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Title: Sample variance in weak lensing: How many simulations are required?

Constraining cosmology using weak gravitational lensing consists of comparing a measured feature vector of dimension Nb with its simulated counterpart. An accurate estimate of the Nb × Nb feature covariance matrix C is essential to obtain accurate parameter confidence intervals. When C is measured from a set of simulations, an important question is how large this set should be. To answer this question, we construct different ensembles of Nr realizations of the shear field, using a common randomization procedure that recycles the outputs from a smaller number Ns ≤ Nr of independent ray-tracing N-body simulations. We study parameter confidence intervals as a function of (Ns, Nr) in the range 1 ≤ Ns ≤ 200 and 1 ≤ Nr ≲ 105. Previous work [S. Dodelson and M. D. Schneider, Phys. Rev. D 88, 063537 (2013)] has shown that Gaussian noise in the feature vectors (from which the covariance is estimated) lead, at quadratic order, to an O(1/Nr) degradation of the parameter confidence intervals. Using a variety of lensing features measured in our simulations, including shear-shear power spectra and peak counts, we show that cubic and quartic covariance fluctuations lead to additional O(1/N2r) error degradation that is not negligible when Nr ismore » only a factor of few larger than Nb. We study the large Nr limit, and find that a single, 240 Mpc/h sized 5123-particle N-body simulation (Ns = 1) can be repeatedly recycled to produce as many as Nr = few × 104 shear maps whose power spectra and high-significance peak counts can be treated as statistically independent. Lastly, a small number of simulations (Ns = 1 or 2) is sufficient to forecast parameter confidence intervals at percent accuracy.« less
 [1] ;  [2] ;  [3]
  1. Columbia Univ., New York, NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
  2. Brookhaven National Lab. (BNL), Upton, NY (United States)
  3. Columbia Univ., New York, NY (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 2470-0010; PRVDAQ; KA2301020
Grant/Contract Number:
SC00112704; AC02-98CH10886; SC0012704; ACI-1053575
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 93; Journal Issue: 6; Journal ID: ISSN 2470-0010
American Physical Society (APS)
Research Org:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1243154