Machine learning constraints on deviations from general relativity from the large scale structure of the Universe

We use a particular machine learning approach, called the genetic algorithms (GA), in order to place constraints on deviations from general relativity (GR) via a possible evolution of Newton's constant $\mu\equiv G_\mathrm{eff}/G_\mathrm{N}$ and of the dark energy anisotropic stress $\eta$, both defined to be equal to one in GR. Specifically, we use a plethora of background and linear-order perturbations data, such as type Ia supernovae, baryon acoustic oscillations, cosmic chronometers, redshift space distortions and $E_g$ data. We find that although the GA is affected by the lower quality of the currently available data, especially from the $E_g$ data, the reconstruction of Newton's constant is consistent with a constant value within the errors. On the other hand, the anisotropic stress deviates strongly from unity due to the sparsity and the systematics of the $E_g$ data. Finally, we also create synthetic data based on a next-generation survey and forecast the limits of any possible detection of deviations from GR. In particular, we use two fiducial models: one based on the cosmological constant $\Lambda$CDM model and another on a model with an evolving Newton's constant, dubbed $\mu$CDM. We find that the GA reconstructions of $\mu(z)$ and $\eta(z)$ can be constrained to within a few percent of the fiducial models and in the case of the $\mu$CDM mocks, they can also provide a strong detection of several $\sigma$s, thus demonstrating the utility of the GA reconstruction approach.