# Unveiling acoustic physics of the CMB using nonparametric estimation of the temperature angular power spectrum for Planck

## Abstract

Estimation of the angular power spectrum is one of the important steps in Cosmic Microwave Background (CMB) data analysis. Here, we present a nonparametric estimate of the temperature angular power spectrum for the Planck 2013 CMB data. The method implemented in this work is model-independent, and allows the data, rather than the model, to dictate the fit. Since one of the main targets of our analysis is to test the consistency of the ΛCDM model with Planck 2013 data, we use the nuisance parameters associated with the best-fit ΛCDM angular power spectrum to remove foreground contributions from the data at multipoles ℓ ≥50. We thus obtain a combined angular power spectrum data set together with the full covariance matrix, appropriately weighted over frequency channels. Our subsequent nonparametric analysis resolves six peaks (and five dips) up to ℓ ∼1850 in the temperature angular power spectrum. We present uncertainties in the peak/dip locations and heights at the 95% confidence level. We further show how these reflect the harmonicity of acoustic peaks, and can be used for acoustic scale estimation. Based on this nonparametric formalism, we found the best-fit ΛCDM model to be at 36% confidence distance from the center of the nonparametric confidence set—thismore »

- Authors:

- Asia Pacific Center for Theoretical Physics, Nam-Gu, Pohang, 790-784 (Korea, Republic of)
- Korea Astronomy and Space Science Institute, Daejeon, 305-348 (Korea, Republic of)
- Centre for Modeling and Simulation, Savitribai Phule Pune University, Ganeshkhind, Pune, 411 007 India (India)
- Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune, 411 007 India (India)

- Publication Date:

- OSTI Identifier:
- 22381999

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 02; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGY; DATA ANALYSIS; DISTANCE; HEIGHT; MATRICES; MULTIPOLES; PEAKS; RELICT RADIATION; SPECTRA

### Citation Formats

```
Aghamousa, Amir, Shafieloo, Arman, Arjunwadkar, Mihir, and Souradeep, Tarun, E-mail: amir@apctp.org, E-mail: shafieloo@kasi.re.kr, E-mail: mihir@cms.unipune.ac.in, E-mail: tarun@iucaa.ernet.in.
```*Unveiling acoustic physics of the CMB using nonparametric estimation of the temperature angular power spectrum for Planck*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/02/007.

```
Aghamousa, Amir, Shafieloo, Arman, Arjunwadkar, Mihir, & Souradeep, Tarun, E-mail: amir@apctp.org, E-mail: shafieloo@kasi.re.kr, E-mail: mihir@cms.unipune.ac.in, E-mail: tarun@iucaa.ernet.in.
```*Unveiling acoustic physics of the CMB using nonparametric estimation of the temperature angular power spectrum for Planck*. United States. doi:10.1088/1475-7516/2015/02/007.

```
Aghamousa, Amir, Shafieloo, Arman, Arjunwadkar, Mihir, and Souradeep, Tarun, E-mail: amir@apctp.org, E-mail: shafieloo@kasi.re.kr, E-mail: mihir@cms.unipune.ac.in, E-mail: tarun@iucaa.ernet.in. Sun .
"Unveiling acoustic physics of the CMB using nonparametric estimation of the temperature angular power spectrum for Planck". United States.
doi:10.1088/1475-7516/2015/02/007.
```

```
@article{osti_22381999,
```

title = {Unveiling acoustic physics of the CMB using nonparametric estimation of the temperature angular power spectrum for Planck},

author = {Aghamousa, Amir and Shafieloo, Arman and Arjunwadkar, Mihir and Souradeep, Tarun, E-mail: amir@apctp.org, E-mail: shafieloo@kasi.re.kr, E-mail: mihir@cms.unipune.ac.in, E-mail: tarun@iucaa.ernet.in},

abstractNote = {Estimation of the angular power spectrum is one of the important steps in Cosmic Microwave Background (CMB) data analysis. Here, we present a nonparametric estimate of the temperature angular power spectrum for the Planck 2013 CMB data. The method implemented in this work is model-independent, and allows the data, rather than the model, to dictate the fit. Since one of the main targets of our analysis is to test the consistency of the ΛCDM model with Planck 2013 data, we use the nuisance parameters associated with the best-fit ΛCDM angular power spectrum to remove foreground contributions from the data at multipoles ℓ ≥50. We thus obtain a combined angular power spectrum data set together with the full covariance matrix, appropriately weighted over frequency channels. Our subsequent nonparametric analysis resolves six peaks (and five dips) up to ℓ ∼1850 in the temperature angular power spectrum. We present uncertainties in the peak/dip locations and heights at the 95% confidence level. We further show how these reflect the harmonicity of acoustic peaks, and can be used for acoustic scale estimation. Based on this nonparametric formalism, we found the best-fit ΛCDM model to be at 36% confidence distance from the center of the nonparametric confidence set—this is considerably larger than the confidence distance (9%) derived earlier from a similar analysis of the WMAP 7-year data. Another interesting result of our analysis is that at low multipoles, the Planck data do not suggest any upturn, contrary to the expectation based on the integrated Sachs-Wolfe contribution in the best-fit ΛCDM cosmology.},

doi = {10.1088/1475-7516/2015/02/007},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 02,

volume = 2015,

place = {United States},

year = {Sun Feb 01 00:00:00 EST 2015},

month = {Sun Feb 01 00:00:00 EST 2015}

}