CHARM2.0: Cosmic History Agnostic Reconstruction Method

Reconstructing cosmic expansion history (cosmic energy density as a function of redshift) without assuming a specific type of matter distribution in the Universe. Data are distance moduli and redshifts from Supernovae Ia from the Union2.1 compilation and Pantheon+ Analysis.

Powered by NIFTy (v8).

Original CHARM by Natalia Porqueres et al. 2017 + geoVI instead of an iterative MAP approach.

Requirements

• NIFTy can be installed using pip:

  pip install nifty8
  

• If necessary, after NIFTy installation: Numpy, Scipy, Pandas, pickle, matplotlib, seaborn

Note

Pickle files will be overwritten if new inference run starts and pickles are not manually renamed. See folder structure down below.

Warning

When visualizing the power spectrum of the posterior by using the function visualize_and_analyze_posterior_power_spectrum(), the mean and uncertainty of fluctuations and loglogavgslope is returned. This only holds if the parameters of the correlated field model have no standard deviation, i.e. the second number in the parameter tuple is e.g. $10^{-16}$. These parameters are found by fitting the posterior power spectrum in a log-log coordinate system and use a preliminary numerical relation that will be replaced in the future, so interpret these values with caution. This numerical relation also only holds for fixed length of the signal domain, which has been chosen here to be $x_{max}=6.7$.

Usage and Workflow

• Download a local copy of this project per the green code button above (e.g. as zip). Unpack, move into directory and run

  python synthetic_catalogue.py
  

• There will be four matplotlib figures showing up, each need to be closed for the program to continue running

• Inference run with synthetic data: synthetic_catalogue.py. Inference run with real data: cosmological_tomography.py

• After inference run, posterior samples can be re-visualized in the program visualize_pickle_data.py in the 📂pickles subfolder, by calling

    posterior_realizations = unpickle_me_this("synthetic_posterior_realizations.pickle")
  

• For the visualization from the pickles directory, the keyword from_pickles_folder will be have to be set to True for each plot function

• At the beginning of the inference scripts following boolean variables can be set: switch1-8; set if visualizations of data, posterior, power spectrum etc. should be shown via plt.show() or saved in the 📂figures folder. use_union_data; Uses Union2.1 data if True, Pantheon+ data if False

.
├── 🐍 cosmological_tomography.py    # Inference with real data
├── 🐍 synthetic_catalogue.py        # Inference with synthetic data 
├── 📂 figures                       # Place where figures are stored. Contains figures examples.
├── 📂 raw data                      # Folder containing moduli, redshifts, covariances ...
├── 📂 helpers                       
│   ├── 🐍 plotters.py               # Convenience plotting functions
│   └── 🐍 functions.py              # Important custom operators and other helper functions
│   
└── 📂pickles                        # Important subfolder: Contains pickles (serialized python objects) from posterior samples.
    └── 🐍 visualize_pickle_data.py  # After inference run, posterior samples can be re-visualized here.

Elements of time

Runtime synthetic data $\approx 3-5 \hspace{1mm}$ min

Runtime Union2.1 data $\approx 40-60 \hspace{1mm}$ min

Runtime Pantheon+ data $\approx 10-15 \hspace{1mm}$ hrs