Joint Galaxy-Lensing Observables and the Dark Energy

TL;DR

The paper addresses extracting dark energy information from joint galaxy clustering and weak lensing observables in photometric surveys, by coupling three two-point statistics through a Limber-projected framework and a halo-model description of galaxies. It develops a Fisher-forecast approach to quantify constraints on dark energy parameters ($\Omega_{DE}$, $w_{pivot}$, $w_a$) and on halo-model functions, showing that a 4000 deg$^2$ survey can reach $\sigma(\Omega_{DE})=0.005$, $\sigma(w_{\rm pivot})=0.02$, and $\sigma(w_a)=0.17$ (with Planck priors improving to $\sigma(\Omega_{DE})=0.004$, $\sigma(w_{\rm pivot})=0.01$, $\sigma(w_a)=0.08$). The analysis demonstrates that combining galaxy-galaxy, galaxy-shear, and shear-shear data both tightens dark energy constraints and provides robustness against systematic errors in shear measurements and halo modeling, while enabling consistency checks across probes and redshift evolution of halo parameters. The work highlights the power of joint analyses for upcoming surveys and lays a path for extending to higher-order statistics and more detailed galaxy–halo modeling.

Abstract

Deep multi-color galaxy surveys with photometric redshifts will provide a large number of two-point correlation observables: galaxy-galaxy angular correlations, galaxy-shear cross correlations, and shear-shear correlations between all redshifts. These observables can potentially enable a joint determination of the dark energy dependent evolution of the dark matter and distances as well as the relationship between galaxies and dark matter halos. With recent CMB determinations of the initial power spectrum, a measurement of the mass clustering at even a_single_ redshift will constrain a well-specified combination of dark energy parameters in a flat universe; we provide convenient fitting formulae for such studies. The combination of galaxy-shear and galaxy-galaxy correlations can determine this amplitude at_multiple_ redshifts. We illustrate this ability in a description of the galaxy clustering with 5 free functions of redshift which can be fitted from the data. The galaxy modeling is based on a mapping onto halos of the same abundance that models a flux-limited selection. In this context, a 4000 deg2 galaxy-lensing survey can achieve a_statistical_ precision of sigma(Omega_DE)=0.005 for the dark energy density, sigma(w_DE)=0.02 and sigma(w_a)=0.17 for its equation of state and evolution, evaluated at dark energy matter equality z~0.4, as well as constraints on the 5 halo functions out to z=1. More importantly, a joint analysis can make dark energy constraints robust against systematic errors in the shear-shear correlation and halo modeling.

Figures (12)

• Figure 1: Lensing efficiency ratio and 68% CL forecasts on a two parameter model for the dark energy ($\Omega_{\rm DE}$, $w_{\rm DE}$). With two or more source galaxy populations, here $N_S=2$, the ratios of galaxy-shear power spectra provides a measure of distances through the efficiency ratio. Here we take $N_L=10$ lens galaxy populations and marginalize the amplitude of the galaxy-mass power spectrum in all bandpower and redshift bins. The inner contour shows the effect of neglecting the sampling errors and shows that sample and shot noise are comparable for a shear noise of $\gamma_{\rm rms}=0.3$ and a source density of $\bar{n}_{A}=70$ arcmin$^{-2}$. These parameters and a 4000 deg$^2$ survey are assumed here and throughout.
• Figure 2: Galaxy-shear power spectrum 68% CL constraints on a two parameter dark energy model ($\Omega_{\rm DE}$, $w_{\rm DE}$) with power spectrum information out to $l_P=1000$ (upper) and $3000$ (lower). Galaxy-shear constraints (dashed lines) are complementary to the efficiency ratio test (this solid) and are assisted by the addition of galaxy-galaxy constraints (thick solid) which help determine the $5 N_L=50$ halo parameters. Joint constraint (shaded) is only weakly dependent on $l_{P}$ and hence non-Gaussian errors. Here the number of source redshift distributions $N_S=2$.
• Figure 3: 68% CL constraints in a three parameter dark energy model ($w_{\rm pivot}$, $w_{a}$, $\Omega_{\rm DE}$) for shear-shear correlations only (light shaded ellipse) and all 2-point correlations (dark shaded ellipses) with $N_L=10$ and $N_S=5$ and $l_{P}=3000$. Also shown for comparison are the efficiency ratio constraints (dashed lines) and joint galaxy-shear and galaxy-galaxy correlations (dotted lines). Even after marginalizing over $5 N_L=50$ halo model parameters, galaxy-shear with galaxy-galaxy power spectra have comparable constraining power on the dark energy as shear-shear power spectra. Errors between $w_{\rm pivot}$ and $w_{a}$ are uncorrelated by definition. The pivot point $z_{\rm pivot}=0.36$ and is close to the epoch of dark energy domination.
• Figure 4: Example of combining external constraints. The $w_{\rm pivot}$ galaxy-lensing constraints can be transformed into other dark energy parameterization conventions (here $\Omega_{\rm DE}$, $w_0$, $w_a$) for comparison and joint studies. Dashed lines represent the improvement to the 68% CL region due to the addition of projected CMB constraints for the Planck satellite which mainly constrain the angular diameter distance to recombination.
• Figure 5: Halo parameter errors as a function of redshift for the $N_L=10$ lens galaxy bins and $N_S=5$ source galaxy bins with all 2-point information to $l_{P}=3000$ and the efficiency ratio on all scales. Parameters at different redshifts are largely uncorrelated whereas those at the same redshift are highly correlated. Linear combinations that control the shape and amplitude of the power spectra are better constrained (see text).