CLASS_EDE: CLASS for Early Dark Energy

A modified version of the publicly available Einstein-Boltzmann code CLASS to implement Early Dark Energy (EDE). CLASS_EDE solves for the evolution of the scalar field perturbations directly using the perturbed Klein-Gordon equation and implements adiabatic initial conditions for the scalar field fluctuations. The code allows one to specify the EDE model parameters in terms of the particle physics parameters f and m or effective EDE parameters f_EDE and z_c.

See Hill et al. where CLASS_EDE is implemented to test the validity of the EDE model.

CLASS edited by

• J. Colin Hill; jch2200 at columbia.edu
• Evan McDonough; e.mcdonough at uwinnipeg.ca
• Michael W. Toomey; mtoomey at mit.edu

Installation

After cloning or downloading the repository, compile CLASS_EDE with make.

$ make class

Examples

Python

Jupyter notebooks with worked out examples in Python can be found in notebooks-ede.

C

CLASS_EDE can be run in C just as normal CLASS. See explanatory-EDE.ini for EDE implementation details.

$ ./class explanatory-EDE.ini

Modifications to CLASS

Modifications are explained below. All edits are flagged in the code by "EDE-edit".

(1) Scalar field parameters:

The syntax for entering scalar field parameters has been changed to the following: the user must input one of {m_scf,log10m_scf,log10z_c} and one of {f_scf,log10f_scf,fEDE}, as well the power law n_scf, the initial field displacement thetai (=\phi_i /f), and an additive constant CC_scf. The units of f_scf and m_scf are eV. Note that fEDE may only be input if log10z_c is also input.

(2) Background dynamics:

The scalar field is implemented in background.c in a seemingly trivial way, with the key detail that V(\phi) includes an additive constant. This is used as the "tuning parameter" in all CLASS runs, and the explicit Omega_Lambda is set to 0.

(3) To run as LCDM:

Works the same as normal CLASS. Note the CC is now handled by Omega_Lambda!

(4) Perturbations:

Adiabatic initial conditions for the scalar field are implemented in perturbations.c .

(5) fEDE and z_c:

We have implemented the calculation of f_EDE and z_c into the background module and python wrapper. We have also implemented a the built-in shooting algorithm for fEDE and log10z_c, in input.c, allowing the user to specify {fEDE,log10z_c,thetai} and CLASS will find the corresponding {f_scf,m_scf,thetai}.

(6) Exit codes:

Large values of f_{EDE} (>.9) will crash CLASS (often the thermodynamics module). Such large values are not physical. To avoid crashing an MCMC run, an error code has been added to background.c, "fEDE = %e instead of < 0.5"

(7) fsigma8:

Defined a function fsigma8 = f(z)*sigma8(z) for use with RSD likelihoods.

(8) P_k_max_h/Mpc too small:

CLASS run in c, i.e. with the command ./class xxxx.ini , throws a warning if you try to compute the non-linear P(k) at high-z, requiring too high k values (as set by P_k_max). The python wrapper flags this warning as a CosmoSevereError and will kill the evaluation. This will crash an MCMC sampler like Cobaya; the DES likelihood sets P_k_max=15 (overwriting the user-input value), which is too low for some corners of parameter space in certain models. This problem has been resolved by CosmoSevereError-->CosmoComputationError in classy.pyx, and with an exception added to Cobaya's classy.py .

The previous version of class_ede can be found here.