# Tensor perturbations during inflation in a spatially closed Universe

## Abstract

In a recent paper [1], we studied the evolution of the background geometry and scalar perturbations in an inflationary, spatially closed Friedmann-Lemaȋtre-Robertson-Walker (FLRW) model having constant positive spatial curvature and spatial topology S{sup 3}. Due to the spatial curvature, the early phase of slow-roll inflation is modified, leading to suppression of power in the scalar power spectrum at large angular scales. In this paper, we extend the analysis to include tensor perturbations. We find that, similarly to the scalar perturbations, the tensor power spectrum also shows suppression for long wavelength modes. The correction to the tensor spectrum is limited to the very long wavelength modes, therefore the resulting observable CMB B-mode polarization spectrum remains practically the same as in the standard scenario with flat spatial sections. However, since both the tensor and scalar power spectra are modified, there are scale dependent corrections to the tensor-to-scalar ratio that leads to violation of the standard slow-roll consistency relation.

- Authors:

- Institute for Gravitation and the Cosmos and Physics Department, The Pennsylvania State University, 104 Lavey Lab, University Park, PA 16802 (United States)

- Publication Date:

- OSTI Identifier:
- 22676218

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 05; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; DISTURBANCES; EVOLUTION; INFLATIONARY UNIVERSE; PERTURBATION THEORY; POLARIZATION; RELICT RADIATION; SPECTRA; UNIVERSE; WAVELENGTHS

### 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.
```*Tensor perturbations during inflation in a spatially closed Universe*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/05/021.

```
Bonga, Béatrice, Gupt, Brajesh, & Yokomizo, Nelson, E-mail: bpb165@psu.edu, E-mail: bgupt@gravity.psu.edu, E-mail: yokomizo@gravity.psu.edu.
```*Tensor perturbations during inflation in a spatially closed Universe*. United States. doi:10.1088/1475-7516/2017/05/021.

```
Bonga, Béatrice, Gupt, Brajesh, and Yokomizo, Nelson, E-mail: bpb165@psu.edu, E-mail: bgupt@gravity.psu.edu, E-mail: yokomizo@gravity.psu.edu. Mon .
"Tensor perturbations during inflation in a spatially closed Universe". United States.
doi:10.1088/1475-7516/2017/05/021.
```

```
@article{osti_22676218,
```

title = {Tensor perturbations during inflation in a spatially closed Universe},

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 = {In a recent paper [1], we studied the evolution of the background geometry and scalar perturbations in an inflationary, spatially closed Friedmann-Lemaȋtre-Robertson-Walker (FLRW) model having constant positive spatial curvature and spatial topology S{sup 3}. Due to the spatial curvature, the early phase of slow-roll inflation is modified, leading to suppression of power in the scalar power spectrum at large angular scales. In this paper, we extend the analysis to include tensor perturbations. We find that, similarly to the scalar perturbations, the tensor power spectrum also shows suppression for long wavelength modes. The correction to the tensor spectrum is limited to the very long wavelength modes, therefore the resulting observable CMB B-mode polarization spectrum remains practically the same as in the standard scenario with flat spatial sections. However, since both the tensor and scalar power spectra are modified, there are scale dependent corrections to the tensor-to-scalar ratio that leads to violation of the standard slow-roll consistency relation.},

doi = {10.1088/1475-7516/2017/05/021},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 05,

volume = 2017,

place = {United States},

year = {Mon May 01 00:00:00 EDT 2017},

month = {Mon May 01 00:00:00 EDT 2017}

}