Cosmology with photometric weak lensing surveys: Constraints with redshift tomography of convergence peaks and moments

Andrea Petri, Morgan May, and Zoltán Haiman

Phys. Rev. D 94, 063534 – Published 30 September 2016

Abstract

Weak gravitational lensing is becoming a mature technique for constraining cosmological parameters, and future surveys will be able to constrain the dark energy equation of state $w$ . When analyzing galaxy surveys, redshift information has proven to be a valuable addition to angular shear correlations. We forecast parameter constraints on the triplet $(Ω_{m}, w, σ_{8})$ for a LSST-like photometric galaxy survey, using tomography of the shear-shear power spectrum, convergence peak counts and higher convergence moments. We find that redshift tomography with the power spectrum reduces the area of the $1 σ$ confidence interval in $(Ω_{m}, w)$ space by a factor of 8 with respect to the case of the single highest redshift bin. We also find that adding non-Gaussian information from the peak counts and higher-order moments of the convergence field and its spatial derivatives further reduces the constrained area in $(Ω_{m}, w)$ by factors of 3 and 4, respectively. When we add cosmic microwave background parameter priors from Planck to our analysis, tomography improves power spectrum constraints by a factor of 3. Adding moments yields an improvement by an additional factor of 2, and adding both moments and peaks improves by almost a factor of 3 over power spectrum tomography alone. We evaluate the effect of uncorrected systematic photometric redshift errors on the parameter constraints. We find that different statistics lead to different bias directions in parameter space, suggesting the possibility of eliminating this bias via self-calibration.

Received 3 May 2016

DOI:https://doi.org/10.1103/PhysRevD.94.063534

Physics Subject Headings (PhySH)

Cosmological parameters

Astrophysical & cosmological simulations Electromagnetic radiation astronomy

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Andrea Petri^1,2,*, Morgan May², and Zoltán Haiman³

¹Department of Physics, Columbia University, New York, New York 10027, USA
²Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
³Department of Astronomy, Columbia University, New York, New York 10027, USA

^*apetri@phys.columbia.edu

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Vol. 94, Iss. 6 — 15 September 2016

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Images

Figure 1
Parameter space sampling chosen for our simulations. We show the sampling in the $(Ω_{m}, w)$ (left), $(Ω_{m}, σ_{8})$ (center) and $(σ_{8}, w)$ (right) projections of the parameter space. The fiducial cosmology has been marked in red.
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Figure 2
Galaxy distribution assumed throughout this work [see Eq. (2)], along with the choice of the redshift bins ${\bar{z}}_{b}$ . Our galaxy sample consists of $N_{g} = 1 0^{6}$ galaxies. The figure shows the number of galaxies $N_{g} (z)$ at each redshift $z$ .
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Figure 3
$1 σ$ errors on $w$ , marginalized over $(Ω_{m}, σ_{8})$ , as a function of the number of the principal components $N_{c}$ , using the power spectrum (top left), peak counts (top right) and moments (bottom). The thin colored lines refer to single-redshift summary statistics, while the thick black line shows the case in which the joint redshift information is included.
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Figure 4
Comparison between single-redshift $w$ constraints (marginalized over $Ω_{m}$ and $σ_{8}$ ) obtained without PCA (black bars) and with PCA (colored bars) as a function of the redshift bin ${\bar{z}}_{b}$ . We show constraints obtained from the power spectrum (top left), peak counts (top right) and moments (bottom). Note the different scales on the vertical axis in the three different panels. The black dashed lines in the top left panel refer to parameter constraints on $w$ obtained with the public code nicaea [46], assuming a Gaussian covariance model for the power spectrum, as specified by Eq. (23).
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Figure 5
$1 σ$ tomographic constraints on the $(Ω_{m}, w)$ parameter space, marginalized over $σ_{8}$ , obtained using Eq. (15). The covariance matrix $\hat{C}$ and its inverse $\hat{Ψ}$ have been computed from 16000 summary statistics realizations, and have been scaled by a factor $N_{FOV} = 1600$ to mimic the constraining power of a LSST-sized survey. The thick line ellipses in the right panel refer to $(Ω_{m}, w)$ obtained from the weak lensing statistics considered in this work, but subject to Planck priors as described in Eq. (22). The thin solid lines in the left and right panels are the same.
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Figure 6
Distribution of parameter estimates in the $(Ω_{m}, w)$ parameter space using the power spectrum (red), peak counts (green) and moments (blue) to fit 20 LSST-like simulated observations. The parameter deviations $(δ Ω_{m}, δ w)$ are obtained comparing parameter estimates from Eq. (14) with and without photo- $z$ errors. The colored squares and the ellipses correspond respectively to the mean and $1 σ$ level of the $(δ Ω_{m}, δ w)$ distribution, assuming the latter is Gaussian.
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