Planck 2013 results. XV. CMB power spectra and likelihood
We present the Planck likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations. We use this likelihood to derive the Planck CMB power spectrum over three decades in l, covering 2 <= l <= 2500. The main source of error at l...
| Main Authors: | , , , , , , , , , , , , , , , , , , , , , , , , |
|---|---|
| פורמט: | Journal article |
| שפה: | English |
| יצא לאור: |
EDP Sciences
2013
|
| _version_ | 1826293830181191680 |
|---|---|
| author | collaboration, P Ade, P Aghanim, N Armitage-Caplan, C Arnaud, M Ashdown, M Atrio-Barandela, F Aumont, J Baccigalupi, C Banday, A Barreiro, R Bartlett, J Battaner, E Benabed, K Benoit, A Benoit-Levy, A Bernard, J Bersanelli, M Bielewicz, P Bobin, J Bock, J Bonaldi, A Bonavera, L Bond, JR Borrill, J |
| author_facet | collaboration, P Ade, P Aghanim, N Armitage-Caplan, C Arnaud, M Ashdown, M Atrio-Barandela, F Aumont, J Baccigalupi, C Banday, A Barreiro, R Bartlett, J Battaner, E Benabed, K Benoit, A Benoit-Levy, A Bernard, J Bersanelli, M Bielewicz, P Bobin, J Bock, J Bonaldi, A Bonavera, L Bond, JR Borrill, J |
| author_sort | collaboration, P |
| collection | OXFORD |
| description | We present the Planck likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations. We use this likelihood to derive the Planck CMB power spectrum over three decades in l, covering 2 <= l <= 2500. The main source of error at l <= 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher l's. For l < 50, our likelihood exploits all Planck frequency channels from 30 to 353 GHz through a physically motivated Bayesian component separation technique. At l >= 50, we employ a correlated Gaussian likelihood approximation based on angular cross-spectra derived from the 100, 143 and 217 GHz channels. We validate our likelihood through an extensive suite of consistency tests, and assess the impact of residual foreground and instrumental uncertainties on cosmological parameters. We find good internal agreement among the high-l cross-spectra with residuals of a few uK^2 at l <= 1000. We compare our results with foreground-cleaned CMB maps, and with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. The best-fit LCDM cosmology is in excellent agreement with preliminary Planck polarisation spectra. The standard LCDM cosmology is well constrained by Planck by l <= 1500. For example, we report a 5.4 sigma deviation from n_s /= 1. Considering various extensions beyond the standard model, we find no indication of significant departures from the LCDM framework. Finally, we report a tension between the best-fit LCDM model and the low-l spectrum in the form of a power deficit of 5-10% at l <~ 40, significant at 2.5-3 sigma. We do not elaborate further on its cosmological implications, but note that this is our most puzzling finding in an otherwise remarkably consistent dataset. (Abridged) |
| first_indexed | 2024-03-07T03:36:12Z |
| format | Journal article |
| id | oxford-uuid:bc5fc34b-1f82-44b2-bc7b-e5745eb70e4f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:36:12Z |
| publishDate | 2013 |
| publisher | EDP Sciences |
| record_format | dspace |
| spelling | oxford-uuid:bc5fc34b-1f82-44b2-bc7b-e5745eb70e4f2022-03-27T05:24:01ZPlanck 2013 results. XV. CMB power spectra and likelihoodJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bc5fc34b-1f82-44b2-bc7b-e5745eb70e4fEnglishSymplectic Elements at OxfordEDP Sciences2013collaboration, PAde, PAghanim, NArmitage-Caplan, CArnaud, MAshdown, MAtrio-Barandela, FAumont, JBaccigalupi, CBanday, ABarreiro, RBartlett, JBattaner, EBenabed, KBenoit, ABenoit-Levy, ABernard, JBersanelli, MBielewicz, PBobin, JBock, JBonaldi, ABonavera, LBond, JRBorrill, JWe present the Planck likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations. We use this likelihood to derive the Planck CMB power spectrum over three decades in l, covering 2 <= l <= 2500. The main source of error at l <= 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher l's. For l < 50, our likelihood exploits all Planck frequency channels from 30 to 353 GHz through a physically motivated Bayesian component separation technique. At l >= 50, we employ a correlated Gaussian likelihood approximation based on angular cross-spectra derived from the 100, 143 and 217 GHz channels. We validate our likelihood through an extensive suite of consistency tests, and assess the impact of residual foreground and instrumental uncertainties on cosmological parameters. We find good internal agreement among the high-l cross-spectra with residuals of a few uK^2 at l <= 1000. We compare our results with foreground-cleaned CMB maps, and with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. The best-fit LCDM cosmology is in excellent agreement with preliminary Planck polarisation spectra. The standard LCDM cosmology is well constrained by Planck by l <= 1500. For example, we report a 5.4 sigma deviation from n_s /= 1. Considering various extensions beyond the standard model, we find no indication of significant departures from the LCDM framework. Finally, we report a tension between the best-fit LCDM model and the low-l spectrum in the form of a power deficit of 5-10% at l <~ 40, significant at 2.5-3 sigma. We do not elaborate further on its cosmological implications, but note that this is our most puzzling finding in an otherwise remarkably consistent dataset. (Abridged) |
| spellingShingle | collaboration, P Ade, P Aghanim, N Armitage-Caplan, C Arnaud, M Ashdown, M Atrio-Barandela, F Aumont, J Baccigalupi, C Banday, A Barreiro, R Bartlett, J Battaner, E Benabed, K Benoit, A Benoit-Levy, A Bernard, J Bersanelli, M Bielewicz, P Bobin, J Bock, J Bonaldi, A Bonavera, L Bond, JR Borrill, J Planck 2013 results. XV. CMB power spectra and likelihood |
| title | Planck 2013 results. XV. CMB power spectra and likelihood |
| title_full | Planck 2013 results. XV. CMB power spectra and likelihood |
| title_fullStr | Planck 2013 results. XV. CMB power spectra and likelihood |
| title_full_unstemmed | Planck 2013 results. XV. CMB power spectra and likelihood |
| title_short | Planck 2013 results. XV. CMB power spectra and likelihood |
| title_sort | planck 2013 results xv cmb power spectra and likelihood |
| work_keys_str_mv | AT collaborationp planck2013resultsxvcmbpowerspectraandlikelihood AT adep planck2013resultsxvcmbpowerspectraandlikelihood AT aghanimn planck2013resultsxvcmbpowerspectraandlikelihood AT armitagecaplanc planck2013resultsxvcmbpowerspectraandlikelihood AT arnaudm planck2013resultsxvcmbpowerspectraandlikelihood AT ashdownm planck2013resultsxvcmbpowerspectraandlikelihood AT atriobarandelaf planck2013resultsxvcmbpowerspectraandlikelihood AT aumontj planck2013resultsxvcmbpowerspectraandlikelihood AT baccigalupic planck2013resultsxvcmbpowerspectraandlikelihood AT bandaya planck2013resultsxvcmbpowerspectraandlikelihood AT barreiror planck2013resultsxvcmbpowerspectraandlikelihood AT bartlettj planck2013resultsxvcmbpowerspectraandlikelihood AT battanere planck2013resultsxvcmbpowerspectraandlikelihood AT benabedk planck2013resultsxvcmbpowerspectraandlikelihood AT benoita planck2013resultsxvcmbpowerspectraandlikelihood AT benoitlevya planck2013resultsxvcmbpowerspectraandlikelihood AT bernardj planck2013resultsxvcmbpowerspectraandlikelihood AT bersanellim planck2013resultsxvcmbpowerspectraandlikelihood AT bielewiczp planck2013resultsxvcmbpowerspectraandlikelihood AT bobinj planck2013resultsxvcmbpowerspectraandlikelihood AT bockj planck2013resultsxvcmbpowerspectraandlikelihood AT bonaldia planck2013resultsxvcmbpowerspectraandlikelihood AT bonaveral planck2013resultsxvcmbpowerspectraandlikelihood AT bondjr planck2013resultsxvcmbpowerspectraandlikelihood AT borrillj planck2013resultsxvcmbpowerspectraandlikelihood |