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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 $Lambda$CDM model, including massive neutrinos with total mass $M_ u$, and to 3 extended scenarios, including 1) additional relativistic degrees of freedom ($Lambda$CDM + $M_ u$ + $N_mathrm{eff}$), 2) a deviation from the cosmological constant ($Lambda$CDM + $M_ u$ + $w_0$), and 3) a time-varying dark energy equation of state parameter ($Lambda$CDM + $M_ u$ + $left(w_0,w_a right)$). 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 $n_{rm s}$ ($sigma(n_s)=0.00085$), the Hubble constant $H_0$ ($sigma(H_0)=0.141 , {rm km/s/Mpc}$), the total neutrino mass $M_ u$ ($sigma(M_ u)=0.020 , {rm eV}$). Assuming dynamical dark energy we get $sigma(M_ u)=0.030 , {rm eV}$ for the mass and $(sigma(w_0), sigma(w_a)) = (0.0214, 0.071)$ for the equation of state parameters. The predicted sensitivity to $M_ u$ 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.
We review how the Square Kilometre Array (SKA) will address fundamental questions in cosmology, focussing on its use for neutral Hydrogen (HI) surveys. A key enabler of its unique capabilities will be large (but smart) receptors in the form of apertu
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