Cosmology in the era of Euclid and the Square Kilometre Array

Theoretical uncertainties on non-linear scales are among the main obstacles to exploit the sensitivity of forthcoming galaxy and hydrogen surveys like Euclid or the Square Kilometre Array (SKA). Here, we devise a new method to model the theoretical error that goes beyond the usual cut-off on small scales. The advantage of this more efficient implementation of the non-linear uncertainties is tested through a Markov-Chain-Monte-Carlo (MCMC) forecast of the sensitivity of Euclid and SKA to the parameters of the standard $\mathrm{\Lambda }$CDM model, including massive neutrinos with total mass $M_{\nu }$, and to 3 extended scenarios, including 1) additional relativistic degrees of freedom ($\mathrm{\Lambda }$CDM + $M_{\nu }$ + $N_{\mathrm{e}\mathrm{f}\mathrm{f}}$), 2) a deviation from the cosmological constant ($\mathrm{\Lambda }$CDM + $M_{\nu }$ + $w_0$), and 3) a time-varying dark energy equation of state parameter ($\mathrm{\Lambda }$CDM + $M_{\nu }$ + $(w_0,w_a)$). We compare the sensitivity of 14 different combinations of cosmological probes and experimental configurations. For Euclid combined with Planck, assuming a plain cosmological constant, our method gives robust predictions for a high sensitivity to the primordial spectral index $n_{\mathrm{s}}$ ($\sigma (n_s)=0.00085$), the Hubble constant $H_0$ ($\sigma (H_0)=0.141\mathrm{k}\mathrm{m}\mathrm{/}\mathrm{s}\mathrm{/}\mathrm{M}\mathrm{p}\mathrm{c}$), the total neutrino mass $M_{\nu }$ ($\sigma (M_{\nu })=0.020\mathrm{e}\mathrm{V}$). Assuming dynamical dark energy we get $\sigma (M_{\nu })=0.030\mathrm{e}\mathrm{V}$ for the mass and $(\sigma(w_0), \sigma(w_a)) = (0.0214, 0.071)$ for the equation of state parameters. The predicted sensitivity to $M_{\nu }$ is mostly stable against the extensions of the cosmological model considered here. Interestingly, a significant improvement of the constraints on the extended model parameters is also obtained when combining Euclid with a low redshift HI intensity mapping survey by SKA1, demonstrating the importance of the synergy of Euclid and SKA.