Optimizing cosmological surveys in a crowded market

Bruce A. Bassett

Phys. Rev. D 71, 083517 – Published 26 April 2005

Abstract

Optimizing the major next-generation cosmological surveys (such as SNAP, KAOS, etc.) is a key problem given our ignorance of the physics underlying cosmic acceleration and the plethora of surveys planned. We propose a Bayesian design framework which (1) maximizes the discrimination power of a survey without assuming any underlying dark-energy model, (2) finds the best niche survey geometry given current data and future competing experiments, (3) maximizes the cross section for serendipitous discoveries and (4) can be adapted to answer specific questions (such as “is dark energy dynamical?”). Integrated parameter-space optimization (IPSO) is a design framework that integrates projected parameter errors over an entire dark energy parameter space and then extremizes a figure of merit (such as Shannon entropy gain which we show is stable to off-diagonal covariance matrix perturbations) as a function of survey parameters using analytical, grid or MCMC techniques. We discuss examples where the optimization can be performed analytically. IPSO is thus a general, model-independent and scalable framework that allows us to appropriately use prior information to design the best possible surveys.

Received 13 July 2004

DOI:https://doi.org/10.1103/PhysRevD.71.083517

Authors & Affiliations

Bruce A. Bassett

Department of Physics, Kyoto University, Kyoto, Japan & Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 2EG, United Kingdom

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Issue

Vol. 71, Iss. 8 — 15 April 2005

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Images

Figure 1
Flow chart for integrated parameter-space optimization (IPSO). For each survey geometry in a denumerable set (either discrete or continuous) some function of the projected parameter covariance matrix is integrated over the dark energy parameter space $Θ$ to yield a figure of merit (FoM, a positive real number). Optimization proceeds by selecting the candidate survey geometry with the minimum or maximum FoM, depending on the precise FoM used; see Sec. 3.Reuse & Permissions
Figure 2
CPU constraints on the various FoM for case without (main figure) and with (inset) nuisance parameters that must be marginalized over. The main figure (inset) shows CPU times for 2000 (1000) realizations, respectively. The various curves are (a) Fisher-sum, (b) A optimality, (c) determinant and (d) D optimality. Without nuisance parameters the Fisher-sum is significantly faster while A optimality is the worst [since it is the only one that requires the inverse $F^{- 1}$ and since $\det (F^{- 1}) = 1 / \det (F)$ ]. When nuisance parameters must be marginalized over the playing field is much more even and there is little CPU advantage to any of the FoM.Reuse & Permissions
Figure 3
IPSO integrates only over fundamental parameters $θ_{a}$ while marginalizing over the remaining nuisance parameters by extracting the appropriate subcovariance matrix.Reuse & Permissions
Figure 4
Priors and parameter-space averaging affects the golden point. The one-point D-optimum redshift for Hubble constant measurements is given by the zeros of the curves (a)–(e) for a constant $w$ with different priors on the parameter space $θ = {w}$ . The various curves correspond to top-hat priors with upper and lower limits on $w$ , i.e. $[(w_{lower}, w_{upper})$ of: (a) $(- 1.5, - 0.8)$ , (b) $(- 1.5, - 0.6)$ , (c) $Λ$ CDM only, (d) $(- 1, - 0.8)$ and (e) $(- 1, - 0.6)$ . The optimum redshift varies from $z_{opti} = 0.86$ (a) to $z_{opti} = 2.6$ depending on the prior assumed. Allowing larger values of $w$ increases the importance of the dark energy at higher redshift and naturally shifts the golden point to higher redshift. Conversely, for more negative lower-bound forces the golden point to smaller redshifts and makes the change in the optimum sharper.Reuse & Permissions
Figure 5
Four different optimizations differing only by the values of $(θ_{\min}, θ_{\max})$ . Negative $θ_{\min}$ pushes the optimum to lower redshift. However, due to the nontrivial integration structure the results are not obvious and there are multiple extrema.Reuse & Permissions
Figure 6
Schematic illustration of a survey geometry. For a given observable quantity of interest, $X$ (such as luminosity distance), the $1 σ$ error bars, $ϵ_{i}$ , in each of several redshift bins (here $i = 1 \dots 6$ ) are free to vary subject only to a constraint such as Eq. (26).Reuse & Permissions

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