Introducing new models

For a step-by-step example see the exercises on hi_class (Cosmo Tools 2017 @ IFT, Madrid)

All the hi_class related variables are suffixed by the letters smg, standing for scalar modified gravity. This notation allows one to find all the modifications simply by typing grep smg */*.* in the terminal from the hi_class directory. The model for the background expansion and the $\alpha$ functions are set through expansion_model_smg and gravity_model_smg variables. The only methods that depend explicitly on the model are the following:

• input_read_parameters reads the value of gravity_model_smg and expansion_model_smg, together with the parameters describing the parameterisation and the expansion. Then it applies different options and tests depending on the specific case.
• background_gravity_functions computes the value of $\rho_{\rm DE}$ and the $\alpha$ functions and obtains the value of the Hubble rate by solving the Friedmann equation.
• background_initial_conditions sets the initial conditions in the case that some variable needs to be integrated (e.g. the effective Planck mass $M_*^2$ in terms of $\alpha_M$).
• background_gravity_parameters prints the values of the expansion and gravity model and their parameters. This is done automatically if the value of background_verbose is high.

The above methods run a loop over the different expansion and gravity models, as determined by the variables gravity_model_smg and expansion_model_smg in the background structure, with the different possibilities specified through enum gravity_model and enum expansion_model at the beginning of background.h. Other modifications within hi_class do not depend explicitly on the model under consideration. This is the case of the modified perturbation equations (contained in perturb_einstein), which only depend on the values of the α functions and other background quantities.

Introducing a new model (for either expansion or gravity) on top of the ones available by default (summarised in table 1 of the hi_class paper) is as simple as finding all the instances of an already existing case (i.e. type grep propto_omega */*.* in the terminal from the hi_class directory), copying these functions and adapting them to the physics of the new model.

Planck Mass variation: The effective Planck mass $M_^2$ and $\alpha_M$ are related by $ \alpha_M}\equiv\frac{\mathrm{d}\ln M_{}^{2}}{\mathrm{d}\ln a}$ For models with variations of the effective Planck mass $M_*^2$ there are two possibilities:

• By setting M_pl_evolution_smg == _TRUE_ (in input.c) $M_*^2$ is obtained by integrating $\alpha_M$ (with an initial condition)
• Otherwise $\alpha_M$ will be obtained by differentiating $M_*^2$.

This option can be set in input.c for each model.