Fisher Forecasts for Cosmological Yields from $3\!\times\!2$pt Analysis of the Roman Space Telescope High Latitude Imaging Survey

TL;DR

The paper develops and applies Fisher forecasting within the Cobaya-CosmoLike Joint Architecture (CoCoA) framework to predict cosmological constraints from a Roman HLIS 3×2pt analysis (cosmic shear, galaxy–galaxy lensing, and galaxy clustering) using the DC1 data challenge. It demonstrates that, under baseline priors, galaxy–galaxy lensing and clustering dominate the constraints on $σ_8$ and $Ω_m$, with the full 3×2pt combination yielding additional gains; incorporating external priors on the power-spectrum shape further improves FoMs by roughly 1.2–3.5×. The study quantifies how information is distributed across tomographic bins and angular scales, showing that high-redshift and small-scale data are particularly informative, while priors on photometric redshift and shear biases modestly affect the results. It validates the Fisher approach against MCMC, analyzes the role of super-sample covariance, and outlines future enhancements such as baryonic/nonlinear modeling and cosmology-dependent covariance, highlighting the practical utility of fast, flexible forecasts for planning Roman HLIS cosmology analyses.

Abstract

The High Latitude Imaging Survey (HLIS) of NASA's Nancy Grace Roman Space Telescope will provide powerful tests of cosmological models through sensitive measurements of cosmic shear, galaxy-galaxy lensing (GGL), and galaxy clustering. As part of the HLIS Project Infrastructure Team's Data Challenge 1 (DC1), we carry out Fisher forecasts of cosmological parameter constraints from combinations of these probes, focusing on inverse-variance figures of merit (FoMs) for the parameters $σ_8$ and $Ω_{\rm{m}}$, which scale the amplitude of weak lensing signals. We find good agreement between Fisher analysis and Markov chain Monte Carlo (MCMC) analysis of the DC1 baseline data vector, and we exploit the flexibility of Fisher analysis to investigate varied priors on cosmological parameters and on nuisance parameters describing unknown biases in photometric redshifts or shear measurements. Given the benchmark DC1 priors, the forecast constraints from GGL+clustering are substantially stronger than those from cosmic shear, with the combination of all three probes (``$3\!\times\!2$pt'') providing moderate further improvement. Adding tight external priors on the power spectrum shape parameters $n_{\rm{s}}$, $Ω_{\rm{b}}$, and $h_0$ can improve the $(σ_8, Ω_{\rm{m}})$ FoMs by factors of $1.2$--$3.5$. The smallest scale angular bins provide much more information than the largest scale bins, and the highest redshift tomographic bins provide more information than the lowest redshift bins. Factor-of-two changes in the priors on photo-$z$ and shear biases, relative to the benchmark values based on anticipated calibration accuracy, produce changes of $\lesssim 20\%$ in FoMs, implying robust cosmological performance if this demanding level of accuracy can be achieved.

Figures (20)

• Figure 1: Layouts of baseline data vectors in Fourier space (first two rows) and real space (last two rows). The first and third rows present the absolute values of the data vector elements, with positive elements shown in blue and negative elements shown in orange. Most negative elements correspond to GGL measurements in which the lens tomographic bin lies behind the source tomographic bin. The second and fourth rows present the ratios between the absolute values of data vector elements and the corresponding errors. The errors are the square roots of the diagonal elements of the covariance matrices, which are shown later in Section \ref{['ss:cocoa']}. The ordering of sub-blocks is labeled in the first and third rows. $1$ denotes the lowest redshift tomographic bin and $8$ the highest. For GGL, pairs such as $(1, 2)$ and $(2, 1)$ both appear, with the first index denoting the lens bin and the second, the source bin. In real space, all values of $\xi_+$ appear first, then all values of $\xi_-$. The segment for each pair of bins goes from small $\ell$ to large $\ell$ in Fourier space and from small $\theta$ to large $\theta$ in real space.
• Figure 2: Covariance matrices (left column) and their inverses (right column) in Fourier space. The upper row only includes the Gaussian ("G") component of the covariance matrix, while the lower row includes both Gaussian and non-Gaussian ("NG") components. In each panel, a symmetric logarithmic scale is used to better present the structure of the matrix, and boundaries between different segments of the data vector (see Section \ref{['ss:cocoa']}) are marked with black dashed lines. Within each observable, data elements loop first over scale (inner loop) and then over tomographic redshift bin pair (outer loop). Each square block in the $C_{\rm gs} (\ell)$ cells corresponds to a single redshift bin of lens galaxies.
• Figure 3: Same as Figure \ref{['fig:covinv_fourier']}, but in real space.
• Figure 4: Corner plots for representative parameters in Fourier space. $7$ parameters are shown in this figure: all cosmological parameters studied in this work ($\sigma_8$, $n_{\rm s}$, $h_0$, $\Omega_{\rm b}$, and $\Omega_{\rm m}$), as well as multiplicative shear biases ($m_3$ and $m_6$) in the $3^{\rm rd}$ and $6^{\rm th}$ tomographic bins. In the panels above the diagonal, the maximum likelihood results ("ML"; blue) and maximum a posteriori results ("MAP"; orange) are compared. Peak values are shown as dots, and boundaries of $1\sigma$ credible regions are shown as ellipses. In the panels below the diagonal, the MAP results are compared to MCMC results, which are shown in purple, with both $1\sigma$ and $2\sigma$ regions. The diagonal panels show the 1D marginalized distributions from MCMC results and Fisher MAP results. The truth parameter values (i.e., those used to make the "observed" data vector ${\boldsymbol d}$) are marked as gray dotted horizontal and vertical lines. We mark the panels corresponding to ($\sigma_8$, $\Omega_{\rm m}$) constraints, which are the focus of this paper, with a star ($\star$). An extended version with $6$ additional parameters can be found in Appendix \ref{['app:corner']}.
• Figure 5: Same as Figure \ref{['fig:corsub_fourier']}, but in real space. An extended version with $6$ additional parameters can be found in Appendix \ref{['app:corner']}.