Impact and interplay of $Λ$CDM analysis choices for LSST cosmic shear

Abstract

We forecast cosmological parameter constraints for a cosmic shear analysis of the Rubin Observatory Legacy Survey of Space and Time (LSST), defining an analysis framework that can accurately recover the $Λ$CDM model in the presence of astrophysical and data-related systematics. When accounting for our present uncertainty on the suppression of the non-linear matter power spectrum through baryon feedback, we find that the error on the composite parameter $S_8=σ_8\sqrt{Ω_{\rm m}/0.3}$ almost doubles compared to an LSST analysis which neglects this astrophysical phenomenon. After the first year of observations, LSST will extend beyond the magnitude limit of existing representative spectroscopic calibration samples, requiring photometric redshifts to be calibrated using an alternative strategy. Adopting literature measurements of the reduced redshift calibration precision found from galaxy cross-correlation techniques, combined with current levels of baryon feedback uncertainty, we forecast final year LSST cosmic shear constraints that barely improve upon the first year analysis. This forecast therefore serves as encouragement to the community to develop methodology and observations to constrain models of baryon feedback and enhance photometric redshift calibration at depths where spectroscopy is unrepresentative. With tight priors on both these systematic terms, we forecast that LSST cosmic shear can deliver constraints on $S_8$ that are more than five times as constraining as existing cosmic shear surveys.

Figures (13)

• Figure 1: Cosmic shear power spectra, $C_{ }^{ij}$: the ratio between models including baryon feedback and the gravity-only scenario. Each subplot corresponds to a different combination of tomographic bins $i$ and $j$ with the auto-correlations shown on the diagonal. The lower-left panel shows the uncertainty in baryon feedback suppression over the DESCSRD/etal:2018 analysis range $20< <3000$. The upper-right panel zooms into the same data, but over our fiducial analysis range with $K_{\rm max}=0.5$. We model baryon feedback using the FLAMINGO simulations schaye/etal:2023, using their 'L1_m9' simulation as our fiducial case (orange), alongside their weakest ('fgas+2$$' in yellow) and strongest ('Jet_fgas-4$$' in red) scenarios. The shaded regions correspond to the three different $\Theta_{\rm AGN}$ prior ranges considered in our HMCode2020 analysis. We compare an uninformative prior (light-blue), alongside two informative priors: one spans the same region as the FLAMINGO simulations at low-$$ (mid-blue), and one adopts tight constraints from external DESxROSAT data (dark-blue). The vertical dashed grey lines correspond to $K_{\rm max}=[0.1, 0.5, 1.0]$ in the lower-left panel, and $K_{\rm max}=[0.1, 0.5]$ in the upper-right panel.
• Figure 2: LSST $\Lambda$CDM cosmic shear forecasts for $S_8$, $\Omega_{\rm m}$ and the NLA-$z$ intrinsic alignment parameters $A_{\rm IA}$ and $_{\rm IA}$, showing the mean marginal and 68% credible interval. Our Y1 fiducial analysis configuration is shown at the top in pink, with each row that follows presenting a series of variant analyses as detailed in the text. With the exception of the variants noting the use of a 'weak' or 'strong' feedback mock, we incorporate baryon feedback using the fiducial FLAMINGO model shown in Figure \ref{['fig:FLAMINGO']}. Aside from variants noted as using scales up to an $_{\rm max}=5000$, we apply a scale cut of $K_{\rm max}=0.5$. The dark grey region provides an indication of our target accuracy of $\pm 0.5$ uncertainty, about the 'truth' (shown dashed), where $$ is the 68% credible interval from our fiducial Y1 analysis. Note that here we show $S_8 = S_8^{\rm input} + \Delta S_8$, and the equivalent for the other parameters. The input values are listed in Table \ref{['tab:priors']}, with the $\Delta$ offsets determined from the difference between the mean marginal estimates from the 'truth' and 'test' mock analyses (see Section \ref{['sec:truthtest']} for details). For the purpose of this figure, the $0.5$-width is set to the constraining power of our fiducial analysis. The light grey region corresponds to $\pm 1$ uncertainty. Rows 1-7 review the robustness of the Y1 HMCode2020 fiducial pipeline, and an alternative SP(k)-based analysis, to weaker and stronger baryon feedback (Section \ref{['sec:baryon_robustness']}) Rows 8-12 assess the impact of systematics mitigation strategies for Y10 (Section \ref{['sec:Y10']}). Row 13 adopts the alternative TATT intrinsic alignment model for Y1 (Section \ref{['sec:varyIA']}). Rows 14-15 vary the Y1 set of cosmological parameters and priors (Appendix \ref{['app:parametersandpriors']}). The constraints on $S_8$ are tabulated in Appendix \ref{['app:extrastab']}.
• Figure 3: LSST Y1 cosmic shear forecasts on $S_8$ and $\Omega_{\rm m}$ for a 'scale cut only' analysis that does not model baryon feedback. We compare three different redshift-dependent scale cuts: $K_{\rm max}=1$ (blue), $K_{\rm max}=0.5$ (red), and $K_{\rm max}=0.1$ (yellow) (see Appendix \ref{['app:extrastab']} for how $K_{\rm max}$ relates to $_{\rm max}$ in different tomographic bins). As we remove scales, the constraining power and the bias reduce significantly. A $2$ bias on $S_8$ for $K_{\rm max}=1$ decreases to a $0.03$ offset for $K_{\rm max}=0.1$, with the error on $S_8$ tripling and becoming comparable to existing constraints from pre-cursor surveys. These results are all cases of 'test' analyses where the projection 'bias' is low at $\sim 0.1$. In this figure, and all similar contour plots that follow, the dashed black lines indicate the input cosmology (listed in Table \ref{['tab:priors']}), with the marginalised posterior contours showing the 68% (inner) and 95% (outer) credible intervals. The constraints on $S_8$ are tabulated in Table \ref{['tab:scalecuts']}.
• Figure 4: Comparing $S_8$ constraints when varying $K_{\rm max}$ scale-cuts and different baryon feedback priors. Top: Mean marginal 'test' analysis constraints on $S_8$, where the inner and outer error bars correspond to $0.5$ and $1$ respectively, and the dashed line marks the input value. The projection 'bias' is reported in Table \ref{['tab:scalecuts']}, and can be as high as $0.4$. Middle: 68% confidence interval error estimate for $S_8$. Lower: the absolute value of the offset $\Delta S_8 = |(S_8^{\rm truth} - S_8^{\rm test})|$ as a fraction of the error. We define success as a result where $\Delta S_8< 0.5$ (shaded blue). We see that a gravity-only analysis that ignores the impact of baryon feedback (red) is only unbiased when excluding all but the smallest $$-scales in the cosmic shear analysis. When using wide priors to marginalise over baryon feedback uncertainty (Uninformed, orange, and FLAMINGO-informed, yellow), little information is gained by increasing $K_{\rm max}$ to high values. Using external information to constrain the baryon feedback (DESxROSAT, blue) returns precision at the expense of accuracy.
• Figure 5: Varying the baryon feedback strength: comparing constraints on $S_8$, $\Omega_{\rm m}$ and the HMCode2020 baryon feedback parameter $\Theta_{\rm AGN}$ for the weakest (blue) and strongest (pink) feedback scenario from the suite of FLAMINGO simulations. The 'truth' cases quantify the level of 'projection bias' relative to the input cosmology (shown dashed). The 'test' cases (where the mock data doesn't match the analysis framework) recover the matching 'truth' case within our target accuracy of $<0.5$.