Likelihood methods for cluster dark energy surveys

Hu, Wayne; Cohn, J. D.

doi:10.1103/physrevd.73.067301

Cited by 53 publications

(71 citation statements)

References 19 publications

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“…Hence, as shown in LH04, the likelihood function becomes: and via the convolution theorem this can be approximated as a Gaussian with shifted mean and augmented covariance matrix: where . Note that in the above equation, the approximate sign is used since negative number counts are formally forbidden (for a more detailed discussion of this see Hu & Cohn 2006).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

What do cluster counts really tell us about the Universe?

Smith¹,

Marian²

2011

Monthly Notices of the Royal Astronomical Society

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We study the covariance matrix of the cluster mass function in cosmology. We adopt a two-line attack: firstly, we employ the counts-in-cells framework to derive an analytic expression for the covariance of the mass function. Secondly, we use a large ensemble of N-body simulations in the LCDM framework to test this. Our theoretical results show that the covariance can be written as the sum of two terms: a Poisson term, which dominates in the limit of rare clusters; and a sample variance term, which dominates for more abundant clusters. Our expressions are analogous to those of Hu & Kravtsov (2003) for multiple cells and a single mass tracer. Calculating the covariance depends on: the mass function and bias of clusters, and the variance of mass fluctuations within the survey volume. The predictions show that there is a strong bin-to-bin covariance between measurements. In terms of the cross-correlation coefficient, we find r~0.5 for haloes with M<3e14 Msol at z=0. Comparison of these predictions with estimates from simulations shows excellent agreement. We use the Fisher matrix formalism to explore the cosmological information content of the counts. We compare the Poisson likelihood model, with the more realistic likelihood model of Lima & Hu (2004), and all terms entering the Fisher matrices are evaluated using the simulations. We find that the Poisson approximation should only be used for the rarest objects, M>3e14 Msol, otherwise the information content of a survey of size V~13.5 [Gpc/h]^3 would be overestimated, resulting in errors that are ~2 times smaller. As an auxiliary result, we show that the bias of clusters, obtained from the cluster-mass cross-variance, is linear on scales >50 Mpc/h, whereas that obtained from the auto-variance is nonlinear.Comment: Replaced with version accepted for publication in MNRAS. Minor corrections: references updated, typos corrected. 20 pages; 10 figure

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Section: Theoretical Backgroundmentioning

confidence: 99%

What do cluster counts really tell us about the Universe?

Smith¹,

Marian²

2011

Monthly Notices of the Royal Astronomical Society

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“…(9). The expression for the full Fisher matrix for galaxy cluster counts and their covariance is quite complicated (see [53]), but a reasonable approximation is given by [58] …”

Section: Methodsmentioning

confidence: 99%

Primordial non-Gaussianity from the covariance of galaxy cluster counts

2010

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It has recently been proposed that the large-scale bias of dark matter halos depends sensitively on primordial non-Gaussianity of the local form. In this paper we point out that the strong scale dependence of the non-Gaussian halo bias imprints a distinct signature on the covariance of cluster counts. We find that using the full covariance of cluster counts results in improvements on constraints on the non-Gaussian parameter fNL of three (one) orders of magnitude relative to cluster counts (counts + clustering variance) constraints alone. We forecast fNL constraints for the upcoming Dark Energy Survey in the presence of uncertainties in the mass-observable relation, halo bias, and photometric redshifts. We find that the DES can yield constraints on non-Gaussianity of σ(fNL) ∼ 1-5 even for relatively conservative assumptions regarding systematics. Excess of correlations of cluster counts on scales of hundreds of megaparsecs would represent a smoking gun signature of primordial non-Gaussianity of the local type.

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“…Because the bias of halo clustering depends on mass (Figure 1), the amplitude and scale-dependence of clustering provides information about the mass-observable relation. Operationally, one parameterizes this relation, then uses standard likelihood methods to jointly fit for both cosmology and the P (X|M, z) parameters (Hu and Cohn, 2006;Holder, 2006). These types of analyses are often referred to as "selfcalibration" because they do not require "direct" mass calibration data.…”

Section: Calibrating the Observable-mass Relationmentioning

confidence: 99%

Observational probes of cosmic acceleration

et al. 2013

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The accelerating expansion of the universe is the most surprising cosmological discovery in many decades, implying that the universe is dominated by some form of "dark energy" with exotic physical properties, or that Einstein's theory of gravity breaks down on cosmological scales. The profound implications of cosmic acceleration have inspired ambitious efforts to understand its origin, with experiments that aim to measure the history of expansion and growth of structure with percent-level precision or higher. We review in detail the four most well established methods for making such measurements: Type Ia supernovae, baryon acoustic oscillations (BAO), weak gravitational lensing, and the abundance of galaxy clusters. We pay particular attention to the systematic uncertainties in these techniques and to strategies for controlling them at the level needed to exploit "Stage IV" dark energy facilities such as BigBOSS, LSST, Euclid, and WFIRST. We briefly review a number of other approaches including redshift-space distortions, the Alcock-Paczynski effect, and direct measurements of the Hubble constant H 0 . We present extensive forecasts for constraints on the dark energy equation of state and parameterized deviations from General Relativity, achievable with Stage III and Stage IV experimental programs that incorporate supernovae, BAO, weak lensing, and cosmic microwave background data. We also show the level of precision required for clusters or other methods to provide constraints competitive with those of these fiducial programs. We emphasize the value of a balanced program that employs several of the most powerful methods in combination, both to cross-check systematic uncertainties and to take advantage of complementary information. Surveys to probe cosmic acceleration produce data sets that support a wide range of scientific investigations, and they continue the longstanding astronomical tradition of mapping the universe in ever greater detail over ever larger scales.

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Likelihood methods for cluster dark energy surveys

Cited by 53 publications

References 19 publications

What do cluster counts really tell us about the Universe?

What do cluster counts really tell us about the Universe?

Primordial non-Gaussianity from the covariance of galaxy cluster counts

Observational probes of cosmic acceleration

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