Likelihood Analysis of CMB Temperature and Polarization Power Spectra
By Samira Hamimeche, A. Lewis. 2008
208 citations recorded by the source corpus.
Microwave background temperature and polarization observations are a powerful way to constrain cosmological parameters if the likelihood function can be calculated accurately. The temperature and polarization fields are correlated, partial-sky coverage correlates power spectrum estimators at different l, and the likelihood function for a theory spectrum given a set of observed estimators is non-Gaussian. An accurate analysis must model all these properties. Most existing likelihood approximations are good enough for a temperature-only analysis, however they cannot reliably handle temperature-polarization correlations. We give a new general approximation applicable for correlated Gaussian fields observed on part of the sky. The approximation models the non-Gaussian form exactly in the ideal full-sky limit and is fast to evaluate using a precomputed covariance matrix and set of power spectrum estimators. We show with simulations that it is good enough to obtain correct results at l?30 where an exact calculation becomes impossible. We also show that some Gaussian approximations give reliable parameter constraints even though they do not capture the shape of the likelihood function at each l accurately. Finally we test the approximations on simulations with realistically anisotropic noise and asymmetric foreground mask.
Subfields: Astronomy and Astrophysics
View Paper: https://www.semanticscholar.org/paper/6a9cab1f7362572e87857d250c6add25fd9ff3e2
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In Astronomy and Astrophysics
Citations in the corpus
- Improved reconstruction of a stochastic gravitational wave background with LISA (2020, background): “10) would give a result which is systematically biased [50–53], due to the mild non-Gaussianity of the full likelihood of the non-averaged data.”
- A unified pseudo-Cℓ framework (2018, background): “A11, we obtain: vec [〈PCL` (avl ,bwl )〉] = ∑ `′ Msasb``′ · vec [ Cab`′ ] , (9) where we have defined the vectorization operator (Hamimeche & Lewis 2008) vec [( CEE CEB CBE CBB )] ≡ CEE CEB CBE CBB , (10) vec [( CTE CTB )] ≡ ( CTE CTB ) , vec [ CTT ] = CTT , (11) and T here stands for any spin-0…”
- Toward an understanding of foreground emission in the BICEP2 region (2014, methodology): “We have also implemented the Hamimeche-Lewis approximation [30] and find good agreement.”
- Detection of B-mode polarization at degree angular scales by BICEP2. (2014, methodology): “Pursuing this formally, we use simulations of both experiments observing a common sky to construct a combined likelihood function for bandpowers 1–5 of the BICEP2 auto, BICEP1100 auto, and their cross spectrum using the Hamimeche & Lewis (2008) approximation; see B14 for implementation details.”
- Planck2015 results (2015, unknown): “The construction of the full TT,T E, EE likelihood is then a straightforward extension of the TT likelihood using the analytic covariance matrices given by Efstathiou (2006) and Hamimeche & Lewis (2008).”
- Cosmological parameters derived from the final Planck data release (PR4) (2023, methodology): “Similarly to Hamimeche & Lewis (2008), we define where g ( x ) = √ 2( x − ln( x ) − 1), (cid:101) C (cid:96) are the measured cross-power spectra, C (cid:96) are the power spectra of the model to be evaluated, C f is a fiducial CMB model, and O (cid:96) are the o ff sets needed in the case of…”
- Planck intermediate results: LI. features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters (2016, unknown): “Approximations very similar to this have been studied previously by Benabed et al. (2009) and Hamimeche & Lewis (2008).”
- Planck intermediate results. LVII. Joint Planck LFI and HFI data processing (2020, methodology): “Our approach to this problem was described in general form by Jewell et al. (2004), Wandelt et al. (2004), and Eriksen et al.”
- The Simons Observatory: science goals and forecasts (2018, methodology): “This is not guaranteed to be a valid assumption given the reduced sky fraction and possible filtering of the data, and should be replaced in the future by, for example, the more accurate likelihood of Hamimeche and Lewis (2008).”
- Exploring cosmic origins with CORE: Inflation (2016, methodology): “Assuming that CMB anisotropies are Gaussian and statistically isotropic, we use the following χ(2)eff for our science forecasts [56, 173]: χ(2)eff = −2 lnL = ∑”