*Planck* 2015 Constraints on the Non-flat ΛCDM Inflation Model

## Abstract

We observe Planck 2015 cosmic microwave background (CMB) anisotropy data using the energy density inhomogeneity power spectrum generated by quantum fluctuations during an early epoch of inflation in the non-flat ΛCDM model. Unlike earlier assessment of non-flat models, which assumed an inconsistent power-law power spectrum of energy density inhomogeneities, we find that the Planck 2015 data alone, and also in conjunction with baryon acoustic oscillation measurements, are reasonably well fit by a closed ΛCDM model in which spatial curvature contributes a few percent of the current cosmological energy density budget. In this model, the measured Hubble constant and nonrelativistic matter density parameter are in good agreement with values determined using most other data. Relying on parameter values, the closed ΛCDM model has reduced power, relative to the tilted, spatially flat ΛCDM case, and can partially alleviate the low multipole CMB temperature anisotropy deficit and can help partially reconcile the CMB anisotropy and weak lensing σ 8 constraints, at the expense of somewhat worsening the fit to higher multipole CMB temperature anisotropy data. Our results are interesting but tentative; a more thorough analysis is needed to properly gauge their significance.

- Authors:

- Nagoya Univ. (Japan)
- Kansas State Univ., Manhattan, KS (United States)
- Nagoya Univ. (Japan); Univ. of Tokyo (Japan)

- Publication Date:

- Research Org.:
- Kansas State Univ., Manhattan, KS (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1542030

- Grant/Contract Number:
- SC0011840

- Resource Type:
- Accepted Manuscript

- Journal Name:
- The Astrophysical Journal (Online)

- Additional Journal Information:
- Journal Name: The Astrophysical Journal (Online); Journal Volume: 864; Journal Issue: 1; Journal ID: ISSN 1538-4357

- Publisher:
- Institute of Physics (IOP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; cosmic background radiation; cosmological parameters; cosmology: observations; inflation; large-scale structure of universe

### Citation Formats

```
Ooba, Junpei, Ratra, Bharat, and Sugiyama, Naoshi. Planck 2015 Constraints on the Non-flat ΛCDM Inflation Model. United States: N. p., 2018.
Web. doi:10.3847/1538-4357/aad633.
```

```
Ooba, Junpei, Ratra, Bharat, & Sugiyama, Naoshi. Planck 2015 Constraints on the Non-flat ΛCDM Inflation Model. United States. doi:10.3847/1538-4357/aad633.
```

```
Ooba, Junpei, Ratra, Bharat, and Sugiyama, Naoshi. Fri .
"Planck 2015 Constraints on the Non-flat ΛCDM Inflation Model". United States. doi:10.3847/1538-4357/aad633. https://www.osti.gov/servlets/purl/1542030.
```

```
@article{osti_1542030,
```

title = {Planck 2015 Constraints on the Non-flat ΛCDM Inflation Model},

author = {Ooba, Junpei and Ratra, Bharat and Sugiyama, Naoshi},

abstractNote = {We observe Planck 2015 cosmic microwave background (CMB) anisotropy data using the energy density inhomogeneity power spectrum generated by quantum fluctuations during an early epoch of inflation in the non-flat ΛCDM model. Unlike earlier assessment of non-flat models, which assumed an inconsistent power-law power spectrum of energy density inhomogeneities, we find that the Planck 2015 data alone, and also in conjunction with baryon acoustic oscillation measurements, are reasonably well fit by a closed ΛCDM model in which spatial curvature contributes a few percent of the current cosmological energy density budget. In this model, the measured Hubble constant and nonrelativistic matter density parameter are in good agreement with values determined using most other data. Relying on parameter values, the closed ΛCDM model has reduced power, relative to the tilted, spatially flat ΛCDM case, and can partially alleviate the low multipole CMB temperature anisotropy deficit and can help partially reconcile the CMB anisotropy and weak lensing σ 8 constraints, at the expense of somewhat worsening the fit to higher multipole CMB temperature anisotropy data. Our results are interesting but tentative; a more thorough analysis is needed to properly gauge their significance.},

doi = {10.3847/1538-4357/aad633},

journal = {The Astrophysical Journal (Online)},

number = 1,

volume = 864,

place = {United States},

year = {2018},

month = {8}

}

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