🍬 CANDI

Code for ANalysis of modified Distance-duality with cosmological Inference

Welcome to the CANDI code!

This repository provides a cosmological analysis code to place constraints from supernovae (SN), baryon acoustic oscillations (BAO), and gravitational waves (GW) through distance measurements.

It allows you to:

• Run likelihood analyses using current and simulated data.
• Implement custom cosmologies beyond ΛCDM, including models that break the distance–duality relation (DDR).
• Use different samplers (MCMC or nested sampling) to obtain posterior constraints.

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✨ What’s inside?

Here you can find:

• 📈 Likelihoods for SN, BAO, and simulated Einstein Telescope (ET) standard sirens.
• 🧩 A custom cosmology API (Application Programming Interface) that lets you plug in your own models easily.
• 🔓 Tools to test DDR-breaking parametrizations.
• 🎲 Built-in support for Cobaya MCMC and Nautilus nested sampling.
• 📂 Ready-to-use example settings and demo notebooks to get you started quickly.

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⚙️ Installation

Requirements

• Python ≥ 3.9
• numpy, scipy, pandas, pyyaml
• cobaya, camb, getdist, nautilus

⚡ Quickstart

# Clone the repository
git clone https://github.com/chiaradeleo1/CANDI.git
cd CANDI

# Install dependencies
pip install -r requirements.txt

📂 Data

The data are not included in this repository.

To reproduce the results in of (arXiv:2505.13613), you can simulate datasets and run chains using the package in Zenodo (https://doi.org/10.5281/zenodo.17043955).

The package contains a notebook to generate simulated data for:

• 🟠 LSST Supernovae (SN)
• 🔵 SKAO Baryon Acoustic Oscillations (BAO)
• 🟣 Einstein Telescope (ET) Standard Sirens (GW)

The settings files to run the different scenarios discussed in the paper are provided in the settings/ folder and can be run using run_paper.py

How to run it?

Each run is controlled via a YAML settings file.

Key entries include:

• output: name of the run / output folder
• SN_data, BAO_data, GW_data: specify which datasets to include
• cosmology: choose the expansion model
• DDR_options: enable DDR-breaking models
• sampler: choose between mcmc or nautilus

Examples of YAML files can be found in the settings/ folder for different cosmological models, while interactive notebook examples are provided under the name DEMO_

🧩 Custom Cosmology

You can implement your own cosmological model by following
theory_code/expansion_models/example_custom_cosmology.py.

A valid cosmology must provide at least:

• H(z) — Hubble expansion rate
• comoving(z) — comoving distance

With this interface you can:

• ✨ Implement your own DDR-breaking model (see e.g. arXiv:/2505.13613).
• 🌌 Modify the expansion history of the universe by introducing alternative cosmologies (see e.g. arXiv:2507.13890).

This makes it easy to go beyond ΛCDM and test custom scenarios with SN, BAO, and GW probes.

📜 Citation

• If you use this code, please cite our papers:

  C. De Leo et. al , Distinguishing Distance Duality breaking models using electromagnetic and gravitational waves measurements, arXiv:2505.13613

  E. Fazzari, C. De Leo et. al , Investigating f(R)-Inflation: background evolution and constraints, arXiv:2507.13890

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