4.2. The datasets

We list and detail below the datasets already implemented and give instructions on how to include other data.

Type Ia supernovae

Two types of analyses can be made with the JLA catalogue. Here we are using the binned data consisting of distance modulus estimates at 31 points (defining 30 bins of redshift). This dataset is select via the JLAsimple entry in the list of data sources. If you want to use the full dataset (which makes the analysis much slower since it involves three more nuisance parameters and requires the program to invert a 740 by 740 matrix at every iteration for the calculation of the JLA likelihood), insert SNeJLA instead. Also, you need to download the full data from http://supernovae.in2p3.fr/sdss_snls_jla/ReadMe.html or from my copy on Google Drive. Since the data files are too big, EPIC includes only the jla_likelihood_v4/data folder. In this case you will need the jla_likelihood_v4/covmat. Make sure to properly include it in you installation directory.

Either way, the argument is the same data folder jla_likelihood_v4. Note that the binned dataset introduces one nuisance parameter M, representing an overall shift in the absolute magnitudes, and the full dataset introduce other four nuisance parameters related to the light-curve parametrization. See Betoule et al. (2014) [1] for more details.

Note

This version of EPIC supports version V4 (June 2014) of the dataset release. Current version is V6 (March 2015). An update to implement use of V6 is being considered for the near future.

CMB distance priors

Constraining models with temperature or polarization anisotropy amplitudes is not currently implemented. However, you can include the CMB distance priors from Planck2015 with Planck2015_distances. These data consist of an acoustic scale \(l_A\), a shift parameter \(R\) and the physical density of baryons \(\Omega_{b0}h^2\). You can choose between the data for \(\Lambda\text{CDM}\), \(w\text{CDM}\) and \(\Lambda\text{CDM} + \Omega_k\) models [2], specifying the folders Planck2015_LCDM, Planck2015_wCDM or Planck2015_LCDM+Omega_k, respectively.

BAO data

Measurements of the baryon acoustic scales from the Six Degree Field Galaxy Survey (6dF), the Main Galaxy Sample of Data Release 7 of Sloan Digital Sky Survey (SDSS-MGS), the LOWZ and CMASS galaxy samples of the Baryon Oscillation Spectroscopic Survey (BOSS-LOWZ and BOSS-CMASS), the WiggleZ Dark Energy Survey and the distribution of the Lyman \(\alpha\) forest in BOSS (BOSS-Ly) are compiled file BAO-6dF+SDSS+BOSS+Lyalpha+WiggleZ.txt. The subsamples BAO-6dF+SDSS+BOSS+Lyalpha.txt and BAO-6dF.txt are also available, the first excluding the WiggleZ data and the second only with the 6dF data. Since these files simply contain the redshift of the measurement, the value of the characteristic ratio \(r_{\text{BAO}}(z) \equiv r_s(z_d)/d_V(z)\) between the sound horizon \(r_s\) at decoupling time (\(z_d\)) and the effective BAO distance \(d_V\) and the measurement error, it is really simple to remove or add new measurements of this observable.

\(H(z)\) data

These are the cosmic chronometer data. 30 measurements of the Hubble expansion rate \(H(z)\) at redshifts between 0 and 2, plus a \(2.4\%\) precision local measure of \(H_0\). The values of redshift, \(H\) and the uncertainties are given in the file thirtypointsHz.txt.

\(f\sigma_8\) data

Large-scale structure data from redshift-space distortion and peculiar velocity measurements giving the growth rate times the RMS amplitude of matter perturbations \(f \sigma_8(z)\) can also be used. Notice that in this case you need to provide an analytic evaluation of the growth rate (for example, as \(f = \Omega_m^{\gamma}\)) in your model since this program does not evolve perturbations numerically at the present moment. See for example the implementation in Marcondes et al. (2016) [3].

Including other data

You can include other data if you want. In the simplest case, you will have measurement values and error bars for a certain quantity, say \(f(z)\), at given points. Put them on a text file in three columns separated by TAB or spaces, as in, for example, the SDSS+BOSS.txt file:

0.15        4.47        0.17
0.32        8.47        0.17
0.57        13.77       0.13

Choose a label for this dataset and put it in the .ini file in the data files section:

my_data     my_data_file.txt

Next, you need to tell the code how to read this new type of dataset. In this simple case you add a function like:

def my_data(obsble):
    return simplest_data(obsble, 'my_data', r'$f(z)$')

to the load_data module. The name of this function must be the same as the label that goes in the .ini file. This function, or its more complicated equivalent, is the only change needed to be made in the load_data.py file. In the simplest_data function call, the obsble variable carries the dataset file information (the filename or directory), the second argument is a string to be displayed indicating that your data is loaded. The third argument is a raw string, possibly including \(\LaTeX\) notation, to be displayed in the triangle plots compounding the label that describes the datasets used in this analysis when you plot together results from more than one analysis.

You then need to define the likelihood calculation in the likelihood module. At the end of the file, add to the dictionary allprobes an entry with the key 'my_data' (again the same label) and the likelihood function, say my_data_likelihood, as its value. For a Gaussian likelihood, this function can be:

def my_data_likelihood(datapoints, cosmology):
    return simple(datapoints, observables.my_f, cosmology)

Now, as you may have already figured out, the next step is to add the theoretical calculation my_f of your observable \(f\) to the observables.py file. Of course, this will vary with each case. Do not forget to use the model attribute of the Cosmology class object named cosmology to set different calculations according to each cosmological model you might want to use.

[1]	Betoule M. et al. “Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples”. Astronomy & Astrophysics 568, A22 (2014).

[2]	Huang Q.-G., Wang K. & Wang S. “Distance priors from Planck 2015 data”. Journal of Cosmology and Astroparticle Physics 1512, 022 (2015).

[3]	Marcondes R. J. F., Landim R. C. G., Costa A. A., Wang B. & Abdalla E. “Analytic study of the effect of dark energy-dark matter interaction on the growth of structures”. Journal of Cosmology and Astroparticle Physics 1612, 009 (2016).