# Inflation in the closed FLRW model and the CMB

## Abstract

Recent cosmic microwave background (CMB) observations put strong constraints on the spatial curvature via estimation of the parameter Ω{sub k} assuming an almost scale invariant primordial power spectrum. We study the evolution of the background geometry and gauge-invariant scalar perturbations in an inflationary closed FLRW model and calculate the primordial power spectrum. We find that the inflationary dynamics is modified due to the presence of spatial curvature, leading to corrections to the nearly scale invariant power spectrum at the end of inflation. When evolved to the surface of last scattering, the resulting temperature anisotropy spectrum ( C {sup TT}{sub ℓ}) shows deficit of power at low multipoles (ℓ < 20). By comparing our results with the recent Planck data we discuss the role of spatial curvature in accounting for CMB anomalies and in the estimation of the parameter Ω{sub k}. Since the curvature effects are limited to low multipoles, the Planck estimation of cosmological parameters remains robust under inclusion of positive spatial curvature.

- Authors:

- Institute for Gravitation and the Cosmos and Physics Department, The Pennsylvania State University, University Park, PA 16802 (United States)

- Publication Date:

- OSTI Identifier:
- 22679425

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2016; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANISOTROPY; COMPARATIVE EVALUATIONS; DISTURBANCES; GAUGE INVARIANCE; INCLUSIONS; INFLATIONARY UNIVERSE; MULTIPOLES; PERTURBATION THEORY; RELICT RADIATION; SCATTERING; SPECTRA

### Citation Formats

```
Bonga, Béatrice, Gupt, Brajesh, and Yokomizo, Nelson, E-mail: bpb165@psu.edu, E-mail: bgupt@gravity.psu.edu, E-mail: yokomizo@gravity.psu.edu.
```*Inflation in the closed FLRW model and the CMB*. United States: N. p., 2016.
Web. doi:10.1088/1475-7516/2016/10/031.

```
Bonga, Béatrice, Gupt, Brajesh, & Yokomizo, Nelson, E-mail: bpb165@psu.edu, E-mail: bgupt@gravity.psu.edu, E-mail: yokomizo@gravity.psu.edu.
```*Inflation in the closed FLRW model and the CMB*. United States. doi:10.1088/1475-7516/2016/10/031.

```
Bonga, Béatrice, Gupt, Brajesh, and Yokomizo, Nelson, E-mail: bpb165@psu.edu, E-mail: bgupt@gravity.psu.edu, E-mail: yokomizo@gravity.psu.edu. Sat .
"Inflation in the closed FLRW model and the CMB". United States. doi:10.1088/1475-7516/2016/10/031.
```

```
@article{osti_22679425,
```

title = {Inflation in the closed FLRW model and the CMB},

author = {Bonga, Béatrice and Gupt, Brajesh and Yokomizo, Nelson, E-mail: bpb165@psu.edu, E-mail: bgupt@gravity.psu.edu, E-mail: yokomizo@gravity.psu.edu},

abstractNote = {Recent cosmic microwave background (CMB) observations put strong constraints on the spatial curvature via estimation of the parameter Ω{sub k} assuming an almost scale invariant primordial power spectrum. We study the evolution of the background geometry and gauge-invariant scalar perturbations in an inflationary closed FLRW model and calculate the primordial power spectrum. We find that the inflationary dynamics is modified due to the presence of spatial curvature, leading to corrections to the nearly scale invariant power spectrum at the end of inflation. When evolved to the surface of last scattering, the resulting temperature anisotropy spectrum ( C {sup TT}{sub ℓ}) shows deficit of power at low multipoles (ℓ < 20). By comparing our results with the recent Planck data we discuss the role of spatial curvature in accounting for CMB anomalies and in the estimation of the parameter Ω{sub k}. Since the curvature effects are limited to low multipoles, the Planck estimation of cosmological parameters remains robust under inclusion of positive spatial curvature.},

doi = {10.1088/1475-7516/2016/10/031},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 10,

volume = 2016,

place = {United States},

year = {2016},

month = {10}

}