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+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%     BAORadio : LAL/UPS, Irfu/SPP
+%  21cm LSS P(k) sensitivity and foreground substraction 
+%  R. Ansari, C. Magneville, J. Rich, C. Yeche et al 
+%     2010 - 2011
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%                                                                 aa.dem
+% AA vers. 7.0, LaTeX class for Astronomy & Astrophysics
+% demonstration file
+%                                                 (c) Springer-Verlag HD
+%                                                revised by EDP Sciences
+%-----------------------------------------------------------------------
+%
+%\documentclass[referee]{aa} % for a referee version
+%\documentclass[onecolumn]{aa} % for a paper on 1 column  
+%\documentclass[longauth]{aa} % for the long lists of affiliations 
+%\documentclass[rnote]{aa} % for the research notes
+%\documentclass[letter]{aa} % for the letters 
+%
+\documentclass[structabstract]{aa}  
+%\documentclass[traditabstract]{aa} % for the abstract without structuration 
+                                   % (traditional abstract) 
+%
+\usepackage{amsmath}
+\usepackage{amssymb}
+
+\usepackage{graphicx}
+\usepackage{color}
+
+\newcommand{\HI}{$\mathrm{H_I}$ } 
+\newcommand{\kb}{k_B}         % Constante de Boltzmann 
+\newcommand{\Tsys}{T_{sys}}      % instrument noise (system) temperature    
+\newcommand{\TTnu}{ T_{21}(\vec{\Theta} ,\nu)  } 
+\newcommand{\TTnuz}{ T_{21}(\vec{\Theta} ,\nu(z))  } 
+\newcommand{\TTlam}{ T_{21}(\vec{\Theta} ,\lambda)  } 
+\newcommand{\TTlamz}{ T_{21}(\vec{\Theta} ,\lambda(z))  } 
+
+\newcommand{\dlum}{d_L}
+\newcommand{\dang}{d_A}
+\newcommand{\hub}{ h_{70} }
+\newcommand{\hubb}{ h_{100} }
+
+\newcommand{\etaHI}{ \eta_{\tiny HI} }
+\newcommand{\fHI}{ f_{H_I}(z)}
+\newcommand{\gHI}{ g_{H_I}}
+\newcommand{\gHIz}{ g_{H_I}(z)}
+
+\newcommand{\vis}{{\cal V}_{12} }
+ 
+\newcommand{\LCDM}{$\Lambda \mathrm{CDM}$ }
+
+\newcommand{\citep}[1]{ (\cite{#1}) } 
+%% \newcommand{\citep}[1]{ { (\tt{#1}) } } 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{txfonts}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+\begin{document}
+%
+   \title{21 cm observation of LSS at z $\sim$ 1 }
+
+   \subtitle{Instrument sensitivity and foreground subtraction}
+
+   \author{
+          R. Ansari
+          \inst{1} \inst{2}
+          \and
+          J.E. Campagne \inst{3}
+         \and
+          P.Colom  \inst{5} 
+          \and
+          J.M. Le Goff \inst{4}
+          \and
+          C. Magneville \inst{4}
+          \and
+          J.M. Martin  \inst{5} 
+          \and
+          M. Moniez \inst{3}
+        \and 
+          J.Rich \inst{4}
+          \and 
+          C.Y\`eche \inst{4}
+          }
+
+   \institute{
+     Universit\'e Paris-Sud, LAL, UMR 8607, F-91898 Orsay Cedex, France 
+   \and 
+    CNRS/IN2P3,  F-91405 Orsay, France \\
+     \email{ansari@lal.in2p3.fr}
+    \and
+    Laboratoire de lÍAcc\'el\'erateur Lin\'eaire, CNRS-IN2P3, Universit\'e Paris-Sud,
+    B.P. 34, 91898 Orsay Cedex, France
+    % \thanks{The university of heaven temporarily does not
+    %                 accept e-mails}
+    \and 
+    CEA, DSM/IRFU, Centre d'Etudes de Saclay, F-91191 Gif-sur-Yvette, France 
+    \and 
+    GEPI, UMR 8111, Observatoire de Paris, 61 Ave de l'Observatoire, 75014 Paris, France
+   }
+
+   \date{Received December 15, 2010; accepted xxxx, 2011}
+
+% \abstract{}{}{}{}{} 
+% 5 {} token are mandatory
+ 
+  \abstract
+  % context heading (optional)
+  % {} leave it empty if necessary  
+   { Large Scale Structures (LSS) in the universe can be traced using the neutral atomic hydrogen \HI through its 21 
+cm emission. Such a 3D matter distribution map can be used to test the Cosmological model and to constrain the Dark Energy 
+properties or its equation of state. A novel approach, called intensity mapping can be used to map the \HI distribution, 
+using radio interferometers with large instanteneous field of view and waveband}
+ % aims heading (mandatory)
+  { In this paper, we study the sensitivity of different radio interferometer configuration for the observation of large scale structures 
+   and BAO oscillations in 21 cm and we discuss the problem of foreground removal. }
+  % methods heading (mandatory)
+ { For each configuration, we determine instrument response by computing the (u,v) plane (Fourier angular frequency plane) 
+  coverage using visibilities. The (u,v) plane response is then used to compute the three dimensional noise power spectrum, 
+hence the instrument sensitivity for LSS P(k) measurement. We describe also   a simple foreground subtraction method to 
+separate LSS 21 cm signal from the foreground due to the galactic synchrotron and radio sources emission. }
+  % results heading (mandatory)
+   { We have computed the noise power spectrum for different instrument configuration as well as the extracted 
+   LSS power spectrum, after separation of 21cm-LSS signal from the foregrounds. }
+  % conclusions heading (optional), leave it empty if necessary 
+   { We show that an interferometer with few hundred elements and a surface coverage of 
+  $\lesssim 10000 \mathrm{m^2}$ will be able to  detect BAO signal at redshift z $\sim 1$ }
+
+   \keywords{ Cosmology:LSS --
+                 Cosmology:Dark energy 
+               }
+
+   \maketitle
+%
+%________________________________________________________________
+% {\color{red} \large \bf A discuter : liste des auteurs, plans du papier et repartition des taches 
+% Toutes les figures sont provisoires }
+
+\section{Introduction}
+
+% {\color{red} \large \it Jim ( + M. Moniez ) }   \\[1mm] 
+The study of the statistical properties of Large Scale Structure (LSS) in the Universe and their evolution 
+with redshift is one the major tools in observational cosmology. Theses structures are usually mapped through 
+optical observation of galaxies which are used as tracers of the underlying matter distribution. 
+An alternative and elegant approach for mapping the matter distribution, using neutral atomic hydrogen 
+(\HI) as tracer with Total Intensity Mapping, has been proposed in recent years \citep{peterson.06} \citep{chang.08}. 
+Mapping the matter distribution using HI 21 cm emission as a tracer has been extensively discussed in literature
+\citep{furlanetto.06} \citep{tegmark.08} and is being used in projects such as LOFAR \citep{rottgering.06} or
+MWA \citep{bowman.07} to observe reionisation  at redshifts z $\sim$ 10. 
+
+Evidences in favor of the acceleration of the expansion of the universe have been 
+accumulated over the last twelve years, thank to the observation of distant supernovae, 
+CMB anisotropies and detailed analysis of the LSS.  
+A cosmological Constant ($\Lambda$) or new cosmological 
+energy density called {\em Dark Energy} has been advocated as the origin of this acceleration. 
+Dark Energy is considered as one the most intriguing puzzles in Physics and Cosmology. 
+% Constraining the properties of this new cosmic fluid, more precisely 
+% its equation of state is central to current cosmological researches. 
+Several cosmological probes can be used to constrain the properties of this new cosmic fluid, 
+more precisely its equation of state: The Hubble Diagram, or luminosity distance as a function 
+of redshift of supernovae as standard candles, galaxy clusters, weak shear observations 
+and Baryon Acoustic Oscillations (BAO). 
+
+BAO are features imprinted  in the distribution of galaxies, due to the frozen 
+sound waves which were present in the photons baryons plasma prior to recombination 
+at z $\sim$ 1100. 
+This scale, which can be considered as a standard ruler with a comoving 
+length  of $\sim 150 Mpc$.
+Theses features have been first observed in the CMB anisotropies
+and are usually referred to as {\em acoustic pics} \citep{mauskopf.00} \citep{hinshaw.08}. 
+The BAO modulation has been subsequently observed in the distribution of galaxies 
+at low redshift ( $z < 1$) in the galaxy-galaxy correlation function by the SDSS 
+\citep{eisenstein.05}  \citep{percival.07} and 2dGFRS  \citep{cole.05}  optical galaxy surveys.
+
+Ongoing or future surveys plan to measure precisely the BAO scale in the redshift range 
+$0 \lesssim z \lesssim 3$, using either optical observation of galaxies or through 3D mapping 
+Lyman $\alpha$ absorption lines toward distant quasars \citep{baorss} \cite{baolya}. 
+Mapping matter distribution using 21 cm emission of neutral hydrogen appears as 
+a very promising technique to map matter distribution up to redshift $z \sim 3$, 
+complementary to optical surveys, especially in the optical redshift desert range 
+$1 \lesssim z \lesssim 2$. 
+
+In section 2, we  discuss the intensity mapping and its potential for measurement of the
+\HI mass distribution power spectrum. The method used in this paper to characterize 
+a radio instrument response and sensitivity for $P_{\mathrm{H_I}}(k)$ is presented in section 3.
+We show also  the results for the 3D noise power spectrum for several  instrument configurations.
+The contribution of foreground emissions due to the galactic synchrotron and radio sources
+is described in section 4, as well as a simple component separation method  The performance of this 
+method using sky model or known radio sources are also presented in section 4. 
+The constraints which can be obtained on the Dark Energy parameters and DETF figure 
+of merit for typical 21 cm intensity mapping survey are shown in section 5.
+
+\citep{ansari.08}
+
+
+%__________________________________________________________________
+
+\section{Intensity mapping and \HI power spectrum}
+
+% {\color{red} \large \it  Reza (+ P. Colom ?) } \\[1mm] 
+
+\subsection{21 cm intensity mapping}
+%%% 
+Most of the cosmological information in the LSS is located at large scales
+($ \gtrsim 1 \mathrm{deg}$), while the interpretation at smallest scales 
+might suffer from the uncertainties on the non linear clustering effects.  
+The BAO features in particular are at the degree angular scale on the sky 
+and thus can be resolved easily with a rather modest size radio instrument 
+($D \lesssim 100 \mathrm{m}$). The specific BAO clustering scale ($k_{\mathrm{BAO}}$ 
+can be measured both in the transverse plane (angular correlation function, $k_{\mathrm{BAO}}^\perp$) 
+or along the longitudinal (line of sight or redshift, $k_{\mathrm{BAO}}^\parallel$ ) direction. A direct measurement of 
+the Hubble parameter $H(z)$ can be obtained by comparing   the longitudinal and transverse 
+BAO scale. A reasonably good redshift resolution $\delta z \lesssim 0.01$ is needed to resolve 
+longitudinal BAO clustering, which is a challenge for photometric optical surveys.   
+
+In order to obtain a measurement of the LSS power spectrum with small enough statistical
+uncertainties (sample or cosmic variance),  a large volume of the universe should be observed, 
+typically few $Gpc^3$. Moreover, stringent constrain on DE parameters can be obtained when 
+comparing the distance or Hubble parameter measurements as a function of redshift with 
+DE models, which translates into a survey depth $\Delta z \gtrsim 1$.
+
+Radio instruments intended for BAO surveys must thus have large instantaneous field
+of view (FOV $\gtrsim 10 \mathrm{deg^2}$) and large bandwidth ($\Delta \nu \gtrsim 100 \, \mathrm{MHz}$). 
+
+Although the application of 21 cm radio survey to cosmology, in particular LSS mapping has been 
+discussed in length in the framework of large future instruments, such as the SKA (e.g \cite{ska.science}),
+the method envisaged has been mostly through the detection of galaxies as \HI compact sources. 
+However, extremely large radio telescopes are required to detected \HI sources at cosmological distances. 
+The sensitivity (or detection threshold) limit $S_{lim}$ for a radio instrument 
+characterized by an effective collecting area $A$, and system temperature $\Tsys$ can be written as 
+\begin{equation}
+S_{lim} = \frac{ 2 \kb \, \Tsys }{ A \, \sqrt{t_{int} \delta \nu} } 
+\end{equation} 
+where $t_{int}$ is the total integration time $\delta \nu$ is the detection frequency band. In table 
+\ref{slims21} (left)  we have computed the sensitivity for 4 different set of instrument effective area and system 
+temperature, with a total integration time of 86400 seconds (1 day) over a frequency band of 1 MHz. 
+The width of this frequency band is well adapted  to detection of \HI source with an intrinsic velocity 
+dispersion of few 100 km/s. Theses detection limits should be compared with the expected 21 cm brightness
+$S_{21}$ of compact sources which can be computed using the expression below:
+\begin{equation}
+ S_{21}  \simeq  0.021 \mathrm{\mu Jy} \, \frac{M_{H_I} }{M_\odot}   \times 
+\left( \frac{ 1\, \mathrm{Mpc}}{\dlum} \right)^2 \times \frac{200 \, \mathrm{km/s}}{\sigma_v} 
+\end{equation}
+ where $ M_{H_I} $ is the neutral hydrogen mass, $\dlum$ is the luminosity distance and $\sigma_v$ 
+is the source velocity dispersion. 
+{\color{red} Faut-il developper le calcul en annexe ? } 
+ 
+In table \ref{slims21} (right), we show the 21 cm brightness for 
+compact objects with a total \HI \, mass of $10^{10} M_\odot$ and an intrinsic velocity dispersion of 
+$200 \mathrm{km/s}$. The luminosity distance is computed for the standard 
+WMAP \LCDM universe. $10^9 - 10^{10} M_\odot$ of neutral gas mass 
+is typical for large galaxies \citep{lah.09}. It is clear that detection of \HI sources at cosmological distances
+would require collecting area in the range of $10^6 \mathrm{m^2}$. 
+
+Intensity mapping has been suggested as an alternative and economic method to map the 
+3D distribution of neutral hydrogen \citep{chang.08} \citep{ansari.08}. In this approach, 
+sky brightness map with angular resolution $\sim 10-30 \mathrm{arc.min}$ is made for a 
+wide range of frequencies. Each 3D pixel  (2 angles $\vec{\Theta}$, frequency $\nu$ or wavelength $\lambda$)  
+would correspond to a cell with a volume of $\sim 10 \mathrm{Mpc^3}$, containing hundreds of galaxies and a total 
+\HI mass $ \gtrsim 10^{12} M_\odot$. If we neglect local velocities relative to the Hubble flow, 
+the observed frequency $\nu$ would be translated to the emission redshift $z$ through 
+the well known relation:
+\begin{eqnarray}
+ z(\nu) & = & \frac{\nu_{21} -\nu}{\nu} 
+\, ; \, \nu(z) = \frac{\nu_{21}}{(1+z)} 
+\hspace{1mm} \mathrm{with}   \hspace{1mm}  \nu_{21} = 1420.4 \, \mathrm{MHz}  \\
+ z(\lambda) & = & \frac{\lambda - \lambda_{21}}{\lambda_{21}} 
+\, ; \, \lambda(z) = \lambda_{21} \times (1+z) 
+\hspace{1mm} \mathrm{with}   \hspace{1mm}  \lambda_{21} = 0.211 \, \mathrm{m} 
+\end{eqnarray}
+The large scale distribution of the neutral hydrogen, down to angular scales of $\sim 10 \mathrm{arc.min}$ 
+can then be observed without the detection of individual compact \HI sources, using the set of sky brightness 
+map as a function frequency (3D-brightness map) $B_{21}(\vec{\Theta},\lambda)$. The sky brightness $B_{21}$ 
+(radiation power/unit solid angle/unit surface/unit frequency).
+can be converted to brightness temperature using the well known black body Rayleigh-Jeans approximation:
+$$ B(T,\lambda) = \frac{ 2 \kb T }{\lambda^2} $$ 
+ 
+%%%%%%%%
+\begin{table}
+\begin{center}
+\begin{tabular}{|c|c|c|}
+\hline 
+$A (\mathrm{m^2})$ & $ T_{sys} (K) $ & $ S_{lim} \mathrm{\mu Jy} $ \\
+\hline 
+5000 & 50 & 66 \\
+5000 & 25 & 33 \\
+100 000 & 50 & 3.5 \\
+100 000 & 25 & 1.7 \\
+500 000 & 50 & 0.66 \\
+500 000 & 25 & 0.33 \\
+\hline  
+\end{tabular}
+%% 
+\hspace{3mm}
+%% 
+\begin{tabular}{|c|c|c|}
+\hline
+$z$ &  $\dlum \mathrm{(Mpc)}$ & $S_{21}  \mathrm{( \mu Jy)} $ \\
+\hline
+0.25 &  1235   & 140 \\
+0.50 &  2800   & 27 \\
+1.0   &  6600   & 4.8 \\
+1.5   &  10980 & 1.74 \\
+2.0   &  15710  & 0.85 \\
+2.5  &  20690 & 0.49 \\
+\hline
+\end{tabular}
+\caption{Sensitivity or source detection limit for 1 day integration time (86400 s) and 1 MHz 
+frequency band (left). Source 21 cm brightness for $10^{10} M_\odot$ \HI for different redshifts (right)  }
+\label{slims21} 
+\end{center}
+\end{table}
+
+\subsection{ \HI power spectrum and BAO}
+In the absence of any foreground or background radiation, the brightness temperature 
+for a given direction and wavelength $\TTlam$ would be proportional to 
+the local \HI number density $\etaHI(\vec{\Theta},z)$ through the relation:
+\begin{equation}
+  \TTlamz  =   \frac{3}{32 \pi}  \, \frac{h}{\kb} \,  A_{21}  \, \lambda_{21}^2 \times
+  \frac{c}{H(z)} \, (1+z)^2 \times  \etaHI (\vec{\Theta}, z)  
+\end{equation}
+where $A_{21}=1.87 \, 10^{-15} \mathrm{s^{-1}}$ is the spontaneous 21 cm emission 
+coefficient, $h$ is the Planck constant, $c$ the speed of light, $\kb$ the Boltzmann 
+constant and $H(z)$ is the Hubble parameter at the emission redshift.
+For a \LCDM universe and neglecting radiation energy density, the Hubble parameter
+can be expressed as:
+\begin{equation}
+H(z)  \simeq  \hub  \, \left[ \Omega_m (1+z)^3 + \Omega_\Lambda \right]^{\frac{1}{2}} 
+\times  70 \, \, \mathrm{km/s/Mpc}  
+\end{equation}
+Introducing the \HI mass fraction relative to the total baryon mass $\gHI$, the 
+neutral hydrogen number density can be written as:
+\begin{equation}
+\etaHI (\vec{\Theta}, z(\lambda) ) = \gHIz \times \Omega_B  \frac{\rho_{crit}}{m_{H}}  \times 
+\frac{\delta \rho_{H_I}}{\bar{\rho}_{H_I}} (\vec{\Theta},z) 
+\end{equation}
+where $\Omega_B, \rho_{crit}$ are respectively the present day mean baryon cosmological
+and critical densities, $m_{H}$ is the hydrogen atom mass, and 
+$\frac{\delta \rho_{H_I}}{\bar{\rho}_{H_I}}$ is the \HI density fluctuations. 
+
+The present day neutral hydrogen fraction $\gHI(0)$ has been measured to be 
+$\sim 1\%$ of the baryon density \citep{zwann.05}:
+$$ \Omega_{H_I} \simeq 3.5 \, 10^{-4} \sim 0.008 \times \Omega_B $$
+The neutral hydrogen fraction is expected to increase with redshift. Study 
+of Lyman-$\alpha$ absorption indicate a factor 3 increase in the neutral hydrogen
+fraction at $z=1.5$, compared to the its present day value $\gHI(z=1.5) \sim 0.025$
+\citep{wolf.05}. 
+The 21 cm brightness temperature and the corresponding power spectrum can be written as \citep{wyithe.07} :
+\begin{eqnarray}
+  \TTlamz  &  = & \bar{T}_{21}(z) \times \frac{\delta \rho_{H_I}}{\bar{\rho}_{H_I}} (\vec{\Theta},z)  \\
+  P_{T_{21}}(k) & = & \left( \bar{T}_{21}(z)  \right)^2 \, P(k)  \\
+ \bar{T}_{21}(z)  & \simeq & 0.054  \, \mathrm{mK}  
+\frac{ (1+z)^2 \, \hub }{\sqrt{ \Omega_m (1+z)^3 + \Omega_\Lambda } } 
+ \dfrac{\Omega_B}{0.044}  \,  \frac{\gHIz}{0.01} 
+\end{eqnarray}
+
+The table \ref{tabcct21} below shows the mean 21 cm brightness temperature for the 
+standard \LCDM cosmology and either a constant \HI mass fraction $\gHI = 0.01$, or 
+linearly increasing  $\gHI \simeq 0.008 \times (1+z) $. Figure \ref{figpk21} shows the 
+21 cm emission power spectrum at several redshifts, with a constant neutral fraction at 2\%
+($\gHI=0.02$). The matter power spectrum has been computed using the 
+\cite{eisenhu.98} parametrisation. The correspondence  with the angular scales is also 
+shown for the standard WMAP \LCDM cosmology, according to the relation:
+\begin{equation}
+\mathrm{ang.sc} = \frac{2 \pi}{k^{comov} \, \dang(z) \, (1+z) }  
+\hspace{3mm} 
+k^{comov} = \frac{2 \pi}{ \mathrm{ang.sc}  \, \dang(z) \, (1+z) }  
+\end{equation}
+where $k^{comov}$ is the comoving wave vector and $ \dang(z) $ is the angular diameter distance.
+It should be noted that the maximum transverse $k^{comov} $ sensitivity range 
+for an instrument corresponds approximately to half of its angular resolution. 
+{\color{red} Faut-il developper completement le calcul en annexe ? } 
+
+\begin{table}
+\begin{center}
+\begin{tabular}{|l|c|c|c|c|c|c|c|}
+\hline 
+\hline
+   & 0.25 & 0.5 & 1. & 1.5 & 2. & 2.5 & 3. \\
+\hline 
+(a) $\bar{T}_{21}$ (mK) & 0.08 & 0.1 & 0.13 & 0.16 & 0.18 & 0.2 & 0.21 \\
+\hline
+(b) $\bar{T}_{21}$ (mK)  & 0.08 & 0.12 & 0.21 & 0.32 & 0.43 & 0.56 & 0.68 \\
+\hline
+\hline  
+\end{tabular}
+\caption{Mean 21 cm brightness temperature in mK, as a function of redshift, for the 
+standard \LCDM cosmology with constant \HI mass fraction at $\gHIz$=0.01  (a) or linearly 
+increasing mass fraction (b)  $\gHIz=0.008(1+z)$ }
+\label{tabcct21} 
+\end{center}
+\end{table}
+
+\begin{figure}
+\centering
+\includegraphics[width=0.5\textwidth]{Figs/pk21cmz12.pdf}
+\caption{\HI 21 cm emission power spectrum at redshifts z=1 (blue) and z=2 (red), with 
+neutral gas fraction $\gHI=2\%$}
+\label{figpk21}
+\end{figure}
+
+
+\section{interferometric observations and P(k) measurement sensitivity }
+
+\subsection{Instrument response}
+In astronomy we are usually interested in measuring the sky emission intensity,
+$I(\vec{\Theta},\lambda)$ in a given wave band, as a function  the direction. In radio astronomy
+and interferometry in particular, receivers are sensitive to the sky emission complex 
+amplitudes. However, for most sources, the phases vary randomly and bear no information:
+\begin{eqnarray}
+& & 
+I(\vec{\Theta},\lambda)  =  | A(\vec{\Theta},\lambda) |^2  \hspace{2mm} , \hspace{1mm} I \in \mathbb{R}, A \in \mathbb{C} \\
+& & < A(\vec{\Theta},\lambda) A^*(\vec{\Theta '},\lambda) >_{time}  =  \delta(   \vec{\Theta} - \vec{\Theta '} )  I(\vec{\Theta},\lambda)
+\end{eqnarray} 
+A single receiver can be  characterized by its angular complex amplitude response $B(\vec{\Theta},\nu)$ and 
+its position $\vec{r}$ in a reference frame. the waveform complex amplitude $s$ measured by the receiver, 
+for each frequency can be written as a function of the electromagnetic wave vector 
+$\vec{k}_{EM}(\vec{\Theta}, \lambda) $ :
+\begin{equation}
+s(\lambda)  =  \iint d \vec{\Theta} \, \, \, A(\vec{\Theta},\lambda) B(\vec{\Theta},\lambda) e^{i ( \vec{k}_{EM} . \vec{r} )} \\
+\end{equation} 
+We have set the electromagnetic (EM) phase origin at the center of the coordinate frame and 
+the EM wave vector is related to the wavelength $\lambda$ through the usual 
+$ | \vec{k}_{EM} |  =  2 \pi / \lambda $. The receiver beam or antenna lobe $L(\vec{\Theta})$ 
+corresponds to the receiver intensity response:
+\begin{equation}
+L(\vec{\Theta}) = B(\vec{\Theta},\lambda)  \,  B^*(\vec{\Theta},\lambda) 
+\end{equation} 
+The visibility signal between two receivers corresponds to the time averaged correlation between 
+signals from two receivers. If we assume a sky signal with random uncorrelated phase, the 
+visibility $\vis$ signal from two identical receivers, located at the position $\vec{r_1}$ and 
+$\vec{r_2}$ can simply be written as a function their position difference $\vec{\Delta r} = \vec{r_1}-\vec{r_2}$
+\begin{equation}
+\vis(\lambda) = < s_1(\lambda) s_2(\lambda)^* > = \iint d \vec{\Theta} \, \, I(\vec{\Theta},\lambda) L(\vec{\Theta},\lambda) 
+e^{i ( \vec{k}_{EM} . \vec{\Delta r} ) }
+\end{equation} 
+This expression can be simplified if we consider receivers with narrow field of view 
+($ L(\vec{\Theta},\lambda) \simeq  0$ for $| \vec{\Theta} | \gtrsim 10 \mathrm{deg.} $ ), 
+and coplanar in respect to their common axis.
+If we introduce two {\em Cartesian} like angular coordinates $(\alpha,\beta)$ centered at 
+the common receivers axis, the visibilty would be written as the 2D Fourier transform
+of the product of the sky intensity and the receiver beam, for the angular frequency 
+$2 \pi( \frac{\Delta x}{\lambda} ,  \frac{\Delta x}{\lambda} )$:
+\begin{equation}
+\vis(\lambda) \simeq  \iint d\alpha d\beta \, \, I(\alpha, \beta) \,  L(\alpha, \beta) 
+\exp \left[ i 2 \pi \left( \alpha \frac{\Delta x}{\lambda} + \beta  \frac{\Delta y}{\lambda} \right) \right]
+\end{equation} 
+where $(\Delta x, \Delta y)$ are the two receiver distances on a plane perpendicular to 
+the receiver axis. The $x$ and $y$ axis in the receiver plane are taken parallel to the 
+two $(\alpha, \beta)$ angular planes. 
+
+Furthermore, we introduce the conjugate Fourier variables $(u,v)$ and the Fourier transforms
+of the sky intensity and the receiver beam:
+\begin{center}
+\begin{tabular}{ccc}
+$(\alpha, \beta)$ & \hspace{2mm} $\longrightarrow $ \hspace{2mm} & $(u,v)$ \\
+$I(\alpha, \beta, \lambda)$ & \hspace{2mm} $\longrightarrow $ \hspace{2mm} & ${\cal I}(u,v, \lambda)$ \\
+$L(\alpha, \beta, \lambda)$ & \hspace{2mm} $\longrightarrow $ \hspace{2mm} & ${\cal L}(u,v, \lambda)$ \\
+\end{tabular} 
+\end{center}
+
+The visibility can then be interpreted as the weighted sum of the sky intensity, in an angular 
+wave number domain located around 
+$(u, v)_{12}=2 \pi( \frac{\Delta x}{\lambda} ,  \frac{\Delta x}{\lambda} )$. The weight function is 
+given by the receiver beam Fourier transform. 
+\begin{equation}
+\vis(\lambda) \simeq  \iint d u d v \, \, {\cal I}(u,v, \lambda) \, {\cal L}(u - 2 \pi \frac{\Delta x}{\lambda} , v - 2 \pi \frac{\Delta y}{\lambda} , \lambda)
+\end{equation} 
+
+A single receiver instrument would measure the total power integrated in a spot centered around the 
+origin in the $(u,v)$ or the angular wave mode plane. The shape of the spot depends on the receiver 
+beam pattern, but its extent would be $\sim 2 \pi D / \lambda$, where $D$ is the receiver physical 
+size. The correlation signal from a pair of receivers would measure the integrated signal on a similar 
+spot, located around the central angular wave mode  $(u, v)_{12}$ determined by the relative 
+position of the two receivers (see figure \ref{figuvplane}).
+In an interferometer with multiple receivers, the area covered by different receiver pairs in the 
+$(u,v)$ plane might overlap and some pairs might measure the same area (same base lines). 
+Several beam can be formed using different combination of the correlation from different 
+antenna pairs.  
+
+\begin{figure}
+% \vspace*{-2mm}
+\centering
+\mbox{
+\includegraphics[width=0.5\textwidth]{Figs/uvplane.pdf}
+}
+\vspace*{-15mm}
+\caption{Schematic view of the $(u,v)$ plane coverage by interferometric measurement}
+\label{figuvplane}
+\end{figure}
+
+\subsection{Noise power spectrum}
+Let's consider a total power measurement using a receiver at wavelength $\lambda$, over a frequency 
+bandwidth $\delta \nu$, with an integration time $t_{int}$, characterized by a system temperature 
+$\Tsys$. The uncertainty or fluctuations of this measurement due to the receiver noise can be written as 
+$\sigma_{noise}^2 = \frac{4 \Tsys^2}{t_{int} \, \delta \nu}$. This term 
+corresponds also to the noise for the visibility $\vis$ measured from two identical receivers, with uncorrelated 
+noise. If the receiver has an effective area $A \simeq \pi D^2$ or $A \simeq 4 D_x D_y$, the measurement 
+corresponds to the integration of power over a spot in the angular frequency plane with an area $\sim A/\lambda^2$. 
+The sky temperature measurement can thus be characterized by the noise spectral power density in 
+the angular frequencies plane $P_{noise}^{(u,v)} \simeq \frac{\sigma_{noise}^2}{A / \lambda^2}$, in $\mathrm{Kelvin^2}$  
+per unit area of angular frequencies  $\frac{\delta u}{ 2 \pi} \times \frac{\delta v}{2 \pi}$:
+\begin{eqnarray}
+P_{noise}^{(u,v)} & = & \frac{\sigma_{noise}^2}{ A / \lambda^2 }  \\
+P_{noise}^{(u,v)} & \simeq & \frac{ \Tsys^2 }{t_{int}  \, \delta \nu} \, \frac{ \lambda^2 }{ D^2 } 
+\hspace{5mm} \mathrm{units:} \, \mathrm{K^2 \times rad^2} \\
+\end{eqnarray}
+
+In a given instrument configuration, if several ($n$) receiver pairs have the same baseline, 
+the noise power density in the corresponding $(u,v)$ plane area is reduced by a factor $1/n$. 
+When the intensity maps are projected in a 3D box in the universe and the 3D power spectrum 
+$P(k)$ is computed, angles are translated into comoving transverse distance scale, 
+and frequencies or wavelengths into comoving radial distance, using the following relations:
+\begin{eqnarray}
+\delta \alpha , \beta & \rightarrow & \delta \ell_\perp = (1+z) \, \dang(z) \, \delta \alpha,\beta  \\
+\delta \nu & \rightarrow & \delta \ell_\parallel = (1+z) \frac{c}{H(z)} \frac{\delta \nu}{\nu} 
+  = (1+z) \frac{\lambda}{H(z)} \delta \nu \\
+\delta u , v & \rightarrow & \delta k_\perp = \frac{ \delta u , v }{  (1+z) \, \dang(z)  } \\
+\frac{1}{\delta \nu} & \rightarrow & \delta k_\parallel = \frac{H(z)}{c} \frac{1}{(1+z)} \, \frac{\nu}{\delta \nu}
+ =  \frac{H(z)}{c} \frac{1}{(1+z)^2} \, \frac{\nu_{21}}{\delta \nu}
+\end{eqnarray}
+
+The three dimensional projected noise spectral density can then be written as: 
+\begin{equation}
+P_{noise}(k) = \frac{\Tsys^2}{t_{int} \, \nu_{21} } \, \frac{\lambda^2}{D^2}  \, \dang^2(z) \frac{c}{H(z)} \, (1+z)^4  
+\end{equation} 
+
+$P_{noise}(k)$ would be in units of $\mathrm{mK^2 \, Mpc^3}$ with $\Tsys$ expressed in $\mathrm{mK}$, 
+$t_{int}$ in second, $\nu_{21}$ in $\mathrm{Hz}$, $c$ in $\mathrm{km/s}$, $\dang$ in $\mathrm{Mpc}$ and 
+ $H(z)$ in $\mathrm{km/s/Mpc}$. 
+The matter or \HI distribution power spectrum determination statistical errors vary as the number of 
+observed Fourier modes, which is inversely proportional to volume of the universe 
+which is observed (sample variance). 
+
+In the following, we will consider the survey of a fixed
+fraction of the sky, defined by  total solid angle $\Omega_{tot}$, performed during a fixed total 
+observation time $t_{obs}$. We will consider several instrument configurations, having 
+comparable instantaneous bandwidth, and comparable system receiver noise $\Tsys$:  
+\begin{enumerate}
+\item Single dish instrument, diameter $D$ with one or several independent feeds (beams) in the focal plane
+\item Filled square shaped arrays, made of $n = q \times q$ dishes of diameter $D_{dish}$ 
+\item Packed or unpacked cylinder arrays
+\item Semi-filled array of $n$ dishes    
+\end{enumerate}
+
+We  compute below a simple expression for the noise spectral power density for radio 
+sky 3D mapping surveys. 
+It is important to notice that the instruments we are considering do not have a flat 
+response in the $(u,v)$ plane, and the observations provide no information above 
+$u_{max},v_{max}$. One has to take into account either a damping of the 
+observed sky power spectrum or an increase of the noise spectral power if 
+the observed power spectrum is corrected for damping. The white noise 
+expressions given below should thus be considered as a lower limit or floor of the 
+instrument noise spectral density. 
+  
+% \noindent {\bf Single dish instrument} \\
+A single dish instrument with diameter $D$ would have an instantaneous field of view 
+(or 2D pixel size) $\Omega_{FOV} \sim \left( \frac{\lambda}{D} \right)^2$, and would require 
+a number of pointing $N_{point} = \frac{\Omega_{tot}}{\Omega_{FOV}}$ to cover the survey area. 
+The noise power spectral density  could then be written as:
+\begin{equation}
+P_{noise}^{survey}(k) = \frac{\Tsys^2 \, \Omega_{tot} }{t_{obs} \, \nu_{21} } \, \dang^2(z) \frac{c}{H(z)} \, (1+z)^4  
+\end{equation}
+For a single dish instrument equipped with a multi-feed or phase array receiver system, 
+with $n$ independent beam on sky, the noise spectral density decreases by a factor $n$, 
+thanks to the an increase of per pointing integration time. 
+
+For a single dish of diameter $D$, or an interferometric instrument with maximal extent $D$, 
+observations provide information up to $u,v_{max} \lesssim 2 \pi D / \lambda $. This value of 
+$u,v_{max}$ would be mapped to a maximum transverse cosmological wave number
+$k^{comov}_{\perp \, max}$:
+\begin{eqnarray}
+k^{comov}_{\perp} & = & \frac{(u,v)}{(1+z) \dang}  \\
+k^{comov}_{\perp \, max} & \lesssim &  \frac{2 \pi}{\dang \, (1+z)^2} \frac{D}{\lambda_{21}} 
+\end{eqnarray}   
+
+Figure \ref{pnkmaxfz} shows the evolution of a radio 3D  temperature mapping 
+$P_{noise}^{survey}(k)$ as a function of survey redshift. 
+The survey is supposed to cover a quarter of sky $\Omega_{tot} = \pi \mathrm{srad}$, in one 
+year. The maximum comoving wave number $k^{comov}$  is also shown as a function 
+of redshift, for an instrument with $D=100 \mathrm{m}$ maximum extent. In order 
+to take into account the radial component of $\vec{k^{comov}}$ and the increase of 
+the instrument noise level with $k^{comov}_{\perp}$, we have taken:
+\begin{equation}
+k^{comov}_{ max} (z) = \frac{\pi}{\dang \, (1+z)^2} \frac{D=100 \mathrm{m}}{\lambda_{21}} 
+\end{equation}
+
+\begin{figure}
+\vspace*{-10mm}
+\centering
+\mbox{
+\hspace*{-10mm}
+\includegraphics[width=0.6\textwidth]{Figs/pnkmaxfz.pdf}
+}
+\vspace*{-35mm}
+\caption{Minimal noise level for a 100 beam instrument as a function of redshift (top). 
+ Maximum $k$ value for  a 100 meter diameter primary antenna (bottom) }
+\label{pnkmaxfz}
+\end{figure}
+
+
+\subsection{Instrument configurations and noise power spectrum}
+
+We have numerically computed the instrument response in the (u,v) plane for several 
+instrument configurations, at redshift $z=1$.
+\begin{itemize}
+\item[{\bf a} :] A packed array of $n=121 \, D_{dish}=5 \mathrm{m}$ dishes, arranged in 
+a square $11 \times 11$ configuration ($q=11$). This array covers an area of 
+$55 \times 55 \, \mathrm{m^2}$ 
+\item [{\bf b} :] An array of $n=128  \, D_{dish}=5 \mathrm{m}$ dishes, arranged 
+in 8 rows, each with 16 dishes. These 128 dishes are spread over an area 
+$80 \times 80  \, \mathrm{m^2}$ 
+\item [{\bf c} :] An array of $n=129  \, D_{dish}=5 \mathrm{m}$ dishes, arranged 
+ over an area $80 \times 80  \, \mathrm{m^2}$. This configuration has in 
+particular 4 sub-arrays of packed 16 dishes ($4\times4$), located in the 
+four array corners.
+\item [{\bf d} :] A single dish instrument, with diameter $D=75 \mathrm{m}$, 
+equipped with a 100 beam focal plane instrument. 
+\item[{\bf e} :] A packed array of $n=400 \, D_{dish}=5 \mathrm{m}$ dishes, arranged in 
+a square $20 \times 20$ configuration ($q=20$). This array covers an area of 
+$100 \times 100 \, \mathrm{m^2}$ 
+\item[{\bf f} :] A packed array of 4 cylindrical reflectors, each 85 meter long and 12 meter 
+wide. The focal line of each cylinder is equipped with 100 receivers, each with length 
+$2 \lambda$, which corresponds to $\sim 0.85 \mathrm{m}$ at $z=1$. 
+This array covers an area of $48 \times 85 \, \mathrm{m^2}$, and have 
+a total of $400$ receivers per polarisation, as in the (e) configuration.
+We have computed the noise power spectrum for {\em perfect} 
+cylinders, where all receiver pair correlations are used (fp), or for 
+a non perfect instrument, where only correlations between receivers 
+from different cylinders are used.
+\item[{\bf g} :] A packed array of 8 cylindrical reflectors, each 102 meter long and 12 meter 
+wide. The focal line of each cylinder is equipped with 100 receivers, each with length 
+$2 \lambda$, which corresponds to $\sim 0.85 \mathrm{m}$ at $z=1$. 
+This array covers an area of $96 \times 102 \, \mathrm{m^2}$ and has 
+a total of 960  receivers per polarisation. As for the (f) configuration,  
+we have computed the noise power spectrum for {\em perfect} 
+cylinders, where all receiver pair correlations are used (gp), or for 
+a non perfect instrument, where only correlations between receivers 
+from different cylinders are used.
+\end{itemize}
+The array layout for configurations (b) and (c) are shown in figure \ref{figconfab}. 
+\begin{figure}
+\centering
+\vspace*{-15mm}
+\mbox{
+\hspace*{-10mm}
+\includegraphics[width=0.5\textwidth]{Figs/configab.pdf}
+}
+\vspace*{-15mm}
+\caption{ Array layout for configurations (b) and (c) with 128 and 129  D=5 meter 
+diameter dishes. }
+\label{figconfab}
+\end{figure}
+
+We have used simple triangular shaped dish response in the $(u,v)$ plane. 
+However, we have introduced a fill factor or illumination efficiency 
+$\eta$, relating the effective dish diameter $D_{ill}$ to the 
+mechanical dish size $D^{ill} = \eta \, D_{dish}$. 
+\begin{eqnarray}
+{\cal L}_\circ (u,v,\lambda) & = & \bigwedge_{[\pm 2 \pi D^{ill}/ \lambda]}(\sqrt{u^2+v^2})  \\
+ L_\circ (\alpha,\beta,\lambda) & = & \left[ \frac{ \sin (\pi (D^{ill}/\lambda) \sin \theta ) }{\pi (D^{ill}/\lambda) \sin \theta} \right]^2 
+\hspace{4mm} \theta=\sqrt{\alpha^2+\beta^2}
+\end{eqnarray}
+For the multi-dish configuration studied here, we have taken the illumination efficiency factor
+{\bf $\eta = 0.9$}. 
+
+For the receivers along the focal line of cylinders, we have assumed that the 
+individual receiver response in the $(u,v)$ plane corresponds to one from a 
+rectangular shaped antenna. The illumination efficiency factor has been taken 
+equal to $\eta_x = 0.9$ in the direction of the cylinder width, and $\eta_y = 0.8$ 
+along the cylinder length. It should be noted that the small angle approximation 
+used here for the expression of visibilities is not valid for the receivers along 
+the cylinder axis. However, some preliminary numerical checks indicate that 
+the results obtained here for the noise power would not be significantly changed.
+\begin{equation}
+ {\cal L}_\Box(u,v,\lambda)  = 
+\bigwedge_{[\pm 2 \pi D^{ill}_x / \lambda]} (u ) \times
+\bigwedge_{[\pm 2 \pi D^{ill}_y / \lambda ]} (v ) 
+\end{equation}
+Figure \ref{figuvcovabcd} for the four configurations with $\sim 100$ receivers per 
+polarisation. The resulting projected noise spectral power density is shown in figure 
+\ref{figpnoisea2g}. The increase of $P_{noise}(k)$ at low $k^{comov} \lesssim 0.02$ 
+is due to the fact that we have ignored all auto-correlation measurements.  
+It can be seen that an instrument with $100$ beams and $\Tsys = 50 \mathrm{K}$ 
+should have enough sensitivity to map LSS in 21 cm at redshift z=1.
+
+\begin{figure*}
+\centering
+\mbox{
+\hspace*{-10mm}
+\includegraphics[width=0.90\textwidth]{Figs/uvcovabcd.pdf}
+}
+\caption{(u,v) plane coverage for four configurations.
+(a) 121 D=5 meter diameter dishes arranged in a compact, square array 
+of $11 \times 11$, (b) 128 dishes arranged in 8 row of 16 dishes each, 
+(c) 129 dishes arranged as above, single D=65 meter diameter, with 100 beams. 
+color scale : black $<1$, blue, green, yellow, red $\gtrsim 80$ }
+\label{figuvcovabcd}
+\end{figure*}
+ 
+\begin{figure*}
+\vspace*{-10mm}
+\centering
+\mbox{
+\hspace*{-10mm}
+\includegraphics[width=\textwidth]{Figs/pnoisea2g.pdf}
+}
+\vspace*{-10mm}
+\caption{P(k) LSS power  and noise power spectrum for several interferometer 
+configurations ((a),(b),(c),(d),(e),(f),(g)) with 121, 128, 129, 400 and 960 receivers.}
+\label{figpnoisea2g}
+\end{figure*}
+
+
+\section{ Foregrounds and Component separation }
+
+\subsection{ Synchrotron and radio sources }
+% {\color{red}  \large \it  Reza (+  J.M. Martin ?) + CMV   } \\[1mm] 
+
+Description of the radio foregrounds for LSS@21cm and the sky models used
+\begin{itemize}
+\item Galactic synchrotron 
+\item Radio sources : spectral behavior and brightness distribution 
+\item GSM global sky model (Angelica) 
+\item simple sky model : Synchrotron (HASLAM/WMAP) + sources (North20 / NVSS catalogue ) 
+\end{itemize}
+
+\subsection{ LSS signal extraction }
+{\color{red} \large \it  CMV + Reza  +  J.M. Martin  } \\[1mm] 
+Description of the component separation method and the results 
+\begin{itemize}
+\item Component separation method, based on instrument response correction and frequency 
+smoothness / power law 
+\item Foreground power spectrum 
+\item Performance of component separation : comparison of frequency slices of recovered LSS 
+and foreground maps, source catalogs 
+\item Performance in statistical sense (power spectrum) : comparison of recovered P(k)-LSS 
+and true P(k), residual noise/systematic effect power spectrum 
+\end{itemize}
+
+
+\section{ BAO scale determination and constrain on dark energy parameters}
+{\color{red} \large \it  CY ( + JR  )  } \\[1mm] 
+We compute  reconstructed LSS-P(k) (after component separation) at different z's 
+and determine BAO scale as a function of redshifts.
+We can this a large number of time ( ~ 100 \ldots 1000 ) to have the reconstructed P(k) 
+with {\it realistic } errors. We can then determine the error on the reconstructed DE 
+parameters 
+
+\section{Conclusions}
+
+% \begin{acknowledgements}
+% \end{acknowledgements}
+
+%%% Quelques figures pour illustrer les resultats attendus 
+
+
+
+\begin{figure*}
+\centering
+\includegraphics[width=0.85\textwidth]{Figs/compexlss.png}
+\caption{Comparison of the original simulated LSS (frequency plane) and the recovered LSS.
+Color scale in mK }
+\label{figcompexlss}
+\end{figure*}
+
+\begin{figure*}
+\centering
+\includegraphics[width=0.85\textwidth]{Figs/compexfg.png}
+\caption{Comparison of the original simulated foreground  (frequency plane) and 
+the recovered foreground map. Color scale in Kelvin }
+\label{figcompexfg}
+\end{figure*}
+
+\begin{figure*}
+\centering
+\includegraphics[width=0.7\textwidth]{Figs/pklssfg.pdf}
+\caption{Comparison of the LSS power spectrum at 21 cm at 900 MHz ($z \sim 0.6$) 
+and the synchrotron/radio sources - GSM (Global Sky Model) foreground sky cube}
+\label{figcompexfg}
+\end{figure*}
+
+
+\begin{figure*}
+\centering
+\includegraphics[width=0.7\textwidth]{Figs/exlsspk.pdf}
+\caption{Recovered LSS power spectrum, after component separation - - GSM (Global Sky Model) foreground sky cube}
+\label{figexlsspk}
+\end{figure*}
+
+\bibliographystyle{aa}
+
+\begin{thebibliography}{}
+
+%%%
+\bibitem[Ansari et al. (2008)]{ansari.08} Ansari R., J.-M. Le Goff, C. Magneville, M. Moniez, N. Palanque-Delabrouille, J. Rich, 
+    V. Ruhlmann-Kleider, \& C. Y\`eche , 2008 , ArXiv:0807.3614
+
+% MWA description 
+\bibitem[Bowman et al. (2007)]{bowman.07} Bowman, J. D., Barnes, D.G., Briggs, F.H. et al 2007, \aj, 133, 1505-1518  
+
+%  Intensity mapping/HSHS 
+\bibitem[Chang et al. (2008)]{chang.08}  Chang, T.,  Pen, U.-L., Peterson, J.B. \&  McDonald, P. 2008, \prl, 100, 091303
+
+% 2dFRS BAO observation 
+\bibitem[Cole et al. (2005)]{cole.05} Cole, S. Percival, W.J., Peacock, J.A.  {\it et al.} (the 2dFGRS Team) 2005,  \mnras, 362, 505
+
+%  Parametrisation P(k) 
+\bibitem[Eisentein \& Hu  (1998)]{eisenhu.98}  Eisenstein D. \& Hu W. 1998, ApJ 496:605-614 (astro-ph/9709112)
+
+% :SDSS first BAO observation 
+\bibitem[Eisentein et al. (2005)]{eisenstein.05}  Eisenstein D. J., Zehavi, I., Hogg, D.W. {\it et al.}, (the SDSS Collaboration) 2005,  \apj, 633, 560
+
+%   21 cm emission for mapping matter distribution  
+\bibitem[Furlanetto et al. (2006)]{furlanetto.06} Furlanetto, S., Peng Oh, S. \&  Briggs, F. 2006, \physrep, 433, 181-301
+
+%  WMAP CMB anisotropies 2008 
+\bibitem[Hinshaw et al. (2008)]{hinshaw.08}  Hinshaw, G., Weiland, J.L., Hill, R.S.  {\it et al.} 2008, arXiv:0803.0732) 
+
+% HI mass in galaxies 
+\bibitem[Lah et al. (2009)]{lah.09}  Philip Lah, Michael B. Pracy, Jayaram N. Chengalur et al. 
+MNRAS  2009,  ( astro-ph/0907.1416) 
+
+%  Boomerang 2000, Acoustic pics 
+\bibitem[Mauskopf et al. (2000)]{mauskopf.00} Mauskopf, P. D., Ade, P. A. R., de Bernardis, P. {\it et al.}  2000, \apjl, 536,59
+
+% Original CRT HSHS paper 
+\bibitem[Peterson et al. (2006)]{peterson.06} Peterson, J.B.,  Bandura, K., \& Pen, U.-L. 2006, arXiv:astro-ph/0606104  
+
+% SDSS BAO 2007 
+\bibitem[Percival et al. (2007)]{percival.07}   Percival, W.J., Nichol, R.C., Eisenstein, D.J. {\it et al.}, (the SDSS Collaboration) 2007, \apj, 657, 645
+
+%% LOFAR description 
+\bibitem[Rottering et a,. (2006)]{rottgering.06} Rottgering H.J.A., Braun, r., Barthel, P.D. {\it et al.}  2006, arXiv:astro-ph/0610596
+%%%%
+
+%  Frank H. Briggs, Matthew Colless, Roberto De Propris, Shaun Ferris, Brian P. Schmidt, Bradley E. Tucker
+
+\bibitem[SKA.Science]{ska.science} 
+{\it Science with the Square Kilometre Array}, eds: C. Carilli, S. Rawlings, 
+New Astronomy Reviews, Vol.48, Elsevier, December 2004 \\
+{ \tt http://www.skatelescope.org/pages/page\_sciencegen.htm } 
+
+% FFT telescope 
+\bibitem[Tegmark \& Zaldarriaga (2008)]{tegmark.08} Tegmark, M. \& Zaldarriaga, M. 2008, arXiv:0802.1710 
+
+% Lyman-alpha, HI fraction 
+\bibitem[Wolf et al.(2005)]{wolf.05} Wolfe, A. M., Gawiser, E. \& Prochaska, J.X. 2005  \araa, 43, 861
+
+% 21 cm temperature 
+\bibitem[Wyithe et al.(2007)]{wyithe.07} Wyithe, S., Loeb, A. \& Geil, P. 2007 http://fr.arxiv.org/abs/0709.2955, submitted to \mnras
+
+%% Today HI cosmological density 
+\bibitem[Zwaan et al.(2005)]{zwann.05} Zwaan, M.A., Meyer, M.J., Staveley-Smith, L., Webster, R.L. 2005,  \mnras, 359, L30
+
+\end{thebibliography}
+
+\end{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Examples for figures using graphicx
+% A guide "Using Imported Graphics in LaTeX2e"  (Keith Reckdahl)
+% is available on a lot of LaTeX public servers or ctan mirrors.
+% The file is : epslatex.pdf 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+\end{document}
