## 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 2σ 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 ≤ ℓmore »

- 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-National Energy Research Scientific Computing Center

- 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

- Country of Publication:
- United States

- Language:
- English

### 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. doi:10.1088/1475-7516/2018/02/012.
```

```
Durakovic, Amel, Hunt, Paul, Mukherjee, Suvodip, Sarkar, Subir, and Souradeep, Tarun. Thu .
"Reconstruction of a direction-dependent primordial power spectrum from Planck CMB data". United States. doi: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 2σ 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 2.1σ significance. With the second test statistic, sensitive also to the direction, the significance rises to 6.9σ. 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 = {2018},

month = {2}

}

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