This version January 2015.
Originally based on CMBFAST developed by Uros Seljak and Matias Zaldarriaga, itself based on Boltzmann code written by Edmund Bertschinger, Chung-Pei Ma and Paul Bode. For latest information on this program see camb.info.
CAMB is also supplied as part of the CosmoMC parameter estimation package. For an extension including perturbed recombination, 21cm, lensing and number count sources see CAMB sources.
To install and compile yourself you will need a Fortran 90 (or higher) compiler - you can get the free G95 or GFortran compilers, or the optimized Intel compiler ifort is installed on many academic clusters and also supports integrated development and debugging in Visual Studio under Windows. Alternatively you can use CAMB in the pre-configured CosmoBox virtual machine, using the eclipse integrated development environment.To install yourself from the command line:
The Makefile comes set up for Intel machines using Intel's ifort compiler. Just comment the relevant parts to compile on different systems. If you have Intel's Visual Fortran you can use the projects in the VisualStudio folder, no need to use the Makefile. To run on multi-processor machines add the -openmp (or equivalent) option to the Makefile's FFLAGS parameter to compile a parallelized (OPENMP) version.
Martina Schwind has kindly contributed some introductory slides with details of program running and internal structure. For some further technical details about the algorithms, equations and code see the CAMB notes.
The params.ini file specifies the parameters used to run the program. Comments in params.ini should make this fairly self-explanatory, more complicated cases, for example to run with multiple neutrino mass eigenstates and sterile neutrinos at different temperatures see the documentation and examples in the CAMB notes. To produce the matter power spectrum in addition to CMB Cl set get_transfer = T; the do_nonlinear input parameter determines whether this is output as the linear power spectrum or includes non-linear corrections from the Halofit model.
The default params.ini file produces results in μK2 from the given primordial curvature perturbation power (scalar_amp) on 0.05 MPc-1 scales. To get unnormalized dimensionless results set scalar_amp(1)=1 and CMB_outputscale=1. To compute lensed Cls you must set the normalization to some realistic value (the calculation is non-linear, so normalization matters).
Tensor angular power spectra are output to output_root_tensCls.dat if requested.
The columns are
If do_lensing=T and lens_potential_output_file is specified a file is output containing unlensed scalar (+tensor if calculated) spectra along with the lensing potentials in this format:
Outputs
Unlensed scalar angular power spectra are output to output_root_scalCls.dat. The columns are
l CTT CEE CTE [CΦ CΦT]
Here all CX are l(l+1)C_l/2pi except for CΦ and CΦT which are CΦ= l4 ClΦ, where ClΦ is the (CMB) lensing potential power spectrum, and CΦT = l3 ClΦT. The lensing terms in square brackets are only produced if do_lensing = T. If CMB_outputscale = 7.4311e12 ([TCMB106]2, the default), the units are μK2. Note that lensing spectra are also multiplied by CMB_outputscale, so you may want to divide this out of the answer to get a sensible dimensionless spectrum or use the lens_potential_output_file file mentioned below. If requested the lensed power spectrum is output to output_root_lensedCls.dat
l CTT CEE CBB CTE
If scalars and tensors are generated, the total spectrum is in output_root_totCls.dat, in the same format as the tensor output file.
l CTT CEE CBB CTE Cdd CdT CdE
where as before CX are l(l+1)Cl/2π, and d is the deflection angle, so Cdd=[l(l+1)]2ClΦ/2π, CdT=[l(l+1)]3/2ClΦT/2π,
CdE=[l(l+1)]3/2ClΦE/2π. These are the spectra required for simulating lensed skies using LensPix.
If transfer functions are requested the columns in the output_root_transfer.dat output file are:
| 1 | k/h | wavenumber in h Mpc-1 |
| 2 | Delta_CDM/k2 | CDM |
| 3 | Delta_b/k2 | baryons |
| 4 | Delta_g/k2 | photons |
| 5 | Delta_r/k2 | massless neutrinos |
| 6 | Delta_nu/k2 | massive neutrinos |
| 7 | Delta_tot/k2 | CDM+baryons+massive neutrinos |
| 8 | Delta_nonu/k2 | CDM+baryons |
| 9 | Delta_totde/k2 | CDM+baryons+massive neutrinos+ dark energy(numerator only) |
| 10 | Φ | The Weyl potential (φ+ψ)/2 |
| 11 | vel_Newt_cdm/k2 | vel_Newt_cdm is -vcdm k/H (Newtonian-gauge CDM velocity vcdm) |
| 12 | vel_Newt_b/k2 | vel_Newt_b is -vb k/H (Newtonian-gauge baryon velocity vb) |
| 13 | vel_baryon_cdm/k2 | relative baryon-CDM velocity (vb-vcdm) |
output_root_matterpower.dat contains the conventionally normalized matter power spectrum (for baryons+cdm+massive neutrinos), in h/Mpc units.
You can edit the Makefile's EQUATIONS, POWERSPECTRUM, RECOMBINATION and REIONIZATION
variables , which determine which module is used to implement and model various parts of the calculation. The POWERSPECTRUM.f90 file7 contains a module giving the initial
power spectrum, the EQUATIONS.f90 file contains the background evolution
equations and sets of gauge-dependent perturbation
equations (the alternative equations_ppf.f90 is provided to implement the common w, wa varying dark energy parameterization). RECOMBINATION.f90 gives the background recombination history: recfast by default, but you can also compile to use CosmoRec and HyRec. REIONIZATION is by default a simple relatively fast single-step reionization model (following arXiv:0804.3865).
Various other modules can also be changed at compile time if desired.
To avoid problems run make clean after changing the
Makefile before recompiling. You can also use e.g. make RECOMBINATION=cosmorec to override the default and compile with a different module.
You can produce files in FITS
format - to do this you will need to have HEALPIX installed and make
some edits to the Makefile - see the Makefile for details. After compiling with make camb_fits,
you can then use camb_fits instead of camb - the FITS file
produced is given the name specified in params.ini. Note that the FITS file format for polarization changed with HEALPIX 1.2, CAMB uses the new format.
All the equations that need to be modified for
simple non-standard models are in the equations.f90 file. It should be possible to produce other files
for extended models (see the sample quintessence module). (Note that varying
constant - e.g. alpha - models are not quite so simple to plug in; a sample equations_ppf.f90 file provided to implement a varying w dark energy equation of state in the PPF model).
After modifying any of the source code run make clean before running make to recompile (Visual Fortran will re-compile dependent code automatically).
Run make all to build a library libcamb.a that you can use when
linking to other programs. (You will also need to include the module files using -I/cambfolder).
You can download a test suite for comparing accuracy with different parameters and code versions. Just extract the file to your CAMB directory and read the readme.
Some details about what different source code files do are given below, see also the CAMB notes.
January 2010
February 2009
November 2008
September 2008
March 2008
February 2008
November 2006
September 2006
August 2006
July 2006
June 2006
March 2006
April 2005
November 2004
August 2004
Fixed serious problem with tensor mode polarized Cl from reionization (significantly underestimated power).
Changed default tensor pivot scale to 0.05 Mpc-1 (same as for scalars). Flat Bessel functions no longer cached to disk (faster to compute than read in many cases; prevents problems in uses with MPI). New accurate_reionization flag for accurate calculation of large scale scalar EE around the first dip (also outputs computed optical depth due to reionization). Option to output vector mode spectra from regular vorticity mode (astro-ph/0403583) or magnetic field (astro-ph/0406096).
Improved accuracy of non-flat calculation, and allowed for very nearly flat models (ΩK ~ 1e-5). Non-flat code should be as accurate as the flat (0.5%) on most scales. Added run-time parameters do_tensor_neutrinos (to include the neutrino evolution in the tensor equations) and cs2_lam (constant sound speed of the dark energy) instead of having to modify the code. Fixed fatal bug in tensor neutrino setup introduced some time this year. Added parameter CMB_outputscale to scale output Cls by a constant (see comments in params.ini for getting microK^2 output).
Fixed instability in bessels.f90 which gave problem for very nearly flat closed models with abnormal Helium fractions (and possibly other models). Dark energy equations in equations.f90 changed to use simpler general fluid equations for the perturbations (see astro-ph/0307104). inidriver.F90 now reads in scalar amplitude even if computing tensors only (so combination with the initial ratio sets correct tensor amplitude).
Fixed bug in equations.f90 giving errors with non-flat models. Fixed bug in inidriver.F90 setting H0 with use_physical=F. Fixed camb.f90 file in download - missing routines for getting Cl transfer functions.
Some major restructuring, including new functions to return the CMB transfer functions (see camb.f90). The tight coupling code has been re-written, adding quadrupole terms and accounting for the time variation of the opacity numerically. The code should be more accurate and faster, especially on small scales. Minor fixes to RECFAST to match version in CMBFAST (0.01% effect on Cls), and bug fix in output routine (0.3%). Includes constant w dark energy and running spectral index parameters by default (rather than with an add-on). New use_physical parameter to allow alternative model specification by Om_b h^2, Om_b h^2 and Om_k. Polarization .fits files now compatible with HEALPIX 1.2.
Minor changes for greater compiler compatibility, in particular with Visual Fortran. Makefile includes suggested options for a variety of compilers.
Added support for neutrino isocurvature initial conditions, and
totally correlated mixed initial conditions (assuming the same power
spectrum for each mode) - new initial_vector parameter in
params.ini. Partially correlated mixed initial conditions can be
computed by combining results from different runs with totally
correlated initial conditions.
Changes for compatibility with CosmoMC. New option to output matter power spectrum.
Changed default pivot point for tensor initial power spectrum to
0.002 MPc-1 (power_tilt.f90), added pivot point and normalization to
initial power parameters. Minor enhancements to inifile.f90. Utility
routines Re_OpticalDepthAtZ and Transfer_GetMatterPower added to
modules.f90.
Massive neutrino support improved. Background evolution is much
faster, and only ever needs to be computed once for all neutrino
masses. Output transfer function files now include columns for the
massive neutrino and total perturbations. Sigma_8 is now computed
including CDM, baryons and massive neutrinos. Fixed problem computing matter
power spectrum in massive neutrino models. New parameter
massive_nu_approx to control
how the massive neutrinos are evolved - option for new approximate fast scheme
that is quite accurate for the CMB. New feedback_level parameter
that can be used to get useful information about the model being
calculated.
Fixed FITS file output to start at l=0 rather than l=2 to be consistent
with HEALPIX.
The code is now fully internally parallelized and lensing is
supported. Can now use about 16 processors with good efficiency -
just compile with the OpenMP -mp compiler flag. The lensing power
spectrum is computed explicitly and then used to computed the lensed
CMB power spectra using the full-sky results of astro-ph/0001303 (many
thanks for Gayoung Chon for work on the lensed power spectrum
code). To generate the lensed power spectra set do_lensing=T in
params.ini and the output will be in the lensed_output_file. The lensing power spectrum l4 Clφφ is also output as the 5th
column of the scalar_output_file, followed by the cross-correlation
with the temperature l3 ClφT.
Fixed bug in RECFAST - corrects C_l errors at 1-2% level. Background
evolution is now determined from routines in gauge_inv.f90 (and
gauge_sync.f90) - you now only need to edit these files to add
additional matter components, use extended theories, etc. RECFAST now
consistent with massive neutrinos.
Added Makefile for better compilation, and added option to create FITS
format power spectrum files. Changed driver.f90 to driver.F90, and new
file writefits.f90. Some minor changes to ease use with a
wider range of compilers (e.g. NaG F95 for Linux).
May 2001
Fixed the neutrino ratio factor in the normalization of the scalar
power spectrum to be consistent with the power spectrum as defined
since the January 2001 version. Changes to gauge_inv.f90 and gauge_sync.f90.
April 2001
New example
code. These samples show how you can call CAMB from other programs
via a subroutine. There are also improved InitialPower
modules for parameterizing the initial power spectrum to obtain
meaningful tensor/scalar ratios for general models and for
parameterizing in terms of slow-roll inflation parameters.
Fixed a floating error arising when both tensor and scalar spectra are generated but
with ratio zero.
February 2001
Fixed bug in recfast.f90 introduced in August 2000 update (caused
erroneous blip in ionization history).
January 2001
New file power.f90 added to separate out the InitialPower module for
easily modifying the initial power spectrum. The InitialPower module now has
additional parameters to control the normalization of the output Cls,
allowing absolute computations using correctly normalized initial
power spectra (set the UseScalTensRatio parameter to false to compute the
tensor/scalar ratio correctly from the initial power spectra in
general models). The InitialPower module is now commented to fully
explain the definition of the power spectra that should be returned by the TensorPower and
ScalarPower routines.
The transfer functions are now output in terms of k rather than beta
(nu*K) in non-flat models,
and the way to compute the matter power spectrum from the transfer
functions via d2norm is documented. The variables used to propagate
the tensor modes in gauge_inv.f90 have been changed to be equivalent
to the metric variables, improving stability when DoTensorNeutrinos=true.
September 2000
Now uses an accurate approximation to propagate massive neutrino
perturbations once no longer highly relativistic, speeding up
computation by about a factor of two (gauge_inv routine only). All massive
neutrino code is now
re-organized into a module called MassiveNu in modules.f90. The massive
neutrino equations are described in astro-ph/0203507
August 2000
Minor changes to recfast.f90 and modules.f90 to prevent floating
point errors on some systems. (Thanks for Louise Griffiths)
July 2000
Fixes inaccurate computation of the tensor quadrupole in flat
models, pointed out in astro-ph/0006392 . The only code change is to subroutine TensSourceSumIntJl in cmbmain.f90.
February 2000
Massive neutrinos are now supported. The treatment is essentially the
same as CMBFAST. However gauge_inv now includes neutrino anisotropic
stress in the tensor computation by default, accounting for massive neutrinos
when appropriate. You can revert to the old default by changing the
"DoTensorNeutrinos" parameter in gauge_inv.
This version also fixes the tight coupling switch over to give
accurate results with gauge_sync. This fixes errors introduced in
CMBFAST 3.0/CAMB Nov 99.
November 1999
Adds support for RECFAST recombination
and fixes various bugs that were in CMBFAST 2.4.1 but fixed in CMBFAST
3.0. RECFAST is an option via the fifth line in the input file as in
CMBFAST. Using it does not slow things down significantly and corrects
errors at around the 2% level.
The main differences in the non-flat computation lie in how we perform the integral of the source
functions with the hyperspherical Bessel functions. We use
Kosowsky's WKB approximation or the recursion relation to evaluate the Bessel
functions at the starting point of ranges of integration, and then
integrate the differential equation. CMBFAST
integrates up the differential equation from a pre-calculated starting point. Unlike
CMBFAST 3.2 our ranges of integration continue into the Chi > pi/2
region for closed models. We avoid problems with stability of the
integration (contamination with the irregular solution) by cutting off
the integration when the errors become important (where the values in the
dissipative tail are becoming small). This leads to very small errors,
and allows for a much simpler scheme than that used in CMBFAST 3.2 where
the symmetry of the Bessel functions is used to extend to the Chi> Pi/2 region.
From the user's point of view the main point is that this code is
rather faster than CMBFAST in many cases. Assuming same recombination history CAMB agrees with the CMBFAST 4.5 high precision TT calculation to < 1% at low l, and about 0.3% at l>100 in concordance flat models. If CAMB is run with high precision options the agreement is nearly 0.1% at high l. The polarized spectra also agree well except around the first dip in the EE spectrum with reionization (see CAMB's accurate_reionization parameter).
Note that as of March 2008 CAMB's reionization parameterization is slightly different to CMBFAST. CMBFAST 4.5.1 also uses an old version of RECFAST.
CMBFAST 3.2 introduced an include file for adjusting the
l-sampling. In CAMB this is done automatically depending on the model,
so there is no need to modify the l-sampling by hand.
CMBFAST uses the flat sky and Limber approximation and works from the transfer
functions to work out the lensing potential, CAMB uses the full result (agreement is excellent). CAMB uses a full-sky correlation function method rather than the flat sky approx (about max 0.4% effect on EE).
CMBFAST 4 uses a "k-splitting" to allow rapid computation of grids of
models to reasonable accuracy. If you need to generate a large number
of models and accuracy is not vital using CMBFAST 4 would probably
save you some time and effort. CMBFAST 4 also supports some extended models not supported by CAMB, e.g. 5-D models.
CAMB is in Fortran 90 and is more modularized, so using different initial power spectra, modified equations, etc. is often just a case of modifying one or two files and re-compiling.
Note that the conventions for the polarization power spectra output by CAMB agree with those of CMBFAST. This sign convention for the cross-correlation C_l^TE spectrum differs from the definitions in astro-ph/9911481. As from CMBFAST 4.2 the initial power spectrum normalization conventions also agree.
Main wrapper routines for running CAMB in your programs. Add "use
camb" to your programs and call CAMB_GetResults to generate output
from a set of model parameters (specified in the CAMBparams type -
defined at the top of modules.f90). You can call
CAMB_ValidateParams(P) to check that the parameter set is valid, use
CAMB_GetAge to compute the age of a model in gigayears, and
CAMB_GetCls to retrieve the computed Cls. The results can also be
accessed directly using the arrays in the ModelData module (defined in modules.f90).
Sample programs tester.f90 and sigma8.f90 are supplied showing how to
use CAMB from your own programs. You can also use CAMB_GetTransfers to access the C_l transfer functions directly without incorporating the initial power spectrum.
The main subroutine that does integrations, etc. Encompasses CMBFAST's
cmbflat and cmbopen.
equations.f90
Files containing background and perturbation evolution equations. The
perturbations equations used are derived in the covariant approach,
fixing to the CDM (zero acceleration) frame, which are essentially
equivalent to the synchronous gauge equations.
The file defines a module called "GaugeInterface" which provides
the necessary perturbation calculation routines for
"cmbmain".
The subroutine dtauda(a) returns dt/da and is used wherever the
background evolution is needed. It
can be modified for different backgrounds. You may
also need to change the GetOmegak routine if you add additional
components, and can edit the init_background routine to do
additional initialization.
outtransf writes out the matter transfer functions.
The "output" subroutine computes the scalar sources at a given time for a
given wavenumber. These are the temperature, E polarization and (if
doing lensing) the lensing source. By editing the equation for the
lensing source it should be straightforward to compute power
spectra for other matter tracers, e.g. for cross-correlation with
the CMB. The lensing power spectrum is automatically computed if
DoLensing=T.
equations_ppf.f90 is an alternative module that allows evolving dark energy crossing w=-1.
power_tilt.f90
This file defines a module called InitialPower that returns the
initial power spectra. Change this file to use your own initial power
spectrum, change how the spectra are parameterized, or to change how
the Cls are normalized. Comments in the code explain this further.
reionization.f90
This file defines a module called Reionization that parameterizes the reionization history and supplies a function Reionization_xe that gives xe as a function of redshift. Optical depth input parameters are mapped into zre (defined as where xe is half its maximum (ex second He reionization)) using a binary search. See the CAMB notes for discussion. This module should be easily modifiable for alternative reionization models.
halofit.f90
Implements the NonLinear module, to calculate non linear scalings of the matter power spectrum as a function of redshift. Uses HALOFIT (astro-ph/0207664, code thanks to Robert Smith, with tweaks
from arXiv:1208.2701 (thanks Ryuichi Takahashi) - see that paper for discussion of numerical accuracy. This module can be replaced to use a different non-linear fitting method if desired.
inidriver.F90
Reads in parameters from a file of name/value pairs and calls CAMB. Modify
this file to generate grids of models, change the parameterization, etc.
modules.f90
Various modules used by the other parts of the program, Module
"ModelParams" contains most of the model parameters. Boolean vars
flat, open and closed determine the model type.
bessels.f90
Module to calculate spherical and hyper-spherical Bessel
functions. Hyper-spherical functions generated by use of
either the recursion relation or Kosowsky's WKB approximation. Based on
Arthur Kosowsky's "hyperjl.c".
lensing.f90
Lensing module for computing the lensed CMB power spectra from the
unlensed spectra and a lensing power spectrum. See astro-ph/0502425.
Various subroutines for interpolation, and modified Runge-Kutta
dverk for parallelized evolution.
writefits.f90
Subroutine WriteFitsCls that uses HEALPIX routines to output power spectrum
in FITS format.
recfast.f90
RECFAST integrator for Cosmic Recombination of Hydrogen and Helium
by Douglas Scott (with minor modifications for CMBFAST and the
CAMB). See RECFAST
for the original code. This module implements the RECOMBINATION module required by CAMB, and could be replaced by more detailed codes. Sample wrappers are also provided for CosmoRec and HyRec, but the libraries for these must be installed separately.
SeparableBispectrum.f90
Implements calculation of simple separable primordial bispectra, specifically the local constant fNL model, and the CMB lensing bispectrum due to the linear temperature and polarization cross-correlation with the lensing potential. Compile with FISHER defined in the makefile to also calculate Fisher elements, including the effects of lensing signal variance (edit Makefile to link to LAPACK if necessary). Note that the primordial bispectra here are unlensed (see arXiv:0905.4732 for a calculation), but the lensed bispectra are calculated non-perturbatively (but approximately) using the lensed small-scale CMB power spectra. Note that calculating primordial bispectra is significantly slower than doing standard power spectrum calculations, however it parallelizes well.
Extreme models (e.g. scale > 4, h>1) may give errors of 5% or more.
Tensor errors around 2% or more on small scales (e.g. due to l-interpolation). Low l accuracy somewhat worse than scalars (typically < 1%). Turn on neutrinos in the input file for accurate results (automatic on high accuracy setting).
Hierarchy truncation errors up to 5% at high l (>1500) in some
closed models
You can improve or check accuracy (or increase speed) by changing
global accuracy parameters at the bottom of the params.ini input file. Convergence and stability can be checked using the test suite.
Some notes and relevant Maple derivations are given here (see also the Appendix of astro-ph/0406096). The CAMB notes outline the equations and approximations used, and relation to standard synchronous-gauge and Newtonian-gauge variables; see also arXiv:1201.3654.
There is a BibTex file of references (including CosmoMC).
CMB power spectrum parameter degeneracies in the era of precision cosmology
Efficient computation of CMB anisotropies in closed FRW Models
Geometric Algebra and
Covariant Methods in Physics and Cosmology, Chapters 6&7
Covariant theory
Cosmic Microwave Background Anisotropies in the CDM model: A
Covariant and Gauge-Invariant Approach Evolution of cosmological dark matter perturbations
Microwave background anisotropies from gravitational waves: the 1+3
covariant approach
Microwave background polarization in cosmological models
CMB anisotropies from primordial inhomogeneous magnetic fields
Initial conditions
The General Primordial Cosmic Perturbation
Observable primordial vector modes
HALOFIT
Stable clustering, the halo model and nonlinear cosmological power spectra
Revising the Halofit Model for the Nonlinear Matter Power Spectrum
RECOMBINATION
A new calculation of the recombination epoch.
How well do we understand cosmological recombination?
Weak lensing of the CMB
lensing_method=2
Gravitational Lensing Effect on Cosmic Microwave Background
Polarization
lensing_method=3
The shape of the CMB lensing bispectrum
The Cosmic Linear Anisotropy Solving System (CLASS) II:
Approximation schemes
CMB power spectrum parameter degeneracies in the era of precision cosmology
Evolution of cosmological dark matter perturbations
Synchronous gauge theory and non-flat models
Complete treatment of CMB anisotropies in a FRW universe
WKB approx to hyperspherical Bessel functions
Efficient Computation of Hyperspherical Bessel Functions
CMBFAST and the line of sight approach
A line of sight integration approach to Cosmic Microwave Background
Anisotropies
Integral solution for the microwave background
anisotropies in nonflat universes
CMBFAST for spatially closed universesCompilation options and code modifications
Version history
January 2015
April 2014
March 2014
December 2013
November 2013
October 2013
September 2013
July 2013
March 2013
October 2012
January 2012
December 2011
October 2011
July 2011
January 2011
Recfast updated to version 1.5 (rising to 2% change at l=2000; added rate fudge to match 0910.4383; use RECFAST_Hswitch = F to recover old result). Added lens_potential_output_file parameter to get sensibly normalized lensing potential ([l(l+1)]2Cl/2π and temperature correlation). Added code parameter do_bispectrum to modules.f90 for parameter tweaks to get accurate transfer functions for fNL calculations.
Fixed serious bug in the calculation of lensed non-flat models (introduced in the Feb 2008 version).
Fixed proton mass error (and hence incorrect baryon evolution on pressure-damping scales; note CAMB is not as accurate as CAMB sources anyway due to use of adiabatic pressure).
Restructured recombination module to allow use of different models. RECFAST default implementation updated to version 1.4.2 (+fixes, tiny change to results). Misc minor changes.
Fixed significant bug affecting very closed models (introduced Feb 2008; slightly closed models were fine).
(26th March, fixed pivot parameters in sample .ini)
New reionization history model: new input parameter re_delta_redshift (does not change optical depth), and option to set re_ionization_frac=-1 to automatically set the reionization fraction from input YHe assuming Helium is singly reionized at the same time as hydrogen (hence mapping of redshift to optical depth different to before at 10% level; see the notes). Reionization history now specified in (replaceable) module in reionization.f90; default includes tiny effect of He double reionization at z~3.5. Some internal reorganization.
Added pivot_scalar and pivot_tensor input parameters for initial power spectrum. output subroutine (equations.f90) re-arranged to separated ISW source terms.
Updated RECFAST to version 1.4 (~0.5% effect at high l; new RECFAST_fudge_He,RECFAST_Heswitch parameters, removed Dubrovich modifications). lensed_total_output_file parameter to get lensed scalar plus tensor power spectrum. Calculates CosmoMC's theta parameter for each model (code in modules.f90). Modules routine MatterPowerData_Load to read in matter power (for splining from pre-computed file); MatterPowerData_k function now extrapolates low-k out of range. transfer_interp_matterpower parameter to switch between interpolated regular grid in log k or array at actual computed values (better for later re-interpolation). Added camb.vfproj Intel Visual Fortran project file. Simplifying internal changes from CAMB sources, e.g. use of Ranges module for setting time steps and k sampling values; also now switches to log k source spacing at very high l to speed up calculation where spectra smooth. More diagnostics and options in the test suite.
Updated RECFAST to version 1.3 (0.1% effect on Cl). Tweak to get <0.3% error in matter power spectrum around the peak when transfer_high_precision = T.
Fixed problem generating combinations of scalars and tensors in camb.f90 (since August version).
Speeded calculation of lensed spectra and lensing power spectrum by using Limber approximation on small scales (no loss of accuracy). Fixed missing f_K in source term for non-flat lensing potential. Minor changes to default parameters and compatibility tweaks. Can download test suite for comparing accuracy and code versions.
Fixed bug setting default neutrino degeneracy if none specified and initialization of nu_mass_eigenstates for programmatic access. Other minor fixes.
Added support for arbitrary neutrino mass splittings. New option to set transfer_k_per_logint=0 to get automatic accurate k-sampling of the matter power spectrum. Fixed Transfer_GetMatterPower at large scales for non-flat models. New setting value massive_nu_approx=3 to use whatever method is good to get fast accurate results. Other internal changes.
Fixed bug lensing scalar spectrum when generated at the same time as tensors. New (hard coded) parameter lmin in modules.f90 - set to 1 if you want to generate temperature and lensing potential l=1 (Newtonian Gauge) Cl.
Added do_nonlinear option to apply non-linear corrections from HALOFIT (astro-ph/0207664). do_nonlinear = 1 applies just to the matter power spectra, do_nonlinear=2 applies corrections to the lensed CMB power spectra (important for BB). HALOFIT should only be used for standard adiabatic ΛCDM models with power law initial power spectra.
New recombination option (1 does RECFAST as before, 2 uses modified version from astro-ph/0501672). New option do_late_rad_trunction to turn off the small scale radiation hierarchies after matter domination (see astro-ph/0503277 and the notes) - saves some time. New output_root option to prefix output file names and generate output_root_params.ini file of input parameters for the run.
Default lensing routine (lensing_method=1) changed to use new full-sky correlation function method (astro-ph/0502425) in preference to the harmonic method of astro-ph/0001303 (lensing_method=3; inaccurate at l>1000 at ~1.5% level by l=2000). The lensed result is now significantly faster and more accurate.
Also added flat-sky method (lensing_method=2) of astro-ph/9505109 and astro-ph/9803150 as in CMBFAST (accurate to 0.4%). New accurate_BB parameter to get lensed BB accurately (within assumptions of linearity and given k_max, l_max, etc.). Note lensed_output_file no longer contains any tensor contribution. Various changes for better accuracy and compiler compatibility, including same accuracy with massive neutrinos as with massless.
Fixed effect of reionization on the lensed Cl (0.5% on small scale TT).
Fix - 17 Dec: corrected problem with significantly non-flat models (e.g. ΩK=-0.1, H0=40)
Fixed rare problem computing closed models, and bug in computation of
closed transfer functions. The names of the massive neutrino
subroutines have been changed because the argument that is passed has changed.
Comparison with CLASS
The CLASS CMB code is written independently of CAMB and CMBFAST and is in pure C (not C++, despite the name). The basic equations and algorithm are substantially the same as CMBFAST in both cases, with CLASS having a C implementation of CAMB's lensed power spectrum method, and CAMB implementing in F90 some of the new very-sub-horizon approximations introduced in CLASS (which make little difference at WMAP precision, but significantly increase speed for small-scales and high accuracy). The codes use different combinations of approximation schemes and sampling for massive neutrinos. For standard models at CAMB's default accuracy settings speeds should be similar depending on compilers used, with CAMB's high_accuracy_default option being similar to CLASS's cl_permille.pre.
Comparison with CMBFAST
This code was originally developed from CMBFAST 2.4.1 to support closed models
and gauge invariant variables. After releasing this code CMBFAST 3.2
was released which also supports closed models. These codes were
developed independently and so are somewhat different, and both codes
have developed independently since then.
The source files
camb.f90
Accuracy
Scalar numerical errors should rarely exceed 0.3% for min(2500, L well into the damping tail) at default accuracy setting, and 0.1% for 500<L<2000 with high_accuracy_default=T. Matter power spectrum errors are usually dominated by interpolation in the acoustic oscillations, with about 0.2% accuracy with high_accuracy_default (but much better rms accuracy). For a detailed study of numerical accuracy as of January 2012 see arXiv:1201.3654.
See also comparison with CMBFAST. Accuracy of course assumes the model is correct, and is dependent on RECFAST being the correct ionization history. Lensed C_l TT, TE and EE are accurate at the same level (to within the approximation that the lensing potential is linear, or the accuracy of the HALOFIT non-linear model).
Add-ons, extensions, external sites
REFERENCES
Cullan Howlett, Antony Lewis, Alex Hall, Anthony Challinor arXiv:1201.3654.
Antony Lewis, Anthony Challinor and Anthony Lasenby astro-ph/9911177 Ap. J. 538:473-476, 2000.
PhD thesis, Antony Lewis 2000. PostScript.
Anthony Challinor and Anthony Lasenby, astro-ph/9804301
Ap. J. 513:1 1-22, 1999
Antony Lewis and Anthony Challinor astro-ph/0203507
Phys. Rev. D66, 023531 (2002)
Anthony Challinor, astro-ph/9906474
Anthony Challinor, astro-ph/9911481
Antony Lewis, astro-ph/0406096
(The appendix contains general derivations of the multipole equations and Cl as used in CAMB)
Martin Bucher, Kavilan Moodley and Neil Turok, astro-ph/9904231
(These results extended to the non-flat case; see the theory page)
Antony Lewis, astro-ph/0403583
Smith, R. E. and others, astro-ph/0207664.
Ryuichi Takahashi and others, arXiv:1208.2701.
Seager, S., Sasselov, D. & Scott, D., 1999, ApJ, 523, L1, astro-ph/9909275.
Wong, Wan Yan and Moss, Adam and Scott, Douglas, arXiv:0711.1357.
lensing_method=1
Bispectra
Lensed CMB power spectra from all-sky correlation functions
A. Challinor and A. Lewis. astro-ph/0502425. (For Maple derivations see the theory page.)
Also: Weak Lensing of the CMB, astro-ph/0601594.
Gravitational lensing effect on cosmic microwave background
anisotropies: A Power spectrum approach
Uros Seljak. astro-ph/9505109
Uros Seljak and Matias Zaldarriaga. astro-ph/9803150
Weak Lensing of the CMB: A Harmonic Approach
Wayne Hu. astro-ph/0001303
See also astro-ph/0301064, astro-ph/0301031
Antony Lewis, Anthony Challinor and Duncan Hanson arXiv:1101.2234
Blas, Diego and Lesgourgues, Julien and Tram, Thomas. arXiv:1104.2933
Cullan Howlett, Antony Lewis, Alex Hall, Anthony Challinor.
arXiv:1201.3654
JCAP 04(2012)027
Antony Lewis and Anthony Challinor astro-ph/0203507
Phys. Rev. D66, 023531 (2002)
Wayne Hu, Uros Seljak and Matias Zaldarriaga.
Phys. Rev. D57:6, 3290-3301, 1998. astro-ph/9709066.
Arthur Kosowsky, astro-ph/9805173
Uros Seljak and Matias Zaldarriaga, astro-ph/9603033
Ap.J. 469:2 437-444, 1996
Matias Zaldarriaga, Uros Seljak, Edmund Bertschinger.
ApJ. 494:491-501, 1998. astro-ph/9704265.
Uros Seljak and Matias Zaldariaga, astro-ph/9911219