Analytic Calculation of Covariance between Cosmological Parameters from Correlated Data Sets, with an Application to SPTpol
Consistency checks of cosmological data sets are an important tool because they may suggest systematic errors or the type of modifications to ΛCDM necessary to resolve current tensions. In this work, we derive an analytic method for calculating the level of correlations between model parameters from...
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ftpubmed:oai:pubmedcentral.nih.gov:7121275 2023-05-15T18:23:01+02:00 Analytic Calculation of Covariance between Cosmological Parameters from Correlated Data Sets, with an Application to SPTpol Kable, Joshua A. Addison, Graeme E. Bennett, Charles L. 2019-12-31 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7121275/ http://www.ncbi.nlm.nih.gov/pubmed/32255817 https://doi.org/10.3847/1538-4357/ab54cc en eng http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7121275/ http://www.ncbi.nlm.nih.gov/pubmed/32255817 http://dx.doi.org/10.3847/1538-4357/ab54cc Astrophys J Article Text 2019 ftpubmed https://doi.org/10.3847/1538-4357/ab54cc 2021-01-03T01:27:34Z Consistency checks of cosmological data sets are an important tool because they may suggest systematic errors or the type of modifications to ΛCDM necessary to resolve current tensions. In this work, we derive an analytic method for calculating the level of correlations between model parameters from two correlated cosmological data sets, which complements more computationally expensive simulations. This method is an extension of the Fisher analysis that assumes a Gaussian likelihood and a known data covariance matrix. We apply this method to the South Pole Telescope Polarimeter (SPTpol) temperature and polarization cosmic microwave background (CMB) spectra (TE and EE). We find weak correlations between ΛCDM parameters with a 9% correlation between the TE-only and EE-only constraints on H(0) and a 25% and 32% correlation for log(A(s)) and n(s) respectively. The TE–EE parameter differences are consistent with zero, with a probability to exceed of 0.53. Using simulations we show that this test is independent of the consistency of the SPTpol TE and EE band powers with the best-fit ΛCDM model spectra. Despite the negative correlations between the TE and EE power spectra, the correlations between TE-only and EE-only ΛCDM parameters are positive. Ignoring correlations in the TT–TE and TE–EE comparisons biases the χ(2) low, artificially making parameters look more consistent. Therefore, we conclude that these correlations need to be accounted for when performing internal consistency checks of the TT versus TE versus EE power spectra for future CMB analyses. Text South pole PubMed Central (PMC) South Pole The Astrophysical Journal 888 1 26 |
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Article Kable, Joshua A. Addison, Graeme E. Bennett, Charles L. Analytic Calculation of Covariance between Cosmological Parameters from Correlated Data Sets, with an Application to SPTpol |
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Consistency checks of cosmological data sets are an important tool because they may suggest systematic errors or the type of modifications to ΛCDM necessary to resolve current tensions. In this work, we derive an analytic method for calculating the level of correlations between model parameters from two correlated cosmological data sets, which complements more computationally expensive simulations. This method is an extension of the Fisher analysis that assumes a Gaussian likelihood and a known data covariance matrix. We apply this method to the South Pole Telescope Polarimeter (SPTpol) temperature and polarization cosmic microwave background (CMB) spectra (TE and EE). We find weak correlations between ΛCDM parameters with a 9% correlation between the TE-only and EE-only constraints on H(0) and a 25% and 32% correlation for log(A(s)) and n(s) respectively. The TE–EE parameter differences are consistent with zero, with a probability to exceed of 0.53. Using simulations we show that this test is independent of the consistency of the SPTpol TE and EE band powers with the best-fit ΛCDM model spectra. Despite the negative correlations between the TE and EE power spectra, the correlations between TE-only and EE-only ΛCDM parameters are positive. Ignoring correlations in the TT–TE and TE–EE comparisons biases the χ(2) low, artificially making parameters look more consistent. Therefore, we conclude that these correlations need to be accounted for when performing internal consistency checks of the TT versus TE versus EE power spectra for future CMB analyses. |
format |
Text |
author |
Kable, Joshua A. Addison, Graeme E. Bennett, Charles L. |
author_facet |
Kable, Joshua A. Addison, Graeme E. Bennett, Charles L. |
author_sort |
Kable, Joshua A. |
title |
Analytic Calculation of Covariance between Cosmological Parameters from Correlated Data Sets, with an Application to SPTpol |
title_short |
Analytic Calculation of Covariance between Cosmological Parameters from Correlated Data Sets, with an Application to SPTpol |
title_full |
Analytic Calculation of Covariance between Cosmological Parameters from Correlated Data Sets, with an Application to SPTpol |
title_fullStr |
Analytic Calculation of Covariance between Cosmological Parameters from Correlated Data Sets, with an Application to SPTpol |
title_full_unstemmed |
Analytic Calculation of Covariance between Cosmological Parameters from Correlated Data Sets, with an Application to SPTpol |
title_sort |
analytic calculation of covariance between cosmological parameters from correlated data sets, with an application to sptpol |
publishDate |
2019 |
url |
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7121275/ http://www.ncbi.nlm.nih.gov/pubmed/32255817 https://doi.org/10.3847/1538-4357/ab54cc |
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South Pole |
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South Pole |
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South pole |
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South pole |
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Astrophys J |
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7121275/ http://www.ncbi.nlm.nih.gov/pubmed/32255817 http://dx.doi.org/10.3847/1538-4357/ab54cc |
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https://doi.org/10.3847/1538-4357/ab54cc |
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The Astrophysical Journal |
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888 |
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1 |
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26 |
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1766202436347756544 |