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

Abstract

We use a particular machine learning approach, called the genetic algorithms (GAs), in order to place constraints on deviations from general relativity (GR) via a possible evolution of Newton's constant $\ensuremath{\mu}\ensuremath{\equiv}{G}_{\mathrm{eff}}/{G}_{\mathrm{N}}$ and of the dark energy anisotropic stress $\ensuremath{\eta}$, 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 $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model and another on a model with an evolving Newton's constant, dubbed $\ensuremath{\mu}\mathrm{CDM}$. We find that the GA reconstructions of $\ensuremath{\mu}(z)$ and $\ensuremath{\eta}(z)$ can be constrained to within a few percent of the fiducial models and in the case of the $\ensuremath{\mu}\mathrm{CDM}$ mocks, they can also provide a strong detection of several $\ensuremath{\sigma}\mathrm{s}$, thus demonstrating the utility of the GA reconstruction approach.

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