# CAMB¶

Synopsis: Managing the CAMB cosmological code Jesus Torrado and Antony Lewis

This module imports and manages the CAMB cosmological code. It requires CAMB 1.1.3 or higher.

Note

If you use this cosmological code, please cite it as:
A. Lewis, A. Challinor, A. Lasenby, Efficient computation of CMB anisotropies in closed FRW (arXiv:astro-ph/9911177)
C. Howlett, A. Lewis, A. Hall, A. Challinor, CMB power spectrum parameter degeneracies in the era of precision cosmology (arXiv:1201.3654)

## Usage¶

If you are using a likelihood that requires some observable from CAMB, simply add CAMB to the theory block.

You can specify any parameter that CAMB understands in the params block:

theory:
camb:
extra_args:
[any param that CAMB understands, for FIXED and PRECISION]

params:
[any param that CAMB understands, fixed, sampled or derived]


If you want to use your own version of CAMB, you need to specify its location with a path option inside the camb block. If you do not specify a path, CAMB will be loaded from the automatic-install packages_path folder, if specified, or otherwise imported as a globally-installed Python package. Cobaya will print at initialisation where it is getting CAMB from.

### Modifying CAMB¶

If you modify CAMB and add new variables, make sure that the variables you create are exposed in the Python interface (instructions here). If you follow those instructions you do not need to make any additional modification in Cobaya.

You can use the model wrapper to test your modification by evaluating observables or getting derived quantities at known points in the parameter space (set debug: True to get more detailed information of what exactly is passed to CAMB).

In your CAMB modification, remember that you can raise a CAMBParamRangeError or a CAMBError whenever the computation of any observable would fail, but you do not expect that observable to be compatible with the data (e.g. at the fringes of the parameter space). Whenever such an error is raised during sampling, the likelihood is assumed to be zero, and the run is not interrupted.

## Installation¶

### Pre-requisites¶

cobaya calls CAMB using its Python interface, which requires that you compile CAMB using intel’s ifort compiler or the GNU gfortran compiler version 6.4 or later. To check if you have the latter, type gfortran --version in the shell, and the first line should look like

GNU Fortran ([your OS version]) [gfortran version] [release date]


Check that [gfortran's version] is at least 6.4. If you get an error instead, you need to install gfortran (contact your local IT service).

CAMB comes with binaries pre-built for Windows, so if you don’t need to modify the CAMB source code, no Fortran compiler is needed.

If you are using Anaconda you can also install a pre-compiled CAMB package from conda forge using

conda install -c conda-forge camb


### Automatic installation¶

If you do not plan to modify CAMB, the easiest way to install it is using the automatic installation script. Just make sure that theory: camb: appears in one of the files passed as arguments to the installation script.

### Manual installation (or using your own version)¶

If you are planning to modify CAMB or use an already modified version, you should not use the automatic installation script. Use the installation method that best adapts to your needs:

• [Recommended for staying up-to-date] To install CAMB locally and keep it up-to-date, clone the CAMB repository in Github in some folder of your choice, say /path/to/theories/CAMB:

$cd /path/to/theories$ git clone --recursive https://github.com/cmbant/CAMB.git
$cd CAMB$ python setup.py build


To update to the last changes in CAMB (master), run git pull from CAMB’s folder and re-build using the last command. If you do not want to use multiple versions of CAMB, you can also make your local installation available to python generally by installing it using

$python -m pip install -e /path/to/CAMB  • [Recommended for modifying CAMB] First, fork the CAMB repository in Github (follow these instructions) and then follow the same steps as above, substituting the second one with: $ git clone --recursive https://[YourGithubUser]@github.com/[YourGithubUser]/CAMB.git

• To use your own version, assuming it’s placed under /path/to/theories/CAMB, just make sure it is compiled (and that the version on top of which you based your modifications is old enough to have the Python interface implemented.

In the cases above, you must specify the path to your CAMB installation in the input block for CAMB (otherwise a system-wide CAMB may be used instead):

theory:
camb:
path: /path/to/theories/CAMB


Note

In any of these methods, if you intent to switch between different versions or modifications of CAMB you should not install CAMB as python package using python setup.py install, as the official instructions suggest.

## camb class¶

class theories.camb.camb(info=mappingproxy({}), name=None, timing=None, packages_path=None, initialize=True, standalone=True)

CAMB cosmological Boltzmann code cite{Lewis:1999bs,Howlett:2012mh}.

initialize()

Importing CAMB from the correct path, if given.

initialize_with_params()

Additional initialization after requirements called and input_params and output_params have been assigned (but provider and assigned requirements not yet set).

get_can_support_params()

Get a list of parameters supported by this component, can be used to support parameters that don’t explicitly appear in the .yaml or class params attribute or are otherwise explicitly supported (e.g. via requirements)

Returns: iterable of names of parameters
get_allow_agnostic()

Whether it is allowed to pass all unassigned input parameters to this component (True) or whether parameters must be explicitly specified (False).

Returns: True or False
must_provide(**requirements)

Specifies the quantities that this Boltzmann code is requested to compute.

Typical requisites in Cosmology (as keywords, case insensitive):

• Cl={...}: CMB lensed power spectra, as a dictionary {spectrum:l_max}, where the possible spectra are combinations of “t”, “e”, “b” and “p” (lensing potential). Get with get_Cl().
• [BETA: CAMB only; notation may change!] source_Cl={...}: $$C_\ell$$ of given sources with given windows, e.g.: source_name: {"function": "spline"|"gaussian", [source_args]; for now, [source_args] follow the notation of CAMBSources. If can also take lmax: [int], limber: True if Limber approximation desired, and non_linear: True if non-linear contributions requested. Get with get_source_Cl().
• Pk_interpolator={...}: Matter power spectrum interpolator in $$(z, k)$$. Takes "z": [list_of_evaluated_redshifts], "k_max": [k_max], "extrap_kmax": [max_k_max_extrapolated], "nonlinear": [True|False], "vars_pairs": [["delta_tot", "delta_tot"], ["Weyl", "Weyl"], [...]]}. Non-linear contributions are included by default. Note that the nonlinear setting determines whether nonlinear corrections are calculated; the get_Pk_interpolator function also has a nonlinear argument to specify if you want the linear or nonlinear spectrum returned (to have both linear and non-linear spectra available request a tuple (False,True) for the nonlinear argument). All k values should be in units of 1/Mpc.
• Pk_grid={...}: similar to Pk_interpolator except that rather than returning a bicubic spline object it returns the raw power spectrum grid as a (k, z, PK) set of arrays.
• sigma_R{...}: RMS linear fluctuation in spheres of radius R at redshifts z. Takes "z": [list_of_evaluated_redshifts], "k_max": [k_max], "vars_pairs": [["delta_tot", "delta_tot"],  [...]]}, "R": [list_of_evaluated_R]. Note that R is in Mpc, not h^{-1} Mpc.
• Hubble={'z': [z_1, ...]}: Hubble rate at the requested redshifts. Get it with get_Hubble().
• angular_diameter_distance={'z': [z_1, ...]}: Physical angular diameter distance to the redshifts requested. Get it with get_angular_diameter_distance().
• comoving_radial_distance={'z': [z_1, ...]}: Comoving radial distance from us to the redshifts requested. Get it with get_comoving_radial_distance().
• sigma8_z={'z': [z_1, ...]}: Amplitude of rms fluctuations $$\sigma_8$$ at the redshifts requested. Get it with get_sigma8().
• fsigma8={'z': [z_1, ...]}: Structure growth rate $$f\sigma_8$$ at the redshifts requested. Get it with get_fsigma8().
• k_max=[...]: Fixes the maximum comoving wavenumber considered.
• Other derived parameters that are not included in the input but whose value the likelihood may need.
calculate(state, want_derived=True, **params_values_dict)

Do the actual calculation and store results in state dict

Parameters: state – dictionary to store results want_derived – whether to set state[‘derived’] derived parameters params_values_dict – parameter values None or True if success, False for fail
get_Cl(ell_factor=False, units='FIRASmuK2')

Returns a dictionary of lensed CMB power spectra and the lensing potential pp power spectrum.

Set the units with the keyword units=number|'muK2'|'K2'|'FIRASmuK2'|'FIRASK2' (default: ‘FIRASmuK2’ gives FIRAS-calibrated microKelvin^2, except for the lensing potential power spectrum, which is always unitless). Note the muK2 and K2 options use the model’s CMB temperature; experimental data are usually calibrated to the FIRAS measurement which is a fixed temperature. The default FIRASmuK2 takes CMB C_l scaled by 2.7255e6^2 (to get result in muK^2).

If ell_factor=True (default: False), multiplies the spectra by $$\ell(\ell+1)/(2\pi)$$ (or by $$\ell^2(\ell+1)^2/(2\pi)$$ in the case of the lensing potential pp spectrum).

get_sigma8_z(z)

Present day linear theory root-mean-square amplitude of the matter fluctuation spectrum averaged in spheres of radius 8 h^{−1} Mpc.

The redshifts must be a subset of those requested when must_provide() was called.

get_fsigma8(z)

Structure growth rate $$f\sigma_8$$, as defined in eq. 33 of Planck 2015 results. XIII. Cosmological parameters, at the given redshifts.

The redshifts must be a subset of those requested when must_provide() was called.

get_source_Cl()

Returns a dict of power spectra of for the computed sources, with keys a tuple of sources ([source1], [source2]), and an additional key ell containing the multipoles.

get_CAMBdata()

Get the CAMB result object (must have been requested as a requirement).

Returns: CAMB’s CAMBdata result instance for the current parameters
get_can_provide_params()

Get a list of derived parameters that this component can calculate. The default implementation returns the result based on the params attribute set via the .yaml file or class params (with derived:True for derived parameters).

Returns: iterable of parameter names
get_version()

Get version information for this component.

Returns: string or dict of values or None
get_helper_theories()

Transfer functions are computed separately by camb.transfers, then this class uses the transfer functions to calculate power spectra (using A_s, n_s etc).