Model independent approach towards measuring expansion and growth factor from next generation galaxy clustering and lensing angular power spectrum

TL;DR

The paper tackles the challenge of constraining the Universe's expansion and growth of structure without assuming a specific cosmological model. It develops a model-independent Fisher forecasting framework for the 3×2pt galaxy clustering and weak lensing observables, parametrizing the background expansion with $E(z)$ and the linear growth with $G(z)$ across redshift bins, while allowing flexible halo-bias and nonlinear modeling via halo model and excursion-set theory. Applied to Euclid, Rubin, and SKA specifications in the range $0.2\le z \le 1.8$, the approach demonstrates that $E(z)$ can be constrained at the percent level and $G(z)$ at roughly an order of magnitude weaker precision in the most agnostic settings, with nonlinear scales dramatically improving constraints and survey combinations providing the strongest gains. The work highlights that non-linear information, when carefully modeled, enables robust, model-independent constraints on both background evolution and structure formation, underscoring the value of upcoming multi-survey data for precision cosmology.

Abstract

In this work we perform Fisher forecasts on the expansion and the growth factors following model independent approaches from 3x2pt joint analysis of the galaxy lensing, clustering, and their cross-correlated spectra at the linear, and extending as well to non linear scales. For that, instead of choosing a specific model for the matter power spectrum, the main ingredient of these probes, we express it by parametrizing its components, such as the expansion and the growth factor, and those of the standard halo model and excursion set theory in several z bins, besides to the different bias and non-linear bias modelling functions. We apply the technique to Euclid, Rubin and SKA public specifications in the range 0.2 < z < 1.8 and show that one can then obtain model-independent constraints of the expansion E(z i ) and the growth factor G(z i ). We also show the change in gain in precision at each z- shell when going from pessimistic cut at linear scales to more optimistic non-linear settings, or the difference between using each survey alone or a combination of all of them, or the impact from fixing or adding more degrees of freedom in the non-linear modeling. We found that, in the most agnostic case, one can still reach high precision on E(z i ) in the order of the percent level when combining the three surveys at once while the growth factor G(z i ) has for the same settings one order of magnitude weaker constraints. We also found for both factors, an improvement that can reach one order of magnitude in precision when passing from linear to non-linear scales. We conclude that we will be able to constrain the two important factors of the background evolution and structure formation of the Universe when using non linear scales and the combined power of future surveys even in the most agnostic approaches.

Figures (10)

• Figure 1: 1$\sigma$ marginalized forecasted errors on the expansion $E(z_i)$, the growth $G(z_i)$ and the matter density $\Omega_{\rm m,0}$ parameters from Euclid, Rubin and SKA II photometric 3x2pt surveys when the galaxy biases are also left free to vary. Left panels are for when the optimistic settings are adopted, where the wavenumber values till $k_{max}=0.7$ are reached, for the right panels, pessimistic ones are adopted where the wavenumber values are limited to $k_{max}=0.2$ though still staying in the non linear regime.
• Figure 2: Showing the variation of the 1$\sigma$ marginalized forecasted relative errors for different wavenumbers for the growth and expansion factors for the same cases we considered when producing Fig. \ref{['fig:GzEzOm0bz']}
• Figure 3: 1$\sigma$ marginalized forecasted errors on the expansion $E(z_i)$, the growth $G(z_i)$ and the matter density $\Omega_{\rm m,0}$ parameters from the combination of Euclid, Rubin and SKA II photometric 3x2pt surveys when the galaxy biases are left free to vary in comparison to two other cases where, in the first, the non linear halo bias parameters $B_{\rm NL}$ are left free supposing a redshift dependence, and in the second, a further halo mass dependence was considered for $B_{\rm NL}$. Left panels are for when the optimistic settings are adopted, where the wavenumber values till $k_{max}=0.7$ are reached, for the right panels, pessimistic ones are adopted where the wavenumber values are limited to $k_{max}=0.2$ though still staying in the non linear regime.
• Figure 4: Showing the variation of the 1$\sigma$ marginalized forecasted relative errors for different wavenumbers for the growth and expansion factors for the same cases we considered when producing Fig. \ref{['fig:GzEzOm0bzBNLz']}
• Figure 5: 1$\sigma$ marginalized forecasted errors on the expansion $E(z_i)$, the growth $G(z_i)$ and the matter density $\Omega_{\rm m,0}$ parameters from the combination of Euclid, Rubin and SKA II photometric 3x2pt surveys when the galaxy biases are left free to vary, in comparison to a case where the halo model excursion set parameters are also free. In each of this two schemes, we also considered two cases, where in the first, the non linear halo bias parameters $B_{\rm NL}$ are left free supposing a redshift dependence, and in the second, a further halo mass dependence was considered. All panels are for when the optimistic settings are adopted, where the wavenumber values till $k_{max}=0.7$ are reached.