abstract to the table of contents
Le modèle de concordance de la cosmologie, appelé $\Lambda$CDM, est un
succès de la physique moderne, car il est capable de reproduire les
principales observations cosmologiques avec une grande précision et
très peu de paramètres libres. Cependant, il prédit l'existence de
matière noire froide et d'énergie sombre sous la forme d'une constante
cosmologique, qui n'ont pas encore été détectées directement. Par
conséquent, il est important de considérer des modèles allant au-delà
de $\Lambda$CDM et de les confronter aux observations, afin
d'améliorer nos connaissances sur le secteur sombre de l'Univers. Le
futur satellite Euclid, de l'Agence Spatiale Européenne, explorera un
énorme volume de la structure à grande échelle de l'Univers en
utilisant principalement le regroupement des galaxies et la distorsion
de leurs images due aux lentilles gravitationnelles. Dans ce travail,
nous caractérisons de façon quantitative les performances d'Euclid
vis-à-vis des contraintes cosmologiques, à la fois pour le modèle de
concordance, mais également pour des extensions phénoménologiques
modifiant les deux composantes sombres de l'Univers. En particulier,
nous accordons une atten\-tion particulière aux corrélations croisées
entre les différentes sondes d'Euclid lors de leur combinaison et
estimons de façon précise leur impact sur les résultats finaux. D'une
part, nous montrons qu'Euclid fournira d'excellentes contraintes sur les modèles cosmologiques qui définitivement illuminera le secteur sombre. D'autre part, nous montrons que les corrélations croisées entre les sondes d'Euclid ne peuvent pas être négligées dans les analyses futures et, plus important encore, que l'ajout de ces corrélations améliore grandement les contraintes sur les paramètres cosmologiques.
\end{abstract_french}


\begin{abstract}
\addchaptertocentry{\abstractname} % Add the abstract to the table of contents
The concordance model of cosmology, called $\Lambda$CDM, is a
success, since it is able to reproduce the main cosmological
observations with great accuracy and only few parameters. However, it predicts the existence
of cold dark matter and dark energy in the form of a cosmological
constant, which have not been directly detected yet. Therefore, it is
important to consider models going beyond $\Lambda$CDM, and confront them against observations, in order to improve our knowledge on the dark sector
of the Universe. The future Euclid satellite from the European Space
Agency will probe a huge volume of the large-scale structure of the
Universe using mainly the clustering of galaxies and the distortion of their
images due to gravitational lensing. In this work, we quantitatively estimate the
constraining power of the future Euclid data for the
concordance model, as well as for some phenomenological extensions of it,
modifying both dark components of the Universe. In particular, we pay
special attention to the cross-correlations between the different
Euclid probes when combining them, and assess their impact on the final results. On one hand, we show that Euclid will provide
exquisite constraints on cosmological models that
will definitely shed light on the dark sector. On the other
hand, we show that cross-correlations between Euclid probes cannot be
neglected in future analyses, and, more importantly, that the addition of
these correlations largely improves the constraints on the
cosmological parameters.
\end{abstract}

%----------------------------------------------------------------------------------------
%	ACKNOWLEDGEMENTS
%----------------------------------------------------------------------------------------

\begin{acknowledgements}
\addchaptertocentry{\acknowledgementname} % Add the acknowledgements to the table of contents
Acknowledgements




\end{acknowledgements}

%----------------------------------------------------------------------------------------
%	LIST OF CONTENTS/FIGURES/TABLES PAGES
%----------------------------------------------------------------------------------------
%\dominitoc

\tableofcontents % Prints the main table of contents

%\listoffigures % Prints the list of figures

%\listoftables % Prints the list of tables

%----------------------------------------------------------------------------------------
%	ABBREVIATIONS
%----------------------------------------------------------------------------------------

\begin{abbreviations}{ll} % Include a list of abbreviations (a table of two columns)

%\textbf{LAH} & \textbf{L}ist \textbf{A}bbreviations \textbf{H}ere\\
%\textbf{WSF} & \textbf{W}hat (it) \textbf{S}tands \textbf{F}or\\


$\Lambda$\textbf{CDM} & $\Lambda$ and \textbf{C}old \textbf{D}ark
\textbf{M}atter concordance model \\
$\Lambda$\textbf{GDM} & $\Lambda$ and \textbf{G}eneralized \textbf{D}ark
\textbf{M}atter model \\
$\bm{w}$\textbf{CDM} & $\bm{w}$ (dark energy) and \textbf{C}old \textbf{D}ark
\textbf{M}atter model \\
$\bm{w_0w_a}$\textbf{CDM} & $\bm{w_0}$-$\bm{w_a}$ (dark energy) and \textbf{C}old \textbf{D}ark
\textbf{M}atter model \\
\textbf{2dFGRS} & \textbf{2}-\textbf{d}egree \textbf{F}ield
\textbf{G}alaxy \textbf{R}edshift \textbf{S}urvey \\
\textbf{2PCF} & \textbf{2}-\textbf{p}oint-\textbf{c}orrelation
\textbf{f}unction \\
\textbf{6dFGS} & \textbf{6}-\textbf{d}egree \textbf{F}ield
\textbf{G}alaxy \textbf{S}urvey \\

\addlinespace

\textbf{AGN} & \textbf{A}ctive \textbf{G}alactic \textbf{N}uclei \\
\textbf{AIC} & \textbf{A}kaike \textbf{I}nformation \textbf{C}riterion
\\
\textbf{AICc} & \textbf{A}kaike \textbf{I}nformation
\textbf{C}riterion - \textbf{c}orrected
\\
\textbf{AP} & \textbf{A}lcock-\textbf{P}acyznski effect \\
\textbf{BAO} & \textbf{B}aryon \textbf{A}coustic \textbf{O}scillations \\
\textbf{BBN} & \textbf{B}ig \textbf{B}ang \textbf{N}ucleosynthesis \\
\textbf{BIC} & \textbf{B}ayesian \textbf{I}nformation
\textbf{C}riterion \\
\textbf{BOSS} & \textbf{B}aryon \textbf{O}scillation
\textbf{S}pectroscopic \textbf{S}urvey \\
\textbf{CCDs} & \textbf{C}harge \textbf{C}oupled
\textbf{D}evice\textbf{s} \\
\textbf{CDM} & \textbf{C}old \textbf{D}ark \textbf{M}atter \\
\textbf{CFHTLenS} & \textbf{C}anada \textbf{F}rance \textbf{H}awaii
\textbf{Len}sing \textbf{S}urvey \\
\textbf{CMB} & \textbf{C}osmic \textbf{M}icrowave \textbf{B}ackground
\\
\textbf{COBE} & \textbf{CO}smic \textbf{B}ackground \textbf{E}xplorer \\
\textbf{CPL} & \textbf{C}hevallier-\textbf{P}olarski-\textbf{L}inder
parametrization \\
\textbf{CS} & \textbf{C}oasting \textbf{S}plines \\
\textbf{DE} & \textbf{D}ark \textbf{E}nergy \\
\textbf{DES} & \textbf{D}ark \textbf{E}nergy \textbf{S}urvey \\
\textbf{DESI} & \textbf{D}ark \textbf{E}nergy \textbf{S}pectroscopic
\textbf{I}nstrument \\
\textbf{eBOSS} & \textbf{e}xtended \textbf{B}aryon \textbf{O}scillation
\textbf{S}pectroscopic \textbf{S}urvey \\
\textbf{EC} & \textbf{E}uclid \textbf{C}onsortium \\
\textbf{ECB} & \textbf{E}uclid \textbf{C}onsortium \textbf{B}oard \\
\textbf{ECL} & \textbf{E}uclid \textbf{C}onsortium \textbf{L}ead \\
\textbf{eNLA} & \textbf{e}xtended \textbf{N}on-\textbf{L}inear
\textbf{A}lignment model for IA \\
\textbf{ESA} & \textbf{E}uropean \textbf{S}pace \textbf{A}gency \\
\textbf{FLRW} &
\textbf{F}riedmann-\textbf{L}ema\^{i}tre-\textbf{R}obertson-\textbf{W}alker
metric \\
\textbf{FoG} & \textbf{F}ingers-\textbf{o}f-\textbf{G}od \\
\textbf{FoM} & \textbf{F}igure \textbf{o}f \textbf{M}erit \\
\textbf{GC} & \textbf{G}alaxy \textbf{C}lustering \\
\textbf{GCp} & \textbf{G}alaxy \textbf{C}lustering - \textbf{p}hotometric \\
\textbf{GCs} & \textbf{G}alaxy \textbf{C}lustering -
\textbf{s}pectroscopic \\
\textbf{GDM} & \textbf{G}eneralized \textbf{D}ark \textbf{M}atter \\
\textbf{GTD} & \textbf{G}eneralized \textbf{T}ime \textbf{D}ependent
galaxy bias model \\
\texttt{halofit} & \textbf{halofit} non-linear prescription \\
\texttt{HaloModel} & \textbf{Halo Model} non-linear prescription \\
\textbf{HST} & \textbf{H}ubble \textbf{S}pace \textbf{T}elescope \\
\textbf{IA} & \textbf{I}ntrinsic \textbf{A}lignment of galaxies \\
\textbf{IST} & \textbf{I}nter-\textbf{S}cience \textbf{T}askforce for
forecasting \\
\textbf{JLA} & \textbf{J}oint \textbf{L}ight-curve \textbf{A}nalysis \\
\textbf{LRGs} & \textbf{L}uminous \textbf{R}ed
\textbf{G}alaxie\textbf{s} \\
\textbf{LSST} & \textbf{L}arge \textbf{S}ynoptic \textbf{S}urvey
\textbf{T}elescope \\
\textbf{MCMC} & \textbf{M}onte \textbf{C}arlo \textbf{M}arkov
\textbf{C}hain \\
\textbf{NALPL} & \textbf{N}on-\textbf{A}ccelerated \textbf{L}ocal
\textbf{P}ower \textbf{L}aw \\
\textbf{NASA} & \textbf{N}ational \textbf{A}eronautics and
\textbf{S}pace \textbf{A}dministration \\
\textbf{OUs} & \textbf{O}rganizational \textbf{U}nit\textbf{s} \\
\textbf{PLM} & \textbf{P}ay\textbf{L}oad \textbf{M}odule \\
\textbf{PPF} & \textbf{P}arametrized \textbf{P}ost-\textbf{F}riedmann
framework \\
\textbf{QSO} & \textbf{Q}uasi-\textbf{S}tellar \textbf{O}bject \\
\textbf{RPT} & \textbf{R}enormalized \textbf{P}erturbation
\textbf{T}heory \\
\textbf{RSD} & \textbf{R}edshift-\textbf{S}pace \textbf{D}istortions
\\
\textbf{SDCs} & \textbf{S}cience \textbf{D}ata
\textbf{C}enter\textbf{s} \\
\textbf{SDSS} & \textbf{S}loan \textbf{D}igital \textbf{S}ky
\textbf{S}urvey \\
\textbf{SGS} & \textbf{S}cience \textbf{G}round \textbf{S}egment \\
\textbf{SNIa} & \textbf{S}uper\textbf{N}ovae of type \textbf{Ia} \\
\textbf{SNIa+ev} & \textbf{S}uper\textbf{N}ovae of type \textbf{Ia}
with luminosity \textbf{ev}olution \\
\textbf{SOC} & \textbf{S}cience \textbf{O}peration \textbf{C}enter \\
\textbf{SPT} & \textbf{S}tandard \textbf{P}erturbation \textbf{T}heory
\\
\textbf{SVM} & \textbf{S}er\textbf{V}ice \textbf{M}odule \\
\textbf{SWGs} & \textbf{S}cience \textbf{W}orking
\textbf{G}roup\textbf{s} \\
\textbf{VIPERS} & \textbf{VI}MOS \textbf{P}ublic
\textbf{E}xtragalactic \textbf{R}edshift \textbf{S}urvey \\
\textbf{WL} & \textbf{W}eak \textbf{L}ensing \\
\textbf{WMAP} & \textbf{W}ilkinson \textbf{M}icrowave
\textbf{A}nisotropy \textbf{P}robe \\
\textbf{XC} & Cross (\textbf{X}) - \textbf{C}orrelations \\




\end{abbreviations}

%----------------------------------------------------------------------------------------
%	PHYSICAL CONSTANTS/OTHER DEFINITIONS
%----------------------------------------------------------------------------------------

%\begin{constants}{lr@{${}={}$}l} % The list of physical constants is a three column table

% The \SI{}{} command is provided by the siunitx package, see its documentation for instructions on how to use it

%Speed of Light & $c_{0}$ & \SI{2.99792458e8}{\meter\per\second} (exact)\\
%Constant Name & $Symbol$ & $Constant Value$ with units\\

%\end{constants}

%----------------------------------------------------------------------------------------
%	SYMBOLS
%----------------------------------------------------------------------------------------

\begin{symbols}{ll} % Include a list of Symbols (a three column table)

%$a$ & distance & \si{\meter} \\
%$P$ & power & \si{\watt} (\si{\joule\per\second}) \\
%Symbol & Name & Unit \\
%
%
%\addlinespace % Gap to separate the Roman symbols from the Greek
%
%$\omega$ & angular frequency & \si{\radian} \\

$a$ & scale factor \\
$\mathcal{A}_{\rm IA}$ & IA multiplicative nuisance parameter \\
$A_s$ & amplitude of the initial matter power spectrum \\
$b$ & galaxy bias \\
$c$ & speed of light in vacuum \\
$c_a$ & adiabatic sound speed \\
$\mathcal{C}_{\rm IA}$ & IA multiplicative nuisance parameter \\
$C_{ij}^{\delta_{\rm g}\delta_{\rm g}}$ & GCp tomographic angular spectra \\
$C_{ij}^{\delta_{\rm g}\gamma}$ & XC tomographic angular spectra \\
$C_{ij}^{\gamma\gamma}$ & WL tomographic angular spectra \\
$c_s$ & rest-frame sound speed \\
$c_{\text{vis}}$ & GDM viscosity parameter \\
$D_1$ & growth factor \\
$d_{\rm A}$ & angular diameter distance \\
$d_{\rm L}$ & luminosity distance \\
$E$ & dimensionless Hubble parameter \\
$f$ & growth rate \\
$f\sigma_8$ & weighted growth rate \\
$f_{\rm sky}$ & fraction of the sky observed \\
$G$ & Newton's gravitational constant \\
$h$ & reduced Hubble constant \\
$H$ & Hubble parameter \\
$H_0$ & Hubble constant \\
$k$ & modulus of the wave mode in Fourier space \\
$k_{\parallel}$ & $\bm{k}$ component along the line-of-sight \\
$k_{\perp}$ & $\bm{k}$ component perpendicular to the line-of-sight \\
$m_{\rm B}^*$ & SNIa observed peak magnitude in the rest-frame B band
\\
$M_{\rm B}^1$ & SNIa absolute magnitude in the rest-frame B band nuisance parameter \\
$n_e$ & free electron number density \\
$N_{\rm eff}$ & effective number of relativistic degrees of freedom \\
$n_i$ & galaxy number density in the $i$th redshift bin \\
$N_{ij}^{\delta_{\rm g}}$ & GCp shot-noise \\
$N_{ij}^{\epsilon}$ & WL shot-noise \\
$n_s$ & slope of the initial matter power spectrum (spectral index)\\
$N_{\rm ur}$ & number of ultra-relativistic species \\
$p$ & pressure \\
$P_{\rm dw}$ & de-wiggled power spectrum \\
$P_{\rm g}$ & galaxy power spectrum \\
$P_{\rm m}$ (\& $P_{\delta\delta}$) & matter power spectrum \\
$P_{\rm nw}$ & no-wiggles power spectrum \\
$P_s$ & GCs shot-noise \\
$q_0$ & deceleration parameter present value \\
$R$ & scaled distance to recombination \\
$r_{\rm d}$ & BAO standard ruler \\
$r_{\rm s}$ & co-moving sound horizon \\
$t$ & cosmic time \\
$T$ & transfer function \\
$T_{\rm CMB}$ & temperature of the CMB \\
$w$ & equation of state parameter \\
$W_i^{\delta_g}$ & GCp window function in the $i$th redshift bin \\
$\mathcal{W}_i^{\delta_g}$ & GCp window function in the $i$th redshift
bin divided by $\chi$\\
$W_i^{\gamma}$ & shear window function in the $i$th redshift bin \\
$\mathcal{W}_i^{\gamma}$ & shear window function in the $i$th redshift
bin including the IA \\
$W_i^{\rm IA}$ & IA window function in the $i$th redshift bin \\
$X_e$ & free electron fraction \\
$z$ & redshift \\
$z_{*}$ & redshift of the last scattering epoch \\
$z_{\rm d}$ & redshift of the baryon drag epoch \\


\addlinespace

$\alpha$ & SNIa stretch nuisance parameter \\
$\beta$ & SNIa color nuisance parameter \\
$\beta_{\rm IA}$ & IA luminosity nuisance parameter \\
$\chi$ & co-moving distance \\
$\Delta_{\rm M}$ & SNIa host galaxy nuisance parameter \\
$\Delta m_{\rm evo}$ & SNIa luminosity evolution nuisance term \\
$\delta p$ & pressure perturbation \\
$\ell_a$ & angular scale of the sound horizon at recombination \\
$\epsilon$ & ellipticity \\
$\eta_{\rm IA}$ & IA redshift nuisance parameter \\
$\gamma$ & shear \\
$\kappa$ & convergence \\
$\Lambda$ & cosmological constant \\
$\mu$ & distance modulus \\
$\omega_{\rm b}$ & baryon reduced present energy density parameter \\
$\Omega_{\rm b}$ & baryon present energy density parameter \\
$\omega_{\rm cdm}$ & cold dark matter reduced present energy density
parameter \\
$\Omega_{\rm cdm}$ & cold dark matter present energy density parameter
\\
$\omega_{\rm dm}$ & dark matter reduced present energy density
parameter \\
$\Omega_{\rm dm}$ & dark matter present energy density parameter \\
$\Omega_{\rm K}$ & curvature present energy density parameter \\
$\Omega_{\Lambda}$ & $\Lambda$ present energy density parameter \\
$\omega_{\rm m}$ & matter reduced present energy density parameter \\
$\Omega_{\rm m}$ & matter present energy density parameter \\
$\Omega_{\rm r}$ & radiation present energy density parameter \\
$\rho$ & energy density \\
$\rho_{0,\rm crit}$ & critical present energy density \\
$\sigma$ & anisotropic stress \\
$\sigma_8$ & Root mean square mass fluctuations amplitude on
8\,Mpc/$h$ scales at $z=0$ \\
$\sigma_{\rm p}$ & GCs non-linear nuisance parameter \\
$\sigma_{\rm v}$ & GCs non-linear nuisance parameter \\
$\tau$ & re-ionization optical depth \\


\end{symbols}

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%	DEDICATION
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\dedicatory{\hfill à mon grand-père Jean, à mes parents}

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%	THESIS CONTENT - CHAPTERS
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\mainmatter % Begin numeric (1,2,3...) page numbering

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%	THESIS CONTENT - APPENDICES
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\appendix % Cue to tell LaTeX that the following "chapters" are Appendices

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%\include{Appendices/AppendixB}
%\include{Appendices/AppendixC}

\listoffigures

\listoftables


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%	BIBLIOGRAPHY
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\printbibliography[heading=bibintoc]

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\phantomsection
\addcontentsline{toc}{chapter}{Index}
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\end{document}