Planck constraints:

tensor-to-scalar ratio ($r$) vs spectral index ($n_s$) Plot

This repository provides tools to visualize constraints on the spectral index ($n_s$) and tensor-to-scalar ratio ($r$) using data derived from the Planck collaboration's publication: "Planck 2018 results. X. Constraints on inflation."

Overview

The repository includes:

• PLANCK Data.csv: Contains the extracted boundary data for 68% and 95% confidence level (CL) regions from the original plot. This has been done by hand, using Planck2018_BK14_120mm.pdf file in an online tool automeris.io.
• Planck Constraints Plot.nb: A Wolfram Mathematica notebook to visualize the Planck data constraints and compare with your model.
• Planck Constraints Plot.py: A python script to visualize the Planck data constraints.
• plot.pdf: Example output plot generated by the notebook.
• Planck2018_BK14_120mm.pdf: The original $r$ vs $n_s$ graph from the Planck 2018 paper.

Features

1. Data Extraction:

   • The PLANCK Data.csv file contains the extracted boundaries for the 68% and 95% CL regions from the Planck constraints plot.

2. Visualization:

   • The Mathematica notebook, Planck Constraints Plot.nb, generates a plot showing the constraints on $r$ and $n_s$ based on Planck data.

3. Comparison with Models:

   • If you have a theoretical model that predicts the relationship between $n_s$ and $r$, or their dependencies on the number of e-folds ($N$), you can overlay these predictions on the Planck constraints.
   • The notebook produces a plot (plot.pdf) that compares your model's predictions with observational data.

How to Use

1. Prepare Your Model:

   • If you want to compare your model's predictions with data, derive the $n_s$ and $r$ values (or their dependence on $N$ or each other).

2. Run the Notebook:

   • Open Planck Constraints Plot.nb in Mathematica.
   • Follow the instructions

3. Generate the Plot:

   • Execute the notebook to produce a comparison plot. The resulting visualization will highlight how well your model aligns with observational constraints.

Files

File Name	Description
PLANCK Data.csv	Extracted boundary data for 68% and 95% CL regions from Planck constraints.
Planck Constraints Plot.nb	Mathematica notebook for data visualization and comparison with models.
Planck Constraints Plot.py	Do the same thing with mathematica notebook but in python
plot.pdf	Example output plot comparing constraints with a sample model.
Planck2018_BK14_120mm.pdf	Original $r$ vs $n_s$ constraints plot from the Planck 2018 publication.
README.md	This documentation file.

Prerequisites

• Software: Mathematica (to run the notebook).
• Knowledge: Familiarity with inflationary models and the $r$ vs $n_s$ parameter space.

References

• Planck Collaboration (2018). Planck 2018 results. X. Constraints on inflation.

License

This project is open-source and released under the MIT License. Refer to the LICENSE file for details.

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For any questions or issues, feel free to create an issue or contribute to the repository!