4.1. Before starting¶

The problem is set up through a .ini file containing the parameters, priors, model type, data files to be used and tex strings for plotting. The program creates a folder in the working directory with the same name of this .ini file, if not already existing. Another folder is created with the date and time for the output of each run of the code, but you can always continue a previous run from where it stopped, just giving the folder name instead of the .ini file.

The folder epic is the root of the project. The python codes are in the EPIC source folder, where the .ini files should also be placed. The default working directory is the EPIC’s parent directory, i.e., the epic repository folder.

Changing the default working directory¶

By default, the folders with the name of the .ini files are created at the repository root level. But the chains can get very long and you might want to have them stored in a different drive. In order to set a new default location for all the new files, run:

python define_altdir.py

This will ask for the path of the folder where you want to save all the output of the program and keep this information in a file altdir.txt. If you want to revert this change you can delete the altdir.txt file or run again the command above and leave the answer empty when prompted.

The parameters names¶

Each cosmological parameter already implemented has a name to be used in the code that must be respected in the .ini file. The table below lists some of the parameters, their definitions and their names in the program.

Parameter	Description	Name
\(h\)	Reduced Hubble constant	`h`
\(\Omega_{b0} h^2\)	Physical baryonic density parameter	`Obh2`
\(\Omega_{c0} h^2\)	Physical cold dark matter density parameter	`Och2`
\(\Omega_{r0} h^2\)	Physical radiation density parameter	`Orh2`
\(\Omega_{b0}\)	Baryonic density parameter	`Ob0`
\(\Omega_{c0}\)	Cold dark matter density parameter	`Oc0`
\(\Omega_{m0}\)	Matter (baryons plus DM) density parameter	`Om0`
\(\Omega_{d0}\)	Dark energy density parameter	`Oc0`
\(w_d\)	Dark energy equation-of-state parameter	`w` or `wd`

The structure of the `.ini` file¶

Let us work with an example, with a simple flat \(\Lambda\text{CDM}\) model. Suppose we want to constrain its parameters with \(H(z)\), supernovae data, CMB shift parameters and BAO data. The model parameters are the reduced Hubble constant \(h\), the present-day values of the physical density parameters of dark matter \(\Omega_{c0} h^2\), baryons \(\Omega_{b0} h^2\) and radiation \(\Omega_{r0} h^2\). We will not consider perturbations, we are only constraining the parameters at the background level. Since we are using supernovae data we must include a nuisance parameter \(M\), which represents a shift in the absolute magnitudes of the supernovae. It is also possible to use the full JLA catalogue with this program. In this case, we would have to include also the nuisance parameters \(\alpha\), \(\beta\) and \(\Delta M\) from the light-curve fit. The first section of the LCDM.ini file defines the priors and at the same time the names of the parameters. They must be inserted in the following form:

## PRIORS

h       0.6     0.8     4e-4
Och2    0.08    0.20    2e-4
Obh2    0.01    0.08    5e-5
Orh2    4e-5    8e-5    2e-7
M       -0.3    0.3     2e-3    nuisance

## end of priors

Delimiting lines are mandatory: the line defining the beginning of the priors section must contain the word PRIORS. The priors are read until the word end is found. The first column are the names of the parameters in the code. The second and third columns set the flat priors intervals. The fourth column is optional. Gaussian priors are also supported. In this case, one should add gaussian at the end of the line. The second and third values will then be the Gaussian parameters \(\mu\) and \(\sigma\) instead. It gives the standard deviation for each parameter in the covariance of the proposal function. The values will vary according to the problem but a first guess can be 1/10 or other small fraction of the prior interval. Notice that the nuisance parameter is signaled as such by the word nuisance at the end of the line. To remove a parameter, you can just comment out its line with the character #. If the parameter removed is necessary for the model predictions then a default value will be assumed.

After the priors come the type of the model, needed to select the proper functions in the calculation of model predictions, and a display name, both with identifiers MODEL and NAME. They are signaled in the .ini file in the same way of the priors, but since they are single-line the final delimiter is not needed:

## MODEL
lcdm

## NAME
$\Lambda$CDM

The class model could also be wcdm for a \(w\text{CDM}\) model, of which \(\Lambda\text{CDM}\) is a special case. Omitting the dark energy equation of state parameter would automatically set it to -1. Notice that the use of \(\LaTeX\) input is allowed in the model name. Next is the list of observables to be used, with the filename or directory with the data. The list is read until an occurrence of end is found:

## DATA files

JLAsimple               jla_likelihood_v4
Planck2015_distances    Planck2015_LCDM
BAO                     BAO-6dF+SDSS+BOSS+Lyalpha+WiggleZ.txt
CosmicChrono            thirtypointsHz.txt

## end of data

Finally, tex strings must be given to be used in the plots:

## TEX REPRESENTATION

h           h
Och2        \Omega_{c0}h^2
Obh2        \Omega_{b0}h^2
Orh2        \Omega_{r0}h^2
Oc0         \Omega_{c0}
Ob0         \Omega_{b0}
Or0         \Omega_{r0}
Od0         \Omega_{d0}
Om0         \Omega_{m0}
M           \Delta{M}

# end of tex

Here, strings for the derived parameters are also needed. The tex strings should not contain any spaces. If you need to separate a tex command from a following variable, use {} instead, as is done for the last parameter in this example. Also note that the first column needs to be consistent with the names given in the priors and also in the parameters_names.txt dictionary.

To summarize, we end up with the LCDM.ini file in the EPIC folder looking like this:

## PRIORS

h       0.6     0.8     4e-4
Och2    0.08    0.20    2e-4
Obh2    0.01    0.08    5e-5
Orh2    4e-5    8e-5    2e-7
M       -0.3    0.3     2e-3    nuisance

## end of priors


## MODEL
lcdm

## NAME
$\Lambda$CDM

## DATA files

JLAsimple               jla_likelihood_v4
Planck2015_distances    Planck2015_LCDM
BAO                     BAO-6dF+SDSS+BOSS+Lyalpha+WiggleZ.txt
CosmicChrono            thirtypointsHz.txt

## end of data

## TEX REPRESENTATION

h           h
Och2        \Omega_{c0}h^2
Obh2        \Omega_{b0}h^2
Orh2        \Omega_{r0}h^2
Oc0         \Omega_{c0}
Ob0         \Omega_{b0}
Or0         \Omega_{r0}
Od0         \Omega_{d0}
Om0         \Omega_{m0}
M           \Delta{M}

# end of tex

4.1. Before starting¶

Changing the default working directory¶

The parameters names¶

The structure of the .ini file¶

The structure of the `.ini` file¶