skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Optimal constraints on primordial gravitational waves from the lensed CMB

Abstract

We demonstrate how to obtain optimal constraints on a primordial gravitational wave component in lensed Cosmic Microwave Background (CMB) data under ideal conditions. We first derive an estimator of the tensorto- scalar ratio, r, by using an error-controlled close approximation to the exact posterior, under the assumption of Gaussian primordial CMB and lensing deflection potential. This combines fast internal iterative lensing reconstruction with optimal recovery of the unlensed CMB. We evaluate its performance on simulated lownoise polarization data targeted at the recombination peak. We carefully demonstrate our r-posterior estimate is optimal and shows no significant bias, making it the most powerful estimator of primordial gravitational waves from the CMB. We compare these constraints to those obtained from B-mode band-power likelihood analyses on the same simulated data, before and after map-level quadratic estimator delensing, and iterative delensing. Internally, iteratively delensed band powers are only slightly less powerful on average (by less than 10%), promising close-to-optimal constraints from a stage IV CMB experiment.

Authors:
 [1]
  1. Univ. of Sussex, Brighton (United Kingdom)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE
OSTI Identifier:
1544114
Alternate Identifier(s):
OSTI ID: 1494651
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 99; Journal Issue: 4; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS

Citation Formats

Carron, Julien. Optimal constraints on primordial gravitational waves from the lensed CMB. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.99.043518.
Carron, Julien. Optimal constraints on primordial gravitational waves from the lensed CMB. United States. doi:10.1103/PhysRevD.99.043518.
Carron, Julien. Wed . "Optimal constraints on primordial gravitational waves from the lensed CMB". United States. doi:10.1103/PhysRevD.99.043518. https://www.osti.gov/servlets/purl/1544114.
@article{osti_1544114,
title = {Optimal constraints on primordial gravitational waves from the lensed CMB},
author = {Carron, Julien},
abstractNote = {We demonstrate how to obtain optimal constraints on a primordial gravitational wave component in lensed Cosmic Microwave Background (CMB) data under ideal conditions. We first derive an estimator of the tensorto- scalar ratio, r, by using an error-controlled close approximation to the exact posterior, under the assumption of Gaussian primordial CMB and lensing deflection potential. This combines fast internal iterative lensing reconstruction with optimal recovery of the unlensed CMB. We evaluate its performance on simulated lownoise polarization data targeted at the recombination peak. We carefully demonstrate our r-posterior estimate is optimal and shows no significant bias, making it the most powerful estimator of primordial gravitational waves from the CMB. We compare these constraints to those obtained from B-mode band-power likelihood analyses on the same simulated data, before and after map-level quadratic estimator delensing, and iterative delensing. Internally, iteratively delensed band powers are only slightly less powerful on average (by less than 10%), promising close-to-optimal constraints from a stage IV CMB experiment.},
doi = {10.1103/PhysRevD.99.043518},
journal = {Physical Review D},
number = 4,
volume = 99,
place = {United States},
year = {2019},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Reconstruction of lensing from the cosmic microwave background polarization
journal, October 2003


What can be learned from the lensed cosmic microwave background B-mode polarization power spectrum?
journal, January 2006


Two-season Atacama Cosmology Telescope polarimeter lensing power spectrum
journal, June 2017


Non-Gaussian structure of the lensed CMB power spectra covariance matrix
journal, December 2012


CMB Polarization B -mode Delensing with SPTpol and Herschel
journal, August 2017


Delensing the CMB with the cosmic infrared background
journal, August 2015


Weak lensing of the CMB: Sampling errors on B modes
journal, August 2004


Future cosmic microwave background delensing with galaxy surveys
journal, February 2018


Weak gravitational lensing of the CMB
journal, June 2006


Cosmic microwave background lensing reconstruction on the full sky
journal, April 2003


Planck 2015 results : XV. Gravitational lensing
journal, September 2016


Efficient Computation of Cosmic Microwave Background Anisotropies in Closed Friedmann‐Robertson‐Walker Models
journal, August 2000

  • Lewis, Antony; Challinor, Anthony; Lasenby, Anthony
  • The Astrophysical Journal, Vol. 538, Issue 2
  • DOI: 10.1086/309179

Likelihood analysis of CMB temperature and polarization power spectra
journal, May 2008


Numerical approximation of the product of the square root of a matrix with a vector
journal, May 2000


All-sky analysis of polarization in the microwave background
journal, February 1997


General solution to the E B mixing problem
journal, August 2007


Gravitational lensing as a contaminant of the gravity wave signal in the CMB
journal, February 2004


Internal delensing of Planck CMB temperature and polarization
journal, May 2017

  • Carron, Julien; Lewis, Antony; Challinor, Anthony
  • Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 05
  • DOI: 10.1088/1475-7516/2017/05/035

Maximum a posteriori CMB lensing reconstruction
journal, September 2017


Emission-angle and polarization-rotation effects in the lensed CMB
journal, August 2017

  • Lewis, Antony; Hall, Alex; Challinor, Anthony
  • Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 08
  • DOI: 10.1088/1475-7516/2017/08/023

CMB internal delensing with general optimal estimator for higher-order correlations
journal, May 2017


Stochastic determination of matrix determinants
journal, July 2015


The shape of the CMB lensing bispectrum
journal, March 2011

  • Lewis, Antony; Challinor, Anthony; Hanson, Duncan
  • Journal of Cosmology and Astroparticle Physics, Vol. 2011, Issue 03
  • DOI: 10.1088/1475-7516/2011/03/018

Zum Einfluß der Spaltbreite auf die Intensitätsverteilung in Spektrallinien. II
journal, May 1931


Myths and truths concerning estimation of power spectra: the case for a hybrid estimator
journal, April 2004


Signature of Gravity Waves in the Polarization of the Microwave Background
journal, March 1997


Tracing galaxy orbits back in time
journal, September 1989

  • Peebles, P. J. E.
  • The Astrophysical Journal, Vol. 344
  • DOI: 10.1086/185529

Gravitational lensing effect on cosmic microwave background polarization
journal, June 1998


Planck 2015 results : XIII. Cosmological parameters
journal, September 2016


The Quest for B Modes from Inflationary Gravitational Waves
journal, September 2016


Constraints on Primordial Gravitational Waves Using P l a n c k , WMAP, and New BICEP2/ K e c k Observations through the 2015 Season
journal, November 2018


Effect of non-Gaussian lensing deflections on CMB lensing measurements
journal, December 2018


Deconvolution in Astronomy: A Review
journal, October 2002

  • Starck, J. L.; Pantin, E.; Murtagh, F.
  • Publications of the Astronomical Society of the Pacific, Vol. 114, Issue 800
  • DOI: 10.1086/342606

Weak lensing of the CMB
journal, June 2010

  • Hanson, Duncan; Challinor, Anthony; Lewis, Antony
  • General Relativity and Gravitation, Vol. 42, Issue 9
  • DOI: 10.1007/s10714-010-1036-y

Lensing reconstruction in post-Born cosmic microwave background weak lensing
journal, August 2018


Statistics of cosmic microwave background polarization
journal, June 1997

  • Kamionkowski, Marc; Kosowsky, Arthur; Stebbins, Albert
  • Physical Review D, Vol. 55, Issue 12
  • DOI: 10.1103/PhysRevD.55.7368

Multitracer CMB delensing maps from Planck and WISE data
journal, December 2017


Non-Gaussian structure of B-mode polarization after delensing
journal, October 2015


Analysis of CMB polarization on an incomplete sky
journal, December 2001


CMB lensing beyond the power spectrum: Cosmological constraints from the one-point probability distribution function and peak counts
journal, November 2016