wolffem / aquimrichartejupyternotebooksclass_ede

Modified version of CLASS to work with EDE models.

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; evan_mcdonough at brown.edu
• Michael W. Toomey; michael_toomey at brown.edu

Files

All CLASS files in the directory class, the relevant file for the sampler Cobaya is in the directory cobaya.

Installation

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

$ make class

To utilize Cobaya with CLASS_EDE replace stock classy.py with the modified version here.

Examples

Python

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

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 .

Modifications to Cobaya

One should replace stock classy.py from Cobaya with the modified version here.

(1) Error handling:

Cobaya can bypass a CLASS "CosmoComputationError" by assigning it zero likelihood and then continuing to sample. This has been implemented for extremely large values of fEDE, and for cosmologies where P_k_max_h/Mpc=15 [or the value set in _DES_prototype.py] is not sufficient to compute P(k).

(2) For RSD:

Get fsigma8(z) from CLASS