Merge pull request #351 from LSSTDESC/physicaldensity

Physical density function

doc/0000-ccl_note/authors.csv

@@ -30,25 +30,26 @@
 # =============================================================================,,,,,,
 Lastname,Firstname,Authorname,AuthorType,Affiliation,Contribution,Email
 Almoubayyed,Husni,Husni Almoubayyed,Contributor,"McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA","wrote an mcmc jupyter notebook example, reviewed code/contributed to issues.",halmouba@andrew.cmu.edu
-Alonso,David,David Alonso,Contributor,"Department of Physics, University of Oxford, Denys Wilkinson building, Keble Road, Oxford OX1 3RH, United Kingdom","Co-led project; developed structure for angular power spectra; implemented autotools; integrated into LSS pipeline; contributed to: background, power spectrum, mass function, documentation and benchmarks; reviewed code",david.alonso@physics.ox.ac.uk
+Alonso,David,David Alonso,Contributor,"Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom","Co-led project; developed structure for angular power spectra; implemented autotools; integrated into LSS pipeline; contributed to: background, power spectrum, mass function, documentation and benchmarks; reviewed code",david.alonso@physics.ox.ac.uk
 Blazek,Jonathan,Jonathan Blazek,Contributor,"Center for Cosmology and Astroparticle Physics, Ohio State, Columbus, OH 43210, USA",Planning capabilities and structure; documentation and testing.,blazek.35@osu.edu
 Blazek,Jonathan,Jonathan Blazek,Contributor,"Laboratory of Astrophysics, \'Ecole Polytechnique F\'ed\'erale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland",Planning capabilities and structure; documentation and testing.,blazek.35@osu.edu
 Bull,Philip,Philip Bull,Contributor,"California Institute of Technology, Pasadena, CA 91125, USA","Implemented the Python wrapper and wrote documentation for it; general bug fixes, maintenance, and code review; enhanced the installer and error handling system.",philbull@gmail.com
 Bull,Philip,Philip Bull,Contributor,"Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USA","Implemented the Python wrapper and wrote documentation for it; general bug fixes, maintenance, and code review; enhanced the installer and error handling system.",philbull@gmail.com
 Campagne,Jean-\'Eric,Jean-\'Eric Campagne,Contributor,"Laboratoire de l'Acc\'el\'erateur Lin\'eaire, Universit\'e Paris-Sud, CNRS/IN2P3, Universit\'e Paris-Saclay, Orsay, France",Angpow builder and contributed to the interface with CCL.,campagne@lal.in2p3.fr
-Chisari,Elisa,N. Elisa Chisari,Contributor,"Department of Physics, University of Oxford, Denys Wilkinson building, Keble Road, Oxford OX1 3RH, United Kingdom","Co-led project, coordinated hack projects \& communication, contributed to: correlation function \& power spectrum implementation, documentation, and comparisons with benchmarks.",elisa.chisari@physics.ox.ac.uk
+Chisari,Elisa,N. Elisa Chisari,Contributor,"Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom","Co-led project, coordinated hack projects \& communication, contributed to: correlation function \& power spectrum implementation, documentation, and comparisons with benchmarks.",elisa.chisari@physics.ox.ac.uk
 Drlica-Wagner,Alex,Alex Drlica-Wagner,Contact,"Fermi National Accelerator Laboratory, P. O. Box 500, Batavia, IL 60510, USA",Helped with document preparation.,kadrlica@fnal.gov
 Du,Zilong,"Zilong Du",Contributor,"Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA","Implemented the 3d correlation function.",zdu011@ucr.edu
 Eifler,Tim,Tim Eifler,Contributor,"Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA",Reviewed/tested code.,tim.eifler@jpl.nasa.gov
 Eifler,Tim,Tim Eifler,Contributor,"Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA",Reviewed/tested code.,tim.eifler@jpl.nasa.gov
 Ellison,John,"John Ellison",Contributor,"Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA","Implemented the 3d correlation function; wrote text describing 3d correlation function for this note.",john.ellison@ucr.edu
 Hlozek,Ren\'ee,Ren\'ee Hlozek,Contributor,"Dunlap Institute for Astronomy and Astrophysics \& Department for Astronomy and Astrophysics, University of Toronto, ON M5S 3H4","Contributed initial code for error handling structures, reviewed other code edits.", hlozek@dunlap.utoronto.ca
 Ishak, Mustapha,Mustapha Ishak,Contributor,"Department of Physics, The University of Texas at Dallas, Richardson, TX 75083, USA",Contributed to planning of code capabilities and structure; reviewed code; identified and fixed bugs.,mishak@utdallas.edu
+Joudaki,Shahab,Shahab Joudaki,Contributor,"Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom","Created physical density function and documentation.",shahab.joudaki@physics.ox.ac.uk
 Kirby, Matthew,Matthew Kirby, Contributor,"Univeristy of Arizona, Tucson, AZ 85721, USA",Performed comparison of physical constants.,matthewkirby@email.arizona.edu
 Kirkby,David,David Kirkby,Contributor,"Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA","Writing, testing and reviewing code. Asking questions.",dkirkby@uci.edu
 Krause,Elisabeth,Elisabeth Krause,Contributor,"Kavli Institute for Particle Astrophysics and Cosmology, Stanford, CA 94305-4085, USA",Initiated and co-led project; developed CLASS interface and error handling; contributed to other code; reviewed pull requests.,lise@slac.stanford.edu
 Leonard,Danielle,C. Danielle Leonard,Contributor,"McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA","Wrote and tested code for LSST specifications, user-defined photo-z interface, and support of neutrinos; reviewed other code; wrote text for this note.",danielll@andrew.cmu.edu
-Lorenz,Christiane,Christiane S. Lorenz,Contributor,"Department of Physics, University of Oxford, Denys Wilkinson building, Keble Road, Oxford OX1 3RH, United Kingdom","Contributed to accurate high-redshift cosmological background quantities and benchmarked background splines.",christiane.lorenz@physics.ox.ac.uk
+Lorenz,Christiane,Christiane S. Lorenz,Contributor,"Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom","Contributed to accurate high-redshift cosmological background quantities and benchmarked background splines.",christiane.lorenz@physics.ox.ac.uk
 Marshall,Phil,Phil Marshall,Contributor,"SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA",Helped with document preparation.,pjm@slac.stanford.edu
 McClintock, Thomas,Thomas McClintock, Contributor,"Univeristy of Arizona, Tucson, AZ 85721, USA",Wrote Python documentation.,tmcclintock@email.arizona.edu
 McLaughlin, Sean,Sean McLaughlin, Contributor,"Stanford University, Stanford, CA, 94305, USA",Wrote doxygen documentation and fixed bugs/added functionality to distances., swmclau2@stanford.edu

doc/0000-ccl_note/authors.tex

@@ -4,7 +4,7 @@
 \author{Husni Almoubayyed}
 \affiliation{McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA}
 \author{David Alonso}
-\affiliation{Department of Physics, University of Oxford, Denys Wilkinson building, Keble Road, Oxford OX1 3RH, United Kingdom}
+\affiliation{Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom}
 \author{Jonathan Blazek}
 \affiliation{Center for Cosmology and Astroparticle Physics, Ohio State, Columbus, OH 43210, USA}
 \affiliation{Laboratory of Astrophysics, \'Ecole Polytechnique F\'ed\'erale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland}
@@ -14,7 +14,7 @@
 \author{Jean-\'Eric Campagne}
 \affiliation{Laboratoire de l'Acc\'el\'erateur Lin\'eaire, Universit\'e Paris-Sud, CNRS/IN2P3, Universit\'e Paris-Saclay, Orsay, France}
 \author{N. Elisa Chisari}
-\affiliation{Department of Physics, University of Oxford, Denys Wilkinson building, Keble Road, Oxford OX1 3RH, United Kingdom}
+\affiliation{Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom}
 \author{Alex Drlica-Wagner}
 \affiliation{Fermi National Accelerator Laboratory, P. O. Box 500, Batavia, IL 60510, USA}
 \author{Zilong Du}
@@ -28,6 +28,8 @@
 \affiliation{Dunlap Institute for Astronomy and Astrophysics \& Department for Astronomy and Astrophysics, University of Toronto, ON M5S 3H4}
 \author{Mustapha Ishak}
 \affiliation{Department of Physics, The University of Texas at Dallas, Richardson, TX 75083, USA}
+\author{Shahab Joudaki}
+\affiliation{Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom}
 \author{Matthew Kirby}
 \affiliation{Univeristy of Arizona, Tucson, AZ 85721, USA}
 \author{David Kirkby}
@@ -37,7 +39,7 @@
 \author{C. Danielle Leonard}
 \affiliation{McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA}
 \author{Christiane S. Lorenz}
-\affiliation{Department of Physics, University of Oxford, Denys Wilkinson building, Keble Road, Oxford OX1 3RH, United Kingdom}
+\affiliation{Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom}
 \author{Phil Marshall}
 \affiliation{SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA}
 \author{Thomas McClintock}

doc/0000-ccl_note/contributions.tex

@@ -11,6 +11,7 @@
 John Ellison: Implemented the 3d correlation function; wrote text describing 3d correlation function for this note. \\
 Ren\'ee Hlozek: Contributed initial code for error handling structures, reviewed other code edits. \\
 Mustapha Ishak: Contributed to planning of code capabilities and structure; reviewed code; identified and fixed bugs. \\
+Shahab Joudaki: Created physical density function and documentation. \\
 Matthew Kirby: Performed comparison of physical constants. \\
 David Kirkby: Writing, testing and reviewing code. Asking questions. \\
 Elisabeth Krause: Initiated and co-led project; developed CLASS interface and error handling; contributed to other code; reviewed pull requests. \\

doc/0000-ccl_note/main.tex

@@ -292,7 +292,7 @@ \subsection{Density parameter functions}
 The density parameter functions $\Omega_X(a)$ can be calculated for six components:
 \begin{itemize}
 \item matter density parameter $\Omega_M(a) = \Omega_{M,0} H_0^2 / (a^3 H^2(a) )$,
-\item dark energy density parameter $\Omega_\Lambda(a) = \Omega_{\Lambda,0} H_0^2 / H^2(a)$,
+\item dark energy density parameter $\Omega_\Lambda(a) = \Omega_{\Lambda,0} a^{-3(1+w_0+w_a)} \exp[3 w_a (a-1)] H_0^2 / H^2(a)$,
 \item radiation density parameter $\Omega_g(a) = \Omega_{g,0} H_0^2 / (a^4 H^2(a) )$,
 \item curvature density parameter $\Omega_K(a) = \Omega_{K,0} H_0^2 / (a^2 H^2(a) )$,
 \item massless neutrino density parameter $\Omega_{\nu, {\rm rel}}(a) = \Omega_{\nu, {\rm rel},0} H_0^2 / (a^4 H^2(a) )$,
@@ -318,6 +318,24 @@ \subsection{Density parameter functions}
 where $h_{\rm P}$ is Planck's constant and $h$ is $H_0/100$ with $H_0$ in units of km / s / Mpc. $x_{\rm max}$ is set to 1000. The final bracketed term which includes the phase-space integral can be simplified in the limit where $\mu$ is very large or very small: for small $\mu$, it is set to $\frac{7}{8}$, and for large $\mu$, it becomes $\frac{5\zeta(3)}{18\pi^4}\mu\sim 0.2776\mu$.
 
 
+\subsection{Functions of the physical density}
+\label{subsec:physicaldensity}
+
+The routines described in this subsection are implemented in {\tt ccl$\_$background.c}.
+
+The physical density $\rho_X(a)$ can be calculated for seven components:
+\begin{itemize}
+\item critical density $\rho_{\rm crit}(a) = {{3 H^2(a)} \over { 8 \pi G}} = \rho_{\rm crit,0} H^2(a) / H_0^2$,
+\item matter density $\rho_M(a) = \rho_{\rm crit}(a) \Omega_M(a) = \rho_{\rm crit,0} \Omega_{M,0} / a^{3}$,
+\item dark energy density parameter $\rho_\Lambda(a) = \rho_{\rm crit,0} \Omega_{\Lambda,0} a^{-3(1+w_0+w_a)} \exp[3 w_a (a-1)]$,
+\item radiation density parameter $\rho_g(a) = \rho_{\rm crit,0} \Omega_{g,0} / a^{4}$,
+\item curvature density parameter $\rho_K(a) = \rho_{\rm crit,0} \Omega_{K,0} / a^{2}$,
+\item massless neutrino density parameter $\rho_{\nu, {\rm rel}}(a) = \rho_{\rm crit,0} \Omega_{\nu, {\rm rel},0} / a^{4}$,
+\item massive neutrino density parameter $\Omega_{\nu, {\rm m}}(a) = \rho_{\rm crit,0} \Omega_{\nu, {\rm m}}(a) H^2(a) / H_0^2$,
+\end{itemize}
+where $\Omega_{\nu, {\rm m}}(a)$ is given by equation~\ref{Omnu} and the Hubble parameter by equation~\ref{eq:Ha}. \ccl moreover allows for comoving physical densities $\rho_{X, {\rm comoving}}(a) = \rho_X(a) a^3$.
+
+
 \subsection{Growth function}
 \label{sec:growth}
 
@@ -973,7 +991,7 @@ \section{Tests and validation}
 redshifts $z = 0,1,2,3,4,5$.  We then compared with the $\xi(r)$ from CCL with a sampling of $P(k)$ 
 equal to {\tt N$\_$K$\_$3DCOR} bins per decade. The default value of {\tt N$\_$K$\_$3DCOR}~=~100,000 results in a relative agreement 
 at the level of $\Delta \xi(r) / \xi(r) < 2.5 \times 10^{-3}$ for $0.1 < r < 250$~Mpc and redshift zero. The agreement is better for higher redshifts.
-We also compared the absolute value of $r^2 \xi(r)$ and find a maximum difference of \Delta (r^2 \xi(r)) < 3.0 \times 10^{-2}$ for the range 
+We also compared the absolute value of $r^2 \xi(r)$ and find a maximum difference of $\Delta (r^2 \xi(r)) < 3.0 \times 10^{-2}$ for the range 
 $r = 0.1 - 250$~Mpc. This corresponds to approximately 0.08\% of the BAO peak value of $r^2 \xi(r)$. At the BAO peak, the difference is 
 only $9.0 \times 10^{-3}$, or 0.024\% of the peak height. The results are shown in Fig.~\ref{fig:benchmark_xi}
 %
@@ -993,7 +1011,7 @@ \section{Tests and validation}
 \begin{figure*}[htbp]
 \centering
 \includegraphics[width=0.47\textwidth]{analytic_xi}
-\caption{The relative error in the 3d spatial correlation function computed using the CCL algorithm compared to an analytic function $\xi(r) = (r/r_0)^a$ whose inverse transform $P(k)$ is known analytically. In this validation test, the known $P(k)$ was transformed with the CCL algorithm and compared to the known analytic result for $\xi(r).}
+\caption{The relative error in the 3d spatial correlation function computed using the CCL algorithm compared to an analytic function $\xi(r) = (r/r_0)^a$ whose inverse transform $P(k)$ is known analytically. In this validation test, the known $P(k)$ was transformed with the CCL algorithm and compared to the known analytic result for $\xi(r)$.}
 \label{fig:analytic_xi}
 \end{figure*}
 

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