Cosmology in the era of Euclid and the Square Kilometre Array

TL;DR

This paper develops a realistic, scalable method to propagate non-linear theoretical uncertainties into forecasts for upcoming galaxy and 21 cm surveys, moving beyond simple scale cuts. By embedding a correlation-length–driven error model within MCMC analyses, the authors forecast constraints on the baseline $Λ$CDM+$M_ν$ model and three extensions, across 14 experimental configurations combining Euclid and SKA probes (galaxy clustering, cosmic shear, and 21 cm intensity mapping). They find that non-linear uncertainties degrade information at small scales but that a realistic treatment still yields leading constraints on $n_s$, $H_0$, and especially the neutrino mass $M_ν$, with substantial gains when combining Euclid with SKA1 IM. The results underscore the importance of joint Euclid–SKA analyses and motivate further refinement of non-linear modelling and foreground treatment to exploit future data fully.

Abstract

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 $Λ$CDM model, including massive neutrinos with total mass $M_ν$, and to 3 extended scenarios, including 1) additional relativistic degrees of freedom ($Λ$CDM + $M_ν$ + $N_\mathrm{eff}$), 2) a deviation from the cosmological constant ($Λ$CDM + $M_ν$ + $w_0$), and 3) a time-varying dark energy equation of state parameter ($Λ$CDM + $M_ν$ + $\left(w_0,w_a \right)$). 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 $n_{\rm s}$ ($σ(n_s)=0.00085$), the Hubble constant $H_0$ ($σ(H_0)=0.141 \, {\rm km/s/Mpc}$), the total neutrino mass $M_ν$ ($σ(M_ν)=0.020 \, {\rm eV}$). Assuming dynamical dark energy we get $σ(M_ν)=0.030 \, {\rm eV}$ for the mass and $(σ(w_0), σ(w_a)) = (0.0214, 0.071)$ for the equation of state parameters. The predicted sensitivity to $M_ν$ 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.

Figures (11)

• Figure 1: Euclid cosmic shear combined with Planck (see section \ref{['sec:datasets']} for details): sensitivity to a 0.1%-variation of $P(k)$ for different cutoff wavenumbers (always scaled with redshift). The flat $\ell_{max}=5000$ cut-off (blue) shows the amount of information available in absence of a cut-off. The second (green) and third (red) cases are more conservative than a sharp cut-off at $\ell=1310$ would be. For comparison, the dashed line marks $\ell=1310$, corresponding to the $\ell_{\rm max}$ used by the KiDS collaboration in Ref. Kohlinger:2017sxk as a reasonable cut-off producing stable results. The last case (cyan) is a little more constraining than this sharp cut-off, intended to reflect improvements in non-linear modeling in the analysis of future data. For our analysis we will use $k_{\text{NL}}(0)=0.5 h/\text{Mpc}$ (conservative) and $k_{\text{NL}}(0)=2.0 h/\text{Mpc}$ (realistic) as our non-linear cut-off wavenumbers. The corresponding 1-$\sigma$ sensitivity of our MCMC forecasts can be seen in table \ref{['table:lensing_sensitivity']}.
• Figure 2: Sensitivity distribution for all cosmic shear likelihoods. The left panel shows the realistic approach and the right panel the conservative one. The $\Delta \chi^2$-values are contributions for each multipole $l$ obtained by setting $\Delta P = 0.001 P$ for all $k$. We find that SKA1 is not competitive, but that SKA2 will out-perform Euclid.
• Figure 3: Galaxy clustering: Examples for the relative effective errors $\sigma_{\rm eff}/P_g$ in selected redshift bins, decomposed into the contribution from the observational error (blue) and theoretical error (red). To show to which scale the experiment is most sensitive (taking these errors into account), we also show in grey the function $\sim \mathrm{d} \chi^2/(\mathrm{d} k \mathrm{d} \mu)$ arbitrarily normalised to a constant relative difference between the theoretical and observed spectra ($\Delta P_g = \epsilon P_g$). The vertical line marks $k_{\text{NL}}(\bar{z})$, used as a sharp cut-off for the conservative setting.
• Figure 4: Intensity mapping: Examples for relative effective errors $\sigma_{\rm eff}/P_{21}$ and sensitivity contributions $\sim \mathrm{d} \chi^2/(\mathrm{d} k \mathrm{d} \mu)$ arbitrarily normalised to $\Delta P_{21}=\epsilon P_{21}$. The vertical line marks $k_{\text{NL}}(\bar{z})$, used as a sharp cut-off for the conservative setting. Both the realistic and conservative setting make use of the theoretical error (red). Note the different $k_{\text{NL}}(z)$ values, corresponding to the mean redshift of each bin.
• Figure 5: Sensitivity distribution for all three-dimensional power spectrum likelihoods. The left panel shows the realistic approach and the right panel the conservative one. The $\Delta \chi^2$-values are contributions when two of the quantities $k$, $\mu$ and $z$ are integrated or summed over, and $\Delta P = 0.001 P$ everywhere. For intensity mapping (IM), band 1 and 2 of SKA1 are considered.