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Register a new userProbing dark energy with cluster counts and cosmic shear power spectra: including the full covariance
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Masahiro Takada
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(Abridged) Combining cosmic shear power spectra and cluster counts is powerful to improve cosmological parameter constraints and/or test inherent systematics. However they probe the same cosmic mass density field, if the two are drawn from the same survey region, and therefore the combination may be less powerful than first thought. We investigate the cross-covariance between the cosmic shear power spectra and the cluster counts based on the halo model approach, where the cross-covariance arises from the three-point correlations of the underlying mass density field. Fully taking into account the cross-covariance as well as non-Gaussian errors on the lensing power spectrum covariance, we find a significant cross-correlation between the lensing power spectrum signals at multipoles l~10^3 and the cluster counts containing halos with masses M>10^{14}Msun. Including the cross-covariance for the combined measurement degrades and in some cases improves the total signal-to-noise ratios up to plus or minus 20% relative to when the two are independent. For cosmological parameter determination, the cross-covariance has a smaller effect as a result of working in a multi-dimensional parameter space, implying that the two observables can be considered independent to a good approximation. We also discuss that cluster count experiments using lensing-selected mass peaks could be more complementary to cosmic shear tomography than mass-selected cluster counts of the corresponding mass threshold. Using lensing selected clusters with a realistic usable detection threshold (S/N~6 for a ground-based survey), the uncertainty on each dark energy parameter may be roughly halved by the combined experiments, relative to using the power spectra alone.
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We consistently include the effect of massive neutrinos in the thermal Sunyaev Zeldovich (SZ) power spectrum and cluster counts analyses, highlighting subtle dependencies on the total neutrino mass and data combination. In particular, we find that using the transfer functions for Cold Dark Matter (CDM) + baryons in the computation of the halo mass function, instead of the transfer functions including neutrino perturbations, as prescribed in recent work, yields a $approx$ 0.25% downward shift of the $sigma_8$ constraint from tSZ power spectrum data, with a fiducial neutrino mass $Sigma m_ u=0.06$ eV. In $Lambda$CDM, with an X-ray mass bias corresponding to the expected hydrostatic mass bias, i.e., $(1-b)simeq0.8$, our constraints from Planck SZ data are consistent with the latest results from SPT, DES-Y1 and KiDS+VIKING-450. In $ uLambda$CDM, our joint analyses of Planck SZ with Planck 2015 primary CMB yield a small improvement on the total neutrino mass bound compared to the Planck 2015 primary CMB constraint, as well as $(1-b)=0.64pm0.04$~(68%~CL). For forecasts, we find that competitive neutrino mass measurements using cosmic variance limited SZ power spectrum require masking the heaviest clusters and probing the small-scale SZ power spectrum up to $ell_mathrm{max}approx10^4$. Although this is challenging, we find that SZ power spectrum can realistically be used to tightly constrain intra-cluster medium properties: we forecast a 2% determination of the X-ray mass bias by combining CMB-S4 and our mock SZ power spectrum with $ell_mathrm{max}=10^3$.
In this paper we derive a full expression for the propagation of weak lensing shape measurement biases into cosmic shear power spectra including the effect of missing data. We show using simulations that terms higher than first order in bias parameters can be ignored and the impact of biases can be captured by terms dependent only on the mean of the multiplicative bias field. We identify that the B-mode power contains information on the multiplicative bias. We find that without priors on the residual multiplicative bias $delta m$ and stochastic ellipticity variance $sigma_e$ that constraints on the amplitude of the cosmic shear power spectrum are completely degenerate, and that when applying priors the constrained amplitude $A$ is slightly biased low via a classic marginalisation paradox. Using all-sky Gaussian random field simulations we find that the combination of $(1+2delta m)A$ is unbiased for a joint EE and BB power spectrum likelihood if the error and mean (precision and accuracy) of the stochastic ellipticity variance is known to better than $sigma(sigma_e)leq 0.05$ and $Deltasigma_eleq 0.01$, or the multiplicative bias is known to better than $sigma(m)leq 0.07$ and $Delta mleq 0.01$.
(Abridged) We investigate and quantify the impact of finite simulation volume on weak lensing two- and four-point statistics. These {it finite support} (FS) effects are modelled for several estimators, simulation box sizes and source redshifts, and validated against a new large suite of 500 $N$-body simulations. The comparison reveals that our theoretical model is accurate to better than 5 per cent for the shear correlation function $xi_{+}(theta)$ and its error. We find that the most important quantities for FS modelling is the ratio between the measured angle $theta$ and the angular size of the simulation box at the source redshift, $theta_{box}(z_s)$, or the multipole equivalent $ell / ell_{box}(z_s)$. When this ratio reaches 0.1, independently of the source redshift, the shear correlation function $xi_+$ is suppressed by 5, 10, 20 and 25 percent for $L_{box}= 1000$, $500$, $250$ and $147mbox{Mpc}/h$ respectively. When it reaches 0.2, the suppression exceeds 25 percent even for the largest box. The same effect is observed in $xi_{-}(theta)$, but at much larger angles. This has important consequences for cosmological analyses using $N$-body simulations to calibrate the impact of non-linear gravitational clustering or to estimate errors and systematics effects, and should not be overlooked. We propose simple semi-analytic solutions to correct for these finite box effects with and without the presence of survey masks, and the method can be generalized to any weak lensing estimator. This offers a graceful solution to the important problem of estimating accurate covariance matrices for weak lensing studies: there is no need to run extra large simulation volumes, as long as the box effects are corrected.
We measure cosmic weak lensing shear power spectra with the Subaru Hyper Suprime-Cam (HSC) survey first-year shear catalog covering 137deg$^2$ of the sky. Thanks to the high effective galaxy number density of $sim$17 arcmin$^{-2}$ even after conservative cuts such as magnitude cut of $i<24.5$ and photometric redshift cut of $0.3leq z leq 1.5$, we obtain a high significance measurement of the cosmic shear power spectra in 4 tomographic redshift bins, achieving a total signal-to-noise ratio of 16 in the multipole range $300 leq ell leq 1900$. We carefully account for various uncertainties in our analysis including the intrinsic alignment of galaxies, scatters and biases in photometric redshifts, residual uncertainties in the shear measurement, and modeling of the matter power spectrum. The accuracy of our power spectrum measurement method as well as our analytic model of the covariance matrix are tested against realistic mock shear catalogs. For a flat $Lambda$ cold dark matter ($Lambda$CDM) model, we find $S_8equiv sigma_8(Omega_{rm m}/0.3)^alpha=0.800^{+0.029}_{-0.028}$ for $alpha=0.45$ ($S_8=0.780^{+0.030}_{-0.033}$ for $alpha=0.5$) from our HSC tomographic cosmic shear analysis alone. In comparison with Planck cosmic microwave background constraints, our results prefer slightly lower values of $S_8$, although metrics such as the Bayesian evidence ratio test do not show significant evidence for discordance between these results. We study the effect of possible additional systematic errors that are unaccounted in our fiducial cosmic shear analysis, and find that they can shift the best-fit values of $S_8$ by up to $sim 0.6sigma$ in both directions. The full HSC survey data will contain several times more area, and will lead to significantly improved cosmological constraints.
We introduce the Generalised Lensing and Shear Spectra GLaSS code which is available for download from https://github.com/astro-informatics/GLaSS It is a fast and flexible public code, written in Python, that computes generalized spherical cosmic shear spectra. The commonly used tomographic and spherical Bessel lensing spectra come as built-in run-mode options. GLaSS is integrated into the Cosmosis modular cosmological pipeline package. We outline several computational choices that accelerate the computation of cosmic shear power spectra. Using GLaSS, we test whether the assumption that using the lensing and projection kernels for a spatially-flat universe -- in a universe with a small amount of spatial curvature -- negligibly impacts the lensing spectrum. We refer to this assumption as The Spatially-Flat Universe Approximation, that has been implicitly assumed in all cosmic shear studies to date. We confirm that The Spatially-Flat Universe Approximation has a negligible impact on Stage IV cosmic shear experiments.
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