Perturbative approach to covariance matrix of the matter power spectrum
Abstract
We evaluate the covariance matrix of the matter power spectrum using perturbation theory up to dominant terms at 1-loop order and compare it to numerical simulations.We decompose the covariance matrix into the disconnected (Gaussian) part, trispectrum from the modes outside the survey (supersample variance) and trispectrum from the modes inside the survey, and show how the different components contribute to the overall covariance matrix. We find the agreement with the simulations is at a 10 per cent level up to k ~ 1 h Mpc-1. We show that all the connected components are dominated by the large-scale modes (k < 0.1 h Mpc-1), regardless of the value of the wave vectors k, k' of the covariance matrix, suggesting that one must be careful in applying the jackknife or bootstrap methods to the covariance matrix. We perform an eigenmode decomposition of the connected part of the covariance matrix, showing that at higher k, it is dominated by a single eigenmode. The full covariance matrix can be approximated as the disconnected part only, with the connected part being treated as an external nuisance parameter with a known scale dependence, and a known prior on its variance for a given survey volume. Finally,more »
- Authors:
-
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States). Fermilab Center for Particle Astrophysics
- Univ. of California, Berkeley, CA (United States). Physics, Astronomy Dept.; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics, Dept. of Physics, Kavli Inst. for Particle Astrophysics and Cosmology
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States); Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1331777
- Alternate Identifier(s):
- OSTI ID: 1361079; OSTI ID: 1475006
- Report Number(s):
- FERMILAB-PUB-16-247-A; arXiv:1607.00043
Journal ID: ISSN 0035-8711; 1473305
- Grant/Contract Number:
- AC02-07CH11359; AC02-76SF00515; NNX15AL17G; AC02-05CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Additional Journal Information:
- Journal Volume: 466; Journal Issue: 1; Journal ID: ISSN 0035-8711
- Publisher:
- Royal Astronomical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; cosmology: theory; large-scale structure of Universe
Citation Formats
Mohammed, Irshad, Seljak, Uros, and Vlah, Zvonimir. Perturbative approach to covariance matrix of the matter power spectrum. United States: N. p., 2016.
Web. doi:10.1093/mnras/stw3196.
Mohammed, Irshad, Seljak, Uros, & Vlah, Zvonimir. Perturbative approach to covariance matrix of the matter power spectrum. United States. https://doi.org/10.1093/mnras/stw3196
Mohammed, Irshad, Seljak, Uros, and Vlah, Zvonimir. Wed .
"Perturbative approach to covariance matrix of the matter power spectrum". United States. https://doi.org/10.1093/mnras/stw3196. https://www.osti.gov/servlets/purl/1331777.
@article{osti_1331777,
title = {Perturbative approach to covariance matrix of the matter power spectrum},
author = {Mohammed, Irshad and Seljak, Uros and Vlah, Zvonimir},
abstractNote = {We evaluate the covariance matrix of the matter power spectrum using perturbation theory up to dominant terms at 1-loop order and compare it to numerical simulations.We decompose the covariance matrix into the disconnected (Gaussian) part, trispectrum from the modes outside the survey (supersample variance) and trispectrum from the modes inside the survey, and show how the different components contribute to the overall covariance matrix. We find the agreement with the simulations is at a 10 per cent level up to k ~ 1 h Mpc-1. We show that all the connected components are dominated by the large-scale modes (k < 0.1 h Mpc-1), regardless of the value of the wave vectors k, k' of the covariance matrix, suggesting that one must be careful in applying the jackknife or bootstrap methods to the covariance matrix. We perform an eigenmode decomposition of the connected part of the covariance matrix, showing that at higher k, it is dominated by a single eigenmode. The full covariance matrix can be approximated as the disconnected part only, with the connected part being treated as an external nuisance parameter with a known scale dependence, and a known prior on its variance for a given survey volume. Finally, we provide a prescription for how to evaluate the covariance matrix from small box simulations without the need to simulate large volumes.},
doi = {10.1093/mnras/stw3196},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 1,
volume = 466,
place = {United States},
year = {Wed Dec 14 00:00:00 EST 2016},
month = {Wed Dec 14 00:00:00 EST 2016}
}
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