• Author: Kay Lehnert
• Publications:
  • Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
  • PhD Thesis

This repository contains the CLASS¹, MontePython², and Mathematica ³ files for a swampland-inspired model of dark energy in the form of quintessence as a scalar field that is interacting with dynamical dark matter. The interactions and mathematical details of the model are all explained in my PhD thesis ⁴.

The source code in this repository is a fork of the Cosmic Linear Anisotropy Solving System (CLASS) v3.3.3 by Julien Lesgourgues, Thomas Tram, Nils Schoeneberg et al.

If you want to use this code, please cite CLASS II: Approximation schemes as well as my thesis.

The Markov chain Monte Carlo (MCMC) runs to find the best-fit parameters of the model and compare it to $\Lambda$CDM were performed using MontePython v3.6.1 by Thejs Brinckmann, Benjamin Audren, et al.

This repository contains

• parameter-files
• best-fit values
• covariance matrices

These files allow you to fully reproduce my findings:

• The parameter-files recreate the exact MCMC-pipeline, choosing the likelihoods and starting parameters.
• The best-fit values can be used to accelerate the reproduction of my MCMC chains. Those can be passed on to MontePython as a starting value, i.e. your MCMC will then start at the best-fit value right away.
• The covariance matrices can also be passed to MontePython, as initial guess. This also accelerates reproduction of my results.

The Markov chains themselves are too big to be stored on GitHub. You can find them at Zenodo. This allows you to directly analyse the chains yourself.

The following naming scheme is applied to these files:

Type of Dark Matter    -    Type of Dark Energy                                         -    Data Set                                           .    file-type
< CDM | H | I >        -    < pL | c | h | pNG | iPL | exp | SqE | Bean | DoublExp >    -    < plik | PPDESI | PlikPPDESI | CMB-SPA | Full >    .    < param | bestfit | covmat >

For example, the parameter file to test standard CDM with quintessence in the form of a simple exponential scalar field tested against Plank 2018 data is CDM-exp-plik.param.

The types of dark matter are explained in the Wiki, and so are the types of dark energy. The data sets are the following:

• plik: Planck 2018 (Plik),
• PPDESI: PantheonPlus + DESI DR2
• PlikPPDESI: Planck 2018 (Plik) + PantheonPlus + DESI DR2
• CMB-SPA: SPT-3G D1 + ACT DR6 + Planck (Plik)
• Full: CMB-SPA + PantheonPlus + DESI DR2

The Mathematica notebooks contain the derivation of the governing equations, equations of motions, the potentials and their derivatives, as well as additional tests for swampland-compatibility.

• xPert.nb uses the xAct package xPert to derive metric-independent equations of motions from the Lagrangian and the stress–energy tensor. It includes first-order perturbations.
• xPand.nb takes those equations and expresses them with respect to a metric and simplifies the equations using the Newtonian gauge. This notebook uses the xPand plugin.
• rho_cdm.nb computes the derivatives of the interacting dark matter mass $m\left(\phi\right)=1-\tanh\left(c\phi\right)$ and expresses them in trigonometric functions.

My PhD thesis can be found on arXiv, MURAL, as well as in the folder Thesis. This folder contains, besides the PDF, the LaTeX code. The code acts as a template for similar documents and makes the equations available for typesetting.

The thesis template is an adaptation of TeXtured with inspiration taken from Tony Zorman. It is compliant with Maynooth's Doctoral Thesis Layout Recommendations.

Our research complies with FAIR data principles:

• Findable: All data is explained and made available on this GitHub repository. The naming schemes are explained in this README. Keywords are used for Search Engine Optimisation and clear reference.
• Accessible: All data is available on this GitHub repository, except for the Markov chains, which are available on Zenodo. Furthermore, the thesis is available on arXiv and on the Maynooth University Research Archive Library (MURAL)
• Interoperable:
  • The thesis' LaTeX code can be used with any LaTeX engine. If none is available, a PDF output is provided on arXiv, MURAL, as well as here on GitHub.
  • The Mathematica notebooks are provided here. These are not per se 'interoperable', since the closed source software Mathematica must be used to read them. To mitigate this shortcoming, PDF prints of the evaluated notebooks are provided here.
  • The CLASS source code can be compiled with any C compiler.
  • The MontePython related setup files can be used with the open access tool MontePython.
  • The MontePython chains can be analyzed with various tools. Besides open source alternatives, there is Python as well as MATLAB code for analysing the chains in the CLASS folder.
• Reusable:
  • The LaTeX code can act as a template for other theses. The equations can be used for other papers.
  • The Mathematica notebooks can be used to derive the perturbed equations of motions for other systems with only slight modifications, in particular setting the corresponding Lagrangian respectively action terms.
  • The CLASS code can easily be extended by implementing additional types of dark matter or dark energy potentials. Also, except for dark energy related changes, no breaking changes were implemented compared to the official CLASS code. Therefore, our code is perfectly compatible and suitable for extended evaluations of other cosmological models that are already implemented in the official CLASS.
  • The MCMC chains can be analysed with other tools to do additional statistics on them.

The energy consumptions for all involved devices is offset at climeworks. Therefore, I consider my PhD as probably carbon-neutral.

Please reach out to me if you would like to collaborate on a similar project, or if you find bugs in my code!