Reconstruction of a direction-dependent primordial power spectrum from Planck CMB data
Abstract
We consider the possibility that the primordial curvature perturbation is direction-dependent. To first order this is parameterised by a quadrupolar modulation of the power spectrum and results in statistical anisotropy of the CMB, which can be quantified using `bipolar spherical harmonics'. We compute these for the Planck DR2-2015 SMICA map and estimate the noise covariance from Planck Full Focal Plane 9 simulations. A constant quadrupolar modulation is detected with 2.2$$σ$$ significance, dropping to 2$$σ$$ when the primordial power is assumed to scale with wave number k as a power law. Going beyond previous work we now allow the spectrum to have arbitrary scale-dependence. Our non-parametric reconstruction then suggests several spectral features, the most prominent at k ~ 0.006 Mpc-1. When a constant quadrupolar modulation is fitted to data in the range 0.005 ≤ k/Mpc-1 ≤ 0.008, its preferred directions are found to be related to the cosmic hemispherical asymmetry and the CMB dipole. To determine the significance we apply two test statistics to our reconstructions of the quadrupolar modulation from data, against reconstructions of realisations of noise only. With a test statistic sensitive only to the amplitude of the modulation, the reconstructions from the multipole range 30 ≤ ℓ ≤ 1200 are unusual with 2.1$$σ$$ significance. With the second test statistic, sensitive also to the direction, the significance rises to 6.9$$σ$$. Our approach is easily generalised to include other data sets such as polarisation, large-scale structure and forthcoming 21-cm line observations which will enable these anomalies to be investigated further.
- Authors:
-
- Univ. of Copenhagen (Denmark). The Niels Bohr Inst., Niels Bohr International Academy and Discovery Center
- Univ. of Oxford (United Kingdom). Rudolf Peierls Centre for Theoretical Physics
- Flatiron Inst., New York, NY (United States). Center for Computational Astrophysics; Inst. d'Astrophysique de Paris, Paris (France); Sorbonne Univ., Paris (France). Inst. Lagrange de Paris; Inter-Univ. Centre for Astronomy and Astrophysics, Ganeshkind, Pune (India)
- Univ. of Copenhagen (Denmark). The Niels Bohr Inst., Niels Bohr International Academy and Discovery Center; Univ. of Oxford (United Kingdom). Rudolf Peierls Centre for Theoretical Physics
- Inter-Univ. Centre for Astronomy and Astrophysics, Ganeshkind, Pune (India)
- 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:
- 1523614
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Cosmology and Astroparticle Physics
- Additional Journal Information:
- Journal Volume: 2018; Journal Issue: 02; Journal ID: ISSN 1475-7516
- Publisher:
- Institute of Physics (IOP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS
Citation Formats
Durakovic, Amel, Hunt, Paul, Mukherjee, Suvodip, Sarkar, Subir, and Souradeep, Tarun. Reconstruction of a direction-dependent primordial power spectrum from Planck CMB data. United States: N. p., 2018.
Web. doi:10.1088/1475-7516/2018/02/012.
Durakovic, Amel, Hunt, Paul, Mukherjee, Suvodip, Sarkar, Subir, & Souradeep, Tarun. Reconstruction of a direction-dependent primordial power spectrum from Planck CMB data. United States. https://doi.org/10.1088/1475-7516/2018/02/012
Durakovic, Amel, Hunt, Paul, Mukherjee, Suvodip, Sarkar, Subir, and Souradeep, Tarun. Wed .
"Reconstruction of a direction-dependent primordial power spectrum from Planck CMB data". United States. https://doi.org/10.1088/1475-7516/2018/02/012. https://www.osti.gov/servlets/purl/1523614.
@article{osti_1523614,
title = {Reconstruction of a direction-dependent primordial power spectrum from Planck CMB data},
author = {Durakovic, Amel and Hunt, Paul and Mukherjee, Suvodip and Sarkar, Subir and Souradeep, Tarun},
abstractNote = {We consider the possibility that the primordial curvature perturbation is direction-dependent. To first order this is parameterised by a quadrupolar modulation of the power spectrum and results in statistical anisotropy of the CMB, which can be quantified using `bipolar spherical harmonics'. We compute these for the Planck DR2-2015 SMICA map and estimate the noise covariance from Planck Full Focal Plane 9 simulations. A constant quadrupolar modulation is detected with 2.2$σ$ significance, dropping to 2$σ$ when the primordial power is assumed to scale with wave number k as a power law. Going beyond previous work we now allow the spectrum to have arbitrary scale-dependence. Our non-parametric reconstruction then suggests several spectral features, the most prominent at k ~ 0.006 Mpc-1. When a constant quadrupolar modulation is fitted to data in the range 0.005 ≤ k/Mpc-1 ≤ 0.008, its preferred directions are found to be related to the cosmic hemispherical asymmetry and the CMB dipole. To determine the significance we apply two test statistics to our reconstructions of the quadrupolar modulation from data, against reconstructions of realisations of noise only. With a test statistic sensitive only to the amplitude of the modulation, the reconstructions from the multipole range 30 ≤ ℓ ≤ 1200 are unusual with 2.1$σ$ significance. With the second test statistic, sensitive also to the direction, the significance rises to 6.9$σ$. Our approach is easily generalised to include other data sets such as polarisation, large-scale structure and forthcoming 21-cm line observations which will enable these anomalies to be investigated further.},
doi = {10.1088/1475-7516/2018/02/012},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 02,
volume = 2018,
place = {United States},
year = {Wed Feb 07 00:00:00 EST 2018},
month = {Wed Feb 07 00:00:00 EST 2018}
}
Web of Science
Works referenced in this record:
Search for features in the spectrum of primordial perturbations using Planck and other datasets
journal, December 2015
- Hunt, Paul; Sarkar, Subir
- Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 12
SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE ( WMAP ) OBSERVATIONS: ARE THERE COSMIC MICROWAVE BACKGROUND ANOMALIES?
journal, January 2011
- Bennett, C. L.; Hill, R. S.; Hinshaw, G.
- The Astrophysical Journal Supplement Series, Vol. 192, Issue 2
Cosmological parameters from CMB and other data: A Monte Carlo approach
journal, November 2002
- Lewis, Antony; Bridle, Sarah
- Physical Review D, Vol. 66, Issue 10
A hemispherical power asymmetry from inflation
journal, December 2008
- Erickcek, Adrienne L.; Kamionkowski, Marc; Carroll, Sean M.
- Physical Review D, Vol. 78, Issue 12
Planck 2015 results : XII. Full focal plane simulations
journal, September 2016
- Ade, P. A. R.; Aghanim, N.; Arnaud, M.
- Astronomy & Astrophysics, Vol. 594
Inflation driven by a vector field
journal, August 1989
- Ford, L. H.
- Physical Review D, Vol. 40, Issue 4
Asymmetries in the Cosmic Microwave Background Anisotropy Field
journal, April 2004
- Eriksen, H. K.; Hansen, F. K.; Banday, A. J.
- The Astrophysical Journal, Vol. 605, Issue 1
The pesky power asymmetry
journal, June 2013
- Dai, Liang; Jeong, Donghui; Kamionkowski, Marc
- Physical Review D, Vol. 87, Issue 12
Imprints of a primordial preferred direction on the microwave background
journal, April 2007
- Ackerman, Lotty; Carroll, Sean M.; Wise, Mark B.
- Physical Review D, Vol. 75, Issue 8
Odd-parity bipolar spherical harmonics
journal, January 2012
- Book, Laura G.; Kamionkowski, Marc; Souradeep, Tarun
- Physical Review D, Vol. 85, Issue 2
Statistical isotropy violation of CMB Polarization sky due to Lorentz boost
journal, April 2014
- Mukherjee, Suvodip; De, Aritra; Souradeep, Tarun
- Physical Review D, Vol. 89, Issue 8
Statistical isotropy violation in WMAP CMB maps resulting from non-circular beams
journal, June 2016
- Das, Santanu; Mitra, Sanjit; Rotti, Aditya
- Astronomy & Astrophysics, Vol. 591
Predictions from an anisotropic inflationary era
journal, April 2008
- Pitrou, Cyril; Pereira, Thiago S.; Uzan, Jean-Philippe
- Journal of Cosmology and Astroparticle Physics, Vol. 2008, Issue 04
Measuring the Statistical Isotropy of the Cosmic Microwave Background Anisotropy
journal, October 2003
- Hajian, Amir; Souradeep, Tarun
- The Astrophysical Journal, Vol. 597, Issue 1
Peculiar velocity effects in high-resolution microwave background experiments
journal, April 2002
- Challinor, Anthony; van Leeuwen, Floor
- Physical Review D, Vol. 65, Issue 10
Litmus Test for Cosmic Hemispherical Asymmetry in the Cosmic Microwave Background -Mode Polarization
journal, June 2016
- Mukherjee, Suvodip; Souradeep, Tarun
- Physical Review Letters, Vol. 116, Issue 22
Planck 2015 results : XIII. Cosmological parameters
journal, September 2016
- Ade, P. A. R.; Aghanim, N.; Arnaud, M.
- Astronomy & Astrophysics, Vol. 594
Planck 2015 results : XX. Constraints on inflation
journal, September 2016
- Ade, P. A. R.; Aghanim, N.; Arnaud, M.
- Astronomy & Astrophysics, Vol. 594
Inflationary Universe with Anisotropic Hair
journal, May 2009
- Watanabe, Masa-aki; Kanno, Sugumi; Soda, Jiro
- Physical Review Letters, Vol. 102, Issue 19
General quadrupolar statistical anisotropy: Planck limits
journal, March 2017
- Ramazanov, S.; Rubtsov, G.; Thorsrud, M.
- Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 03
Reconstruction of the primordial power spectrum of curvature perturbations using multiple data sets
journal, January 2014
- Hunt, Paul; Sarkar, Subir
- Journal of Cosmology and Astroparticle Physics, Vol. 2014, Issue 01
Planck 2015 results : XVI. Isotropy and statistics of the CMB
journal, September 2016
- Ade, P. A. R.; Aghanim, N.; Akrami, Y.
- Astronomy & Astrophysics, Vol. 594
A Test of Goodness of Fit
journal, December 1954
- Anderson, T. W.; Darling, D. A.
- Journal of the American Statistical Association, Vol. 49, Issue 268
Novel approach to reconstructing signals of isotropy violation from a masked CMB sky
journal, October 2015
- Aluri, Pavan K.; Pant, Nidhi; Rotti, Aditya
- Physical Review D, Vol. 92, Issue 8
Cosmic microwave background statistics for a direction-dependent primordial power spectrum
journal, November 2007
- Pullen, Anthony R.; Kamionkowski, Marc
- Physical Review D, Vol. 76, Issue 10
Instability of the Ackerman-Carroll-Wise model, and problems with massive vectors during inflation
journal, March 2009
- Himmetoglu, Burak; Contaldi, Carlo R.; Peloso, Marco
- Physical Review D, Vol. 79, Issue 6
Instability of Anisotropic Cosmological Solutions Supported by Vector Fields
journal, March 2009
- Himmetoglu, Burak; Contaldi, Carlo R.; Peloso, Marco
- Physical Review Letters, Vol. 102, Issue 11
Measuring Statistical isotropy of the CMB anisotropy
text, January 2003
- Hajian, Amir; Souradeep, Tarun
- arXiv
CMB Anomalies from Relic Anisotropy
text, January 2006
- Gumrukcuoglu, A. E.; Contaldi, Carlo R.; Peloso, Marco
- arXiv
Works referencing / citing this record:
Schwinger mechanism during inflation
journal, May 2019
- Shakeri, Soroush; Gorji, Mohammad Ali; Firouzjahi, Hassan
- Physical Review D, Vol. 99, Issue 10
Quantum Mixmaster as a Model of the Primordial Universe
journal, December 2019
- Bergeron, Hervé; Czuchry, Ewa; Gazeau, Jean Pierre
- Universe, Vol. 6, Issue 1
Schwinger Mechanism During Inflation
text, January 2019
- Shakeri, Soroush; Gorji, Mohammad Ali; Firouzjahi, Hassan
- arXiv
Quantum Mixmaster as a model of the Primordial Universe
text, January 2019
- Bergeron, Hervé; Czuchry, Ewa; Gazeau, Jean-Pierre
- arXiv